Counterparty risk and the pricing of defaultable securities
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Financial Markets and Institutions, 8e (Mishkin)Chapter 20 The Mutual Fund Industry20.1 Multiple Choice1) At the beginning of 2013, mutual funds held about ________ of the U.S. stock market was held by mutual funds.A) 30%B) 50%C) 10%D) 70%Answer: ATopic: Chapter 20.1 The Growth of Mutual FundsQuestion Status: Updated from Previous Edition2) The origins of mutual funds can be traced back to the mid to late 1800s in________.A) England and ScotlandB) New York CityC) BostonD) GermanyAnswer: ATopic: Chapter 20.1 The Growth of Mutual FundsQuestion Status: New Question3) ________ intermediation means that small investors can pool their funds with other investors to purchase high face value securities.A) LiquidityB) FinancialC) DenominationD) ShareAnswer: CTopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition4) Mutual funds offer investors all of the following exceptA) greater-than-average returns.B) diversified portfolios.C) lower transaction costs.D) professional investment management.Answer: ATopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition5) Mutual fundsA) pool the resources of many small investors by selling these investors shares and using the proceeds to buy securities.B) allow small investors to obtain the benefits of lower transaction costs in purchasing securities.C) provide small investors a diversified portfolio that reduces risk.D) do all of the above.E) do only A and B of the above.Answer: DTopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition6) ________ enables mutual funds to consistently outperform a randomly selected group of stocks.A) Managerial expertiseB) DiversificationC) Denomination intermediationD) None of the aboveAnswer: DTopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition7) At the end of 2012 there were over ________ separate mutual funds with total assets over ________.A) 800; $10 trillionB) 7,500; $13 trillionC) 10,000; $10 trillionD) 1,000; $7 trillionAnswer: BTopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Updated from Previous Edition8) Most mutual funds are structured in two ways. The most common structure is a(n) ________ fund, from which shares can be redeemed at any time at a price that is tied to the asset value of the fund. A(n) ________ fund has a fixed number of nonredeemable shares that are traded in the over-the-counter market.A) closed-end; open-endB) open-end; closed-endC) no-load; closed-endD) no-load; loadE) load; no-loadAnswer: BTopic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition9) Which of the following is an advantage to investors of an open-end mutual fund?A) Once all the shares have been sold, the investor does not have to put in more money.B) The investors can sell their shares in the over-the-counter market with low transaction fees.C) The fund agrees to redeem shares at any time.D) The market value of the fund's shares may be higher than the value of the assets held by the fund.Answer: CTopic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition10) The net asset value of a mutual fund isA) determined by subtracting the fund's liabilities from its assets and dividing by the number of shares outstanding.B) determined by calculating the net price of the assets owned by the fund.C) calculated every 15 minutes and used for transactions occurring during the next 15-minute interval.D) calculated as the difference between the fund's assets and its liabilities. Answer: ATopic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition11) ________ funds are the simplest type of investment funds to manage.A) BalancedB) Global equityC) GrowthD) IndexAnswer: DTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition12) The majority of mutual fund assets are now owned byA) individual investors.B) institutional investors.C) fiduciaries.D) business organizations.E) retirees.Answer: ATopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition13) Capital appreciation funds select stocks of ________ and tend to be ________ risky than total return funds.A) large, established companies that pay dividends regularly; moreB) large, established companies that pay dividends regularly; lessC) companies expected to grow rapidly; moreD) companies expected to grow rapidly; lessAnswer: CTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition14) From largest to smallest in terms of total assets, the four classes of mutual funds areA) equity funds, bond funds, hybrid funds, money market funds.B) equity funds, money market funds, bond funds, hybrid funds.C) money market funds, equity funds, hybrid funds, bond funds.D) bond funds, money market funds, equity funds, hybrid funds.Answer: BTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition15) Measured by assets, the most popular type of bond fund is the ________ bond fund.A) state municipalB) strategic incomeC) governmentD) high-yieldAnswer: BTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition16) People who take their money out of insured bank deposits to invest in uninsured money market mutual funds have ________ risk because money market funds invest in ________ assets.A) high; long-termB) low; short-termC) high; short-termD) low; long-termAnswer: BTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition17) The largest share of assets held by money market mutual funds isA) Treasury bills.B) certificates of deposit.C) commercial paper.D) repurchase agreements.Answer: CTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition18) Which of the following is a feature of index funds?A) They have lower fees.B) They select and hold stocks to match the performance of a stock index.C) They do not require managers to select stocks and decide when to buy and sell.D) All of the above.Answer: DTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition19) A deferred-load mutual fund charges a commissionA) when shares are purchased.B) when shares are sold.C) both when shares are purchased and when they are sold.D) when shares are redeemed.Answer: DTopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition20) Over the past twenty years, mutual fund fees have ________, largely because________.A) fallen; SEC fee disclosure rules have led to greater competitionB) risen; investors have learned that funds with high fees provide better performanceC) risen; there has been collusion between large mutual fund companiesD) fallen; advances in information technology have lowered transaction costs Answer: ATopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition21) Which of the following is most likely to be a no-load fund?A) Value fundsB) Hedge fundsC) Growth fundsD) Index fundsAnswer: DTopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition22) When investors switch between funds within the same fund family, mutual funds may chargeA) a contingent deferred sales charge.B) a redemption fee.C) an exchange fee.D) 12b-1 fees.E) an account maintenance fee.Answer: CTopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition23) The Securities Acts of 1933 and 1934 did notA) regulate the activities of investment funds.B) require funds to register with the SEC.C) include antifraud rules covering the purchase and sale of fund shares.D) apply to investment funds.Answer: BTopic: Chapter 20.6 Regulation of Mutual FundsQuestion Status: Previous Edition24) The largest share of total investment in mutual funds is inA) stock funds.B) hybrid funds.C) bond funds.D) money market funds.Answer: ATopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition25) Over ________ of the total daily volume in stocks is due to institutions initiating trades.A) 70%B) 50%C) 25%D) 90%Answer: ATopic: Chapter 20.6 Regulation of Mutual FundsQuestion Status: New Question26) Hedge funds areA) low risk because they are market-neutral.B) low risk if they buy Treasury bonds.C) low risk because they hedge their investments.D) high risk because they are market-neutral.E) high risk, even though they may be market-neutral.Answer: ETopic: Chapter 20.7 Hedge FundsQuestion Status: Previous Edition27) The near collapse of Long Term Capital Management was caused byA) the high management fees charged by the fund's two Nobel Prize winners.B) the fund's high leverage ratio of 20 to 1.C) a sharp decrease in the spread between corporate bonds and Treasury bonds.D) a sharp increase in the spread between corporate bonds and Treasury bonds.E) the fund's shift away from a market-neutral investment strategy.Answer: DTopic: Chapter 20.7 Hedge FundsQuestion Status: Previous Edition28) Conflicts arise in the mutual funds industry because ________ cannot effectively monitor ________.A) investment advisers; directorsB) directors; shareholdersC) shareholders; investment advisersD) investment advisers; stocks that will outperform the overall marketAnswer: CTopic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition29) Late trading is the practice of allowing orders received ________ to trade at the ________ net asset value.A) before 4:00 PM; 4:00 PMB) after 4:00 PM; 4:00 PMC) after 4:00 PM; next day'sD) before 4:00 PM; previous day'sAnswer: BTopic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition30) Market timingA) takes advantage of time differences between the east and west coasts of the United States.B) takes advantage of arbitrage opportunities in foreign stocks.C) takes advantage of the time lag between the receipt and execution of orders.D) is discouraged by the stiff fees mutual funds charge every investor for buying and then selling shares on the same day.Answer: BTopic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition31) Late trading and market timingA) allow large, favored investors in a mutual fund to profit at the expense of other investors in the fund.B) hurt ordinary investors by increasing the number of fund shares and diluting the fund's net asset value.C) are both A and B of the above.D) are none of the above.Answer: CTopic: Chapter 20.8 Conflicts of Interest in the Mutual Fund Industry Question Status: Previous Edition32) Which of the following is not a proposal to deal with abuses in the mutual fund industry?A) Strictly enforce the 4:00 PM net asset value rule.B) Make redemption fees mandatory.C) Disclose compensation arrangements for investment advisers.D) Increase the number of dependent directors.Answer: DTopic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition33) ________ means the investors can convert their investment into cash quickly at a low cost.A) Liquidity intermediationB) Denomination intermediationC) DiversificationD) Managerial expertiseAnswer: ATopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition34) At the start of 2014, one share of Berkshire Hathaway's A-shares was trading at over $150,000. ________ in an mutual fund gives a small investor access to these shares.A) Liquidity intermediationB) Denomination intermediationC) DiversificationD) Managerial expertiseAnswer: BTopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition35) Mutual fund companies frequently offer a number of separate mutual funds called ________.A) indexesB) complexesC) componentsD) actuariesAnswer: BTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition36) Equity funds can be placed in which class according to the Investment Company Institute?A) Capital appreciation fundsB) World fundsC) Total return fundsD) All of the aboveAnswer: DTopic: Chapter 20.4 Investment Objective Classes Question Status: Previous Edition37) Government bonds are essentially default risk-free, ________ returns.A) and will yield highB) and will yield the highestC) but will have relatively lowD) none of the aboveAnswer: CTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition38) ________ bonds combine stocks into one fund.A) HybridB) Money marketC) MunicipalD) EquityAnswer: ATopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition39) All ________ are open-end investment funds that invest only in money market securities.A) Stock fundsB) Bond fundsC) Money market mutual fundsD) all of the aboveAnswer: CTopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition20.2 True/False1) The larger the number of shares traded in a stock transaction, the lower the transaction costs per share.Answer: TRUETopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition2) The increase in the number of defined contribution pension funds has slowed the growth of mutual funds.Answer: FALSETopic: Chapter 20.1 The Growth of Mutual FundsQuestion Status: Previous Edition3) Mutual funds accounted for $5.3 trillion, or 27%, of the $19.5 trillion U.S. retirement market at the beginning of 2013.Answer: TRUETopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Updated from Previous Edition4) Among the investors in mutual funds, only about 25% cite preparing for retirement as one of their main reasons for holding shares.Answer: FALSETopic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Updated from Previous Edition5) Open-end mutual funds are more common than closed-end funds.Answer: TRUETopic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition6) The net asset value of a mutual fund is the average market price of the stocks, bonds, and other assets the fund owns.Answer: FALSETopic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition7) A mutual fund's board of directors picks the securities that will be held and makes buy and sell decisions.Answer: FALSETopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition8) Money market mutual funds originated when the brokerage firm Merrill Lynch offered its customers an account from which funds could be taken to purchase securities and into which funds could be deposited when securities were sold. Answer: TRUETopic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition9) A deferred load is a fee charged when shares in a mutual fund are redeemed. Answer: TRUETopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition10) Several academic research studies show that investors earn higher returns by investing in mutual funds that charge higher fees.Answer: FALSETopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition11) Hedge funds have a minimum investment requirement of between $100,000 and$20 million, with the typical minimum investment being $1 million.Answer: TRUETopic: Chapter 20.7 Hedge FundsQuestion Status: New Question12) SEC research suggests that about three-fourths of mutual funds let privileged shareholders engage in market timing.Answer: TRUETopic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition13) One factor explaining the rapid growth in mutual funds is that they are financial intermediaries that are not regulated by the federal government.Answer: FALSETopic: Chapter 20.1 The Growth of Mutual FundsQuestion Status: Previous Edition14) Whether a fund is organized as a closed- or an open-end fund, is will have the same basic organizational structure.Answer: TRUETopic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition15) The primary purpose of loads is to provide compensation for sales brokers. Answer: TRUETopic: Chapter 20.5 Fee Structure of Investment FundsQuestion Status: Previous Edition16) Mutual funds are regulated under four federal laws designed to protect investors. Answer: TRUETopic: Chapter 20.6 Regulation of Mutual FundsQuestion Status: Previous Edition20.3 Essay1) What benefits do mutual funds offer investors?Topic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: Previous Edition2) How is a mutual fund's net asset value calculated?Topic: Chapter 20.3 Mutual Fund StructureQuestion Status: Previous Edition3) How did money market mutual funds originate and why did they become especially popular in the late 1970s and early 1980s?Topic: Chapter 20.1 The Growth of Mutual FundsQuestion Status: Previous Edition4) How does the governance structure of mutual funds lead to asymmetric information and conflicts of interest?Topic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition5) Describe the practices of late trading and market timing and explain how these practices harm a mutual fund's shareholders.Topic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition6) Discuss the proposals that have been made to reduce the conflict of interest abuses in the mutual funds industry.Topic: Chapter 20.8 Conflicts of Interest in the Mutual Fund IndustryQuestion Status: Previous Edition7) How is an index fund different from the other four primary investment objective classes for mutual funds?Topic: Chapter 20.4 Investment Objective ClassesQuestion Status: New Question8) Discuss the four primary classes of mutual funds available to investors.Topic: Chapter 20.4 Investment Objective ClassesQuestion Status: Previous Edition9) What are the five benefits of mutual funds?Topic: Chapter 20.2 Benefits of Mutual FundsQuestion Status: New Question10) What is the difference between an open-end and a closed-end mutual fund? Topic: Chapter 20.3 Mutual Fund StructureQuestion Status: New Question11) What are two key differences between a traditional mutual fund and a hedge fund?Topic: Chapter 20.7 Hedge FundsQuestion Status: New Question。
芝加哥大学1.金融数学(1) Background requirementsThere are two main criteria for evaluating applications tothe program, the first is by far the most important:∙ A solid background in Mathematics comparableto a bachelor of science degree in mathematics oranother field of physical sciences is essential. Youshould have solid knowledge of multivariablecalculus, linear algebra and differential equations. If you do not have this knowledge you might look into our Financial Mathematics Preparation Course or courses with similar contents at alocal university. Computer programming ability, especially in Matlab and C++, is also useful and is essential in working afterwards. If you don't have programming experience we recommend that you take the optional course in C++ programming. Some exposure to probability andstatistics is also useful. The biggest reason people are not admitted is inadequate mathematical preparation; it is not possible to "figure it out as you go along."∙We also look at prior industrial experience. A bit of experience has the effect of making you confident that this is the career you really want. This requirement is more flexible than the need for mathematical competence.(2) Application requirementsThere are several application requirements. The application form itself provides more details about each of the requirements.∙Both the GRE General Test and the GRE Math Subject Tests are required. However, if you received your bachelor's degree prior to June of 2007, you are exempt from any GRErequirements.Please consult the GRE website for testing dates, and select dates which will provide results in time for application review. Link to ETS website for GRE testing information.We do not require (and are not interested in) other exam scores, such as GMAT..∙TOEFL. Most foreign applicants must take the TOEFL. The exceptions are students from certain English-speaking countries such as Canada and UK. Please visit the Office of InternationalAffairs website for criteria:https:///students/prospective/toefl.shtml∙Three letters of recommendation. We recommend that even students who have been out of school for a while get at least one recommendation from a professor (preferably a mathprofessor) who can attest to their mathematical abilities.Our institution and department codes for the TOEFL and GRE exams are:Institution Code Department CodeTOEFL Exam 1832 72GRE Exam 1832 0799(3) Contact UsExecutive DirectorWilliam A. DeRonne, Ph.D.Phone: (773) 702-1458Email: bderonne@Career DevelopmentEdonna E. LarkinsPhone: (773) 702-0618Email: elarkins@General InformationAshley DossPhone: (773) 834-4385Email: adoss@Saria BartholomewPhone: (773) 702-1902Email: sariab@Multimedia, Web and ITMichael JehlikPhone: (773) 702-7383Email: mjehlik@(4) Faculty & ResearchHenri Berestycki, DirectorHenri Berestycki is Professor and Director of the Centre d'analyse et de mathematique sociales (CAMS) at the Ecole des hautes etudes en sciences sociales (EHESS) in Paris. He has been a regular visiting faculty member of the Department of Mathematics at the University of Chicago since 2005. He has taught at University Paris VI, Ecole normale superieure and Ecole Polytechnique in France. His research interests include partial differential equations, variational calculus, nonlinear analysis, mathematical models of the financial markets, mathematical models in biology and ecology and modeling in social sciences. Among his many recognitions, this year he was awarded the French Legion of Honor.http://cams.ehess.fr/document.php?id=891William DeRonne, Executive DirectorWilliam DeRonne, Ph.D. has more than 30 years of experience in domestic and international financial markets; most recently he was the President, CEO and Chief Compliance Officer of Fox River Financial Resources. He has experience in all the primary markets as well as their derivatives and has worked in China, Japan and Europe. He managed and directed researchers and traders at TradeLink LLC, Market Liquidity Network, LLC and Chicago Research & Trading. He was Senior Vice President and Director of FinancialEngineering/Quantitative Research and Chairman of the Risk Reviewand Management Committee for Nations Bank.Niels O. Nygaard, Founding DirectorProfessor in the Department of Mathematics at the University of Chicago since 1982. Prior to joining the University of Chicago he taught at Princeton University. He holds a Ph.D. in Mathematics from MIT. Professor Nygaard was the Director of the Financial Mathematics Program since its inception in 1996 until April 2010. Besides his interest in Financial Mathematics he has done research in Arithmetic, Algebraic Geometry and Number TheoryNeil A. Chriss, Advisory DirectorNeil Chriss is the Founder, Chief Investment Officer and CEO at Hutchin Hill Capital, LP. Prior to founding Hutchin Hill in October 2007, Neil was a managing director at SAC Capital Management (2003–2007). Previously, Neil was a portfolio manager at Goldman Sachs Asset Management (1998-2000). In 2000, Neil founded ICor Brokerage, an electronic trading platform for swaps and options, which was subsequently acquired by Reuters Plc. Neil holds PhD and BS degrees in Mathematics from the University of Chicago, and an MS in Mathematics from the California Institute of Technology. He has held academic positions in the mathematics departments of Harvard University, the Institute for Advanced Study, and the University of Toronto. Neil serves in an advisory capacity to the Finance Committee of the Institute for Advanced Study in Princeton, NJ (2008–Present). Additionally, he is a founding board member, and a member of the Executive Committee, of Math for America (2003–Present). Neil is an Advisory Director of the University of Chicago’s Financial Mathematics Program. He also serves on the Board of Trustees at Harvey Mudd College in Claremont, CA. Neil holds a patent for his invention, “Method and System for Portfolio Optimization from Ordering Information”.John ZerolisJohn Zerolis is currently Associate Director of the Program on Financial Mathematics, teaches "Portfolio Theory and Risk Management" (with Jon Frye and Paul Staneski), and is also the founder of Angle Vista LLC, which provides quantitative market and credit risk modeling and training to clients. In the course of his career, he has developed leading edge visualization, simulation, and factor modeling techniques for valuing and hedging equity, index and FX options. Previous roles include Head of Risk Analysis at Brinson Partners, Global Head of Risk Analytics at Swiss Bank Corporation, and Vice President of Quantitative Research atO'Connor and Associates, where he was responsible for designing real-time equity option trading and risk control systems.Yuri BalasanovYuri Balasanov, Ph.D. Head of Research and Trading at AQ Strategies, LLC. Yuri has worked in the financial industry since 1991. He has been teaching Financial Mathematics at the University of Chicago since 1997. Prior to launching Alpha Quant Fund at AQ Strategies LLC he worked at Lotsoff Capital Management as Chief Investment Officer; at Ritchie Capital Management as Director of Quantitative Research and Quantitative Trader; at Bank of America as leading quantitative researcher; and at Chicago Research and Trading (CRT) as quantitative researcher. Prior to becoming an industry practitioner Yuri taught at the Moscow State University where he also received his Master’s degree in Applied Mathematics and Ph. D. in Probability and Statistics. Interest Rate DerivativesLida DolocLida Doloc has been an Adjunct Professor in Financial Mathematics at the University of Chicago since 2004. She has been a Quantatative Research Analyst in the Financial Industry for the past fifteen years. Lida studied at the Université Paris Sud (Paris XI) and the Universitatea din Bucuresti.Jon FryeJon Frye is senior economist in global supervision at the Federal Reserve Bank of Chicago, where he researches portfolio credit risk models and their application at banks. Prior to the Fed, he devised market risk and counterparty exposure models at large U.S. banks. He holds a Ph.D. in Economics from Northwestern University.Jon.Frye@ Portfolio Theory and Risk Management IIJeff GrecoPrincipal of Bluehaven Management Group, LLC, an Evanston, Illinois based hedge fund manager. Prior to Bluehaven, he was a Senior Research Analyst with Bank of America's Global Derivative Products Group and Senior Research Associate with Deerfield Capital Management, a Chicago based hedge fund manager. He holds an MS in Applied Mathematics from the University of Chicago and an MS in Mathematics from Carnegie Mellon University. Fixed Income Derivatives I and II; Alfred KanzlerAlfred Kanzler is Director of Risk Management at Vara Capital, a global macro hedge fund. He holds a Ph. D. in Theoretical Chemistry from the University of Chicago. Prior to Vara Capital he was at Ritchie Capital, where he managed the implementation of risk management systems. Prior to Ritchie Capital he developed risk and pricing models and managed software projects for largeinternational banks. Foreign ExchangeGregory F. LawlerGreg Lawler has been Professor of Mathematics and Professor of Statistics at the University of Chicago since 2006 after previously holding positions at Duke and Cornell Universities. He received his Ph.D. in mathematics from Princeton University. His research is in fine properties of random walk and Brownian motion with an emphasis on problems arising in statistical physics. His books include "Intersections of Random Walks", "Introduction to Stochastic Processes", "Conformally Invariant Processes in the Plane", and (with V. Limic) "Random Walk: A Modern Introduction". He has served as editor-in-chief of Annals of Probability and is a Fellow of the American Academy of Arts and Sciences.Roger LeeAssistant Professor in the Department of Mathematics at the University of Chicago. Mathematical Foundations of Option Pricing,Numerical Methods for PDEsJack W. MosevichJack W. Mosevich holds a Ph.D. in Mathematics from the University of British Columbia. He is currently working on return enhancement using derivatives and possible use of new technologies such as neural nets and genetic algorithms. Mr. Mosevich regularly presents talks on derivatives and option risk management. He was formerly Associate professor of Computer Science at The University of Waterloo, Canada. Advanced Option PricingPer A. MyklandProfessor in the Department of Statistics. He holds a Ph.D. in Statistics from the University of California, Berkeley and an M. Sc. in Statistics from the University of Bergen, Norway. His main research interests are: Martingale theory, likelihood theory, and applications of Probability Theory and Statistics in Finance. Mr Mykland has been joint chairman of the Consulting Program at the Department of Statistics and been a statistical consultant to the Norweigan StateOil Corporation. Stochastic CalculusIzzy H. NelkenIzzy H. Nelken is Principal at Supercomputing Applications. He holdsa Ph.D. in Computer Science from Rutgers University. Currently he isediting a book on fixed income options and is the editor of "TheHandbook on Exotic Options." Mr. Nelken has taught courses oncredit derivatives, exotic options, equity swaps and credit and pricerisk of derivatives. Advanced Option PricingPaul StaneskiPaul Staneski is a Managing Director and Head of DerivativesSolutions & Training at Credit Suisse. He has over 30 years ofexperience in the investment industry. Paul has worked as an equityresearch analyst, a quantitative portfolio strategist, and a statisticalanalyst in addition to his current role educating CS clients aboutfinancial markets and products. He also has 10 years of full-timeuniversity teaching experience. He has a B.A. in Economics fromWilliam & Mary and M.S. and Ph.D. degrees in Applied Mathematicsfrom Old Dominion University. He also has a Financial Risk Managercertification from the Global Association of Risk Professionals. (5) Recommended ReadingBelow is a list of recommended texts (several of which will be used in the program). The book by Boas contains most of the mathematics that entering students should be familiar with, while the early chapters in Hull's book are a good introduction to the financial products that are the basis of study for the program.Author TitleMary L. Boas Mathematical Methods in the Physical SciencesSebastien Bossu and Philippe Henrotte Finance and Derivatives: Theory and PracticeJohn C. Hull Options, Futures and Other DerivativesNeil A. Chriss Black-Scholes and Beyond: Option Pricing ModelsP. Wilmott, S. Howison, J. Dewynne The Mathematics of Financial DerivativesPatrick Billingsley Probability and MeasureJonathan E. Ingersoll, Jr. Theory of Financial Decision MakingSome other recommended readings. These are more to get a feel for how business works on Wall Street and not everything is centered around quants. Here are Neil Chriss' picks:Author TitleEdwin Lefevre Reminiscences of a Stock OperatorWarren E. Buffett The Essays of Warren Buffett: Lessons for Corporate America Benjamin Graham, Jason Zweig The Intelligent Investor: The Definitive Book On Value InvestingDaniel Reingold, Jennifer Reingold Confessions of a Wall Street Analyst: A True Story of Inside Information and Corruption in the Stock MarketJoel Greenblatt, Andrew Tobias The Little Book That Beats the MarketJoel Greenblatt, Jr. You Can Be a Stock Market Genius: Uncover the Secret Hiding Places of Stock Market ProfitsPeter Kaufman, Warren E. Buffett, Charles T. Munger Poor Charlie's Almanac Expanded Second Edition. The Wit and Wisdom of Charles T. MungerJohn A. Tracy, CPA How to Read a Financial Report: Wringing Vital Signs Out of the NumbersJohn Burr Williams The Theory of Investment ValueMark Rubinstein A History of the Theory of Investments: My Annotated Bibliography Some picks by Robert Frey:Author TitleMichael Lewis Moneyball: The Art of Winning an Unfair GameEdwin O. Thorp Beat the Dealer: A Winning Strategy for the Game of Twenty-OneWilliam Poundstone Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall StreetRobert J. Frey Lecture notes from Stony Brook, AMS-511 Foundations of Quantitative Finance(6) Online Application申请网址:/new/msfm/prospective/plan_applications.php。
外贸英语试题推荐及答案一、选择题(每题2分,共20分)1. The term "FOB" in international trade refers to:A. Free on BoardB. Free of BoardC. Freight on BoardD. Full of Board答案:A2. What does "CIF" stand for in international trade contracts?A. Cost, Insurance, and FreightB. Cost, Insurance, and FreightingC. Cost, Insurance, FreightD. Cost, Including Freight答案:A3. The abbreviation "L/C" is commonly used for:A. Letter of CreditB. Letter of ContractC. Letter of CommitmentD. Letter of Confirmation答案:A4. In a sales contract, "D/P" stands for:A. Document against PaymentB. Direct PaymentC. Discounted PaymentD. Due Payment答案:A5. The term "T/T" in international trade transactions usually means:A. Transfer of TitleB. Transfer of TradeC. Telegraphic TransferD. Trade Transfer答案:C6. Which of the following is not a type of international trade document?A. Commercial InvoiceB. Bill of LadingC. Certificate of OriginD. Passport答案:D7. The term "EXW" in international trade is known as:A. Ex WorksB. Ex WarehouseC. Exclusive WorksD. Export Works答案:A8. "CIP" in international trade is short for:A. Carriage and Insurance Paid toB. Carriage in ProgressC. Cost, Insurance, and PaymentD. Cost, Including Payment答案:A9. What does "FCA" stand for in international trade?A. Free CarrierB. Full Container atC. Freight Carrier AgreementD. Forwarding Contract Agreement答案:A10. The term "D/A" in international trade usually refers to:A. Document against AcceptanceB. Direct AcceptanceC. Discounted AcceptanceD. Due Acceptance答案:A二、填空题(每题1分,共10分)11. The most common method of payment in international trade is ______.答案:Letter of Credit (L/C)12. When a seller offers goods "FOB", the risk passes to thebuyer when the goods pass over the ______.答案:ship's rail13. "CIF" includes the cost of the goods, ______, and insurance.答案:freight14. A ______ is a document that provides evidence of the origin of goods.答案:Certificate of Origin15. "T/T" can be used for both international and domestic payments and is quick and convenient.答案:Telegraphic Transfer16. "D/P" requires the buyer to pay for the goods before receiving the ______.答案:documents17. "EXW" means that the seller makes the goods available to the buyer at their ______.答案:place of business18. "CIP" terms require the seller to arrange for ______ and insurance.答案:carriage19. "FCA" means that the seller fulfills their obligations when the goods are handed over to the ______.答案:first carrier20. "D/A" is a method of payment where the documents are released to the buyer upon ______ of the draft.答案:acceptance三、简答题(每题5分,共30分)21. Explain the difference between "FOB" and "CIF" terms in international trade.答案:"FOB" (Free on Board) terms mean that the seller's responsibility ends when the goods are loaded onto the ship, and the buyer bears all costs and risks from that point. "CIF" (Cost, Insurance, and Freight) terms include theseller's responsibility for the cost of the goods, freight to the agreed destination, and insurance.22. What are the advantages and disadvantages of using a Letter of Credit (L/C) in international trade?答案:Advantages include security for both the buyer and seller, as payment is guaranteed by a bank. Disadvantages include additional costs for bank fees and potential delays due to the time needed for bank processing.23. Describe the process of a Documentary Collection (D/P) in international trade.答案:In a Documentary Collection, the seller's bank forwards shipping documents to the buyer's bank, which then presents them to the buyer for payment. Once payment。
关于合同谈判纪要的呈批件英文回答:Memorandum.To: Senior Management.From: [Your Name]Date: March 8, 2023。
Subject: Contract Negotiation Memorandum.Introduction.The purpose of this memorandum is to summarize the key points discussed and agreements reached during the recent contract negotiations with [Counterparty Name]. The negotiations covered a range of issues, including pricing, terms of payment, delivery schedule, and dispute resolution.Negotiation Highlights.Pricing: We were able to negotiate a favorable price point that aligns with our budget and business objectives.Terms of Payment: We agreed to a payment schedule that provides flexibility and minimizes financial risk.Delivery Schedule: The delivery schedule was revised to accommodate our operational timelines and ensure timely completion of the project.Dispute Resolution: We established a clear dispute resolution process that promotes timely and efficient resolution of any potential conflicts.Key Agreements.The contract will be for a term of [duration] years.The contract will include a non-disclosure agreementto protect sensitive information.We will have the right to terminate the contract for cause in the event of material breach by the counterparty.The contract will be governed by the laws of [jurisdiction].Next Steps.We are currently working to finalize the contract language and will submit the final draft for your review and approval within the next [number] days. Once the contract is finalized and executed, we will proceed with the implementation of the agreement.Conclusion.The contract negotiations were conducted in a professional and collaborative manner. We believe that the agreements reached serve the best interests of both parties and lay the foundation for a successful partnership.中文回答:呈批件。
derivative securities analysis -回复Derivative securities analysis is a critical aspect of investment management, providing investors with insight into the potential risks and rewards associated with these complex financial instruments. This article aims to break down the concept of derivative securities analysis, exploring the steps and considerations taken in the evaluation process.Step 1: Understanding Derivative SecuritiesDerivative securities are financial contracts whose value is derived from an underlying asset. Common types of derivative securities include options, futures contracts, swaps, and forward contracts. An essential first step in derivative securities analysis is gaining a thorough understanding of these instruments and their characteristics.Step 2: Assessing Market ConditionsOnce the investor understands the basics of derivative securities, the next step involves assessing the market conditions. This includes analyzing factors such as interest rates, exchange rates, market volatility, and economic indicators that impact the underlying asset. Evaluating these conditions helps determine thepotential risks and opportunities associated with the derivative security.Step 3: Identifying Investment ObjectivesBefore delving into the analysis of derivative securities, investors need to identify their investment objectives. This can involve determining the desired risk tolerance, return expectations, and investment time horizon. Different derivative securities offer varying risk-reward profiles, so aligning investment objectives with the appropriate securities is crucial.Step 4: Analyzing the Derivative SecurityThe analysis of a derivative security typically involves conducting a variety of quantitative and qualitative evaluations. Quantitative analysis involves examining the mathematical models used to price the derivative security, such as options pricing models like the Black-Scholes model. This analysis helps assess the fair value of the derivative and potential profit or loss scenarios under different market conditions.Qualitative analysis, on the other hand, involves a deeper assessment of the factors that may impact the derivative security'svalue. This can include evaluating the creditworthiness of counterparties involved in the contract, the regulatory environment, and geopolitical risks.Step 5: Assessing Risk-Return CharacteristicsDerivative securities often come with various risks, including counterparty risk, liquidity risk, and market risk. Evaluating and understanding these risks is crucial in the analysis process. Investors must assess the risks associated with the derivative security and compare them to the potential returns. This analysis helps in determining if the risks are adequately compensated by the potential profits.Step 6: Monitoring and Re-evaluatingOnce an investment decision is made, it is essential to continuously monitor the derivative security's performance and market conditions. Market dynamics can change quickly, impacting the value and risks associated with the security. Regular monitoring and re-evaluation help ensure that investment objectives are continuously met and adjustments can be made if necessary.In conclusion, derivative securities analysis is a comprehensive process that involves understanding the instrument, assessing market conditions, identifying investment objectives, analyzing the security, assessing risk-return characteristics, and monitoring and re-evaluating. By following these steps and considering various factors, investors can make informed decisions about derivative securities and manage their risks effectively.。
随机利率下含信用风险的欧式期权的定价涂淑珍;黄婧;李时银【摘要】In this paper, we derive explicit pricing formula for vulnerable call options where the credit risk is handled in a hybrid model. We describe the process of default via a doubly stochastic Poisson process, and assume that the intensity processλof Poisson process follows an mean-reverting process. Moreover, the default intensity processλcorrelates with the underling asset and the value of the firm mutually. By applying equivalent martingale measure, we derive closed-form solutions of the pricing formulae within a general Gaussian interest rate framework.%采用混合定价方法给出了含信用风险的欧式期权在利率是随机情况下的模型。
采用公司定价模型中的补偿率,同时假定违约过程服从重Poisson随机过程。
其中违约过程的强度函数λ服从均值回复过程,且它与标的资产价格和公司价值相关。
运用等价鞅测度变换,给出了在随机利率框架下,含信用风险的期权价格的闭解。
【期刊名称】《龙岩学院学报》【年(卷),期】2015(000)005【总页数】8页(P18-25)【关键词】随机利率;重Poisson随机过程;信用风险;等价鞅测度【作者】涂淑珍;黄婧;李时银【作者单位】龙岩学院福建龙岩 364000;龙岩学院福建龙岩 364000;厦门大学福建厦门 361005【正文语种】中文【中图分类】O213数学·物理考虑信用风险的期权定价是当今金融研究的一个重要领域.对信用风险的定价模型主要有两种方法:结构模型(公司企业价值模型)和简化模型(强度函数模型).结构模型最早由Black和[1]和[2]提出,若期权到期时, 企业资产总值小于它的负债总额,则违约发生.这个框架内的主要问题是对公司价值以及公司资本结构的变化进行建模,相关研究成果有:Ammann [3], Johnson和[4],Klein和[5].而简化模型则是用一个外生的随机过程(通常用Poisson过程)来描述违约事件的发生,此方法主要要解决的问题是违约过程强度函数的确定,Jarrow和[6],Leung和[7], Guo和Jarrow 等[8]给出了该框架下的相关结论.本文采用混合定价模型来对含信用风险的欧式期权进行定价.用外生的重Poisson 过程来描述违约事件的发生,重Poisson随机过程的强度函数遵从均值回复过程.当违约发生时,采用公司价值模型中的补偿率,即期权多方到期时至多只能得到承诺支付的部分比率,该比率用来表示,其中VT,D分别表示公司资产价值和公司负债.同时,本文假定利率是随机的,服从高斯利率模型,且违约强度函数与标的资产价格和公式资产价值相关.在前人研究的基础上,先给出在远期风险中性测度下,标的资产以及公司资产价值的远期价格,通过等价鞅测度变换给出了含信用风险的欧式期权在远期测度下的定价方程及价格闭解.设(Ω,F,(Ft)t≥0,P) 为一完备的概率空间,(Ft)t≥0 为其上的对t递增的子σ域.假定对随机变量的所有叙述几乎处处成立,或几乎必然成立,P是风险中性概率,是右连续的,F0包含了当前时刻以及之前的所有信息.用(X):=EP(X|Ft)表示随机变量在t时刻以及t之前所有信息都已知情况下的条件期望.假定f(t,T)为远期利率,满足如下微分方程其中W为标准的布朗运动过程是Ft-适应的, 则瞬时利率为特殊的远期利率,满足r(t)=f(t,t),到期日为T的零息债券在t时的价格用远期利率来表示为P(t,T).同时,本文以零息债券价格P(t,T)为计价标准券,则价格变量it的远期价格可表示为.St表示股票的价格,Vt表示公司资产价值,则在风险中性概率测度P下,它们遵从如下几何布朗运动过程:其中r(t)遵从高斯利率模型,σS(t),σV(t) 是时间的确定性函数, 是P测度下的标准布朗运动过程.命题1[9] 在风险中性测度P下,到期日为T的零息债券价格为P(t,T)满足如下微分方程其中s.由命题1,可以得到如下命题.命题2 在风险中性测度P下,的微分形式分别如下设ξt是一重Poisson随机过程,违约强度函数为λt,满足均值回复过程[11],即其中α,m,σλ 为常数, 是标准的布朗运动过程.设期权的到期日为T,违约发生的时间为τ,τ=inf{t|ξt=1,0≤t≤T}表示过程{ξt}(t≥0)第一个事件的到达时间,则滤子,其中≤t),i=S,V,λ以及Ht=σ(I(τ≤s),s≤t).定义一个新的滤子,则τ的条件概率为[12]为简化计算,引入新的等价概率测度F,满足其中为违约风险的市场价格[13].命题3 SF,VF在新测度F下遵循的过程分别为:其中βi(t,T)=σi(t)+σ'(t,T),i=S,V是有界的和时间的确定性的函数.是F测度下的标准布朗运动.命题4[13] λ(t)在新测度F下遵循的过程为由Ito随机微分方程的知识[10],SF,VF和λ(t)的解为计算如下积分其中最后一步的计算应用了Fubini定理.为下文计算方便,定义令,其中i∈{S,V,λ}, 则SF(T,T),是ηS(t,T),ηV(t,T),ηλ(t,T)的函数,SF,VF和可以重新写成标准布朗运动) 的协方差矩阵为由于测度变换并不影响变量间的协方差,因此在F测度下,)的协方差矩阵仍为上式.由标准布朗运动的定义,有ηi(t,T),∀i∈{S,V,λ}遵从均值为0,方差为(t,T)的正态过程. 因此两两之间的协方差为对应的相关系数为为简化计算,作如下定义:由此,得到(ηS,ηV,ηλ)的相关系数矩阵记为从而联合分布函数为引理[14] 设某一风险收益在到期日T的收益为I(t≤τ≤T)δY+I(t>T)Y,若Y,δ是一G-可测的随机变量,τ,G,F的定义如1.2,令,则有进一步,如果Y是一FT-可测的随机变量,则有本文采用含信用风险的期权定价的混合模型.考虑含信用风险的期权具有双重风险:市场风险和违约风险,借助公司价值模型的补偿率,同时采用以强度为基础的的破产函数确定违约的发生.传统模型中假定违约过程是外生的,即违约强度与标的资产价格,企业价值不相关,但在现实经济社会中,违约强度λ与它们紧密相关.同时违约强度λ在实际中不太可能是确定性的,也不会任意变动,而是围绕其均值上下波动,故本文假定λ服从均值回复过程.同时,我们假定无风险利率是随机的,遵从高斯利率模型. 定理用重Poisson的随机过程{ξt}(t≥0)来控制违约过程,其中它的强度过程{λt}(t≥0)遵循均值回复过程,且违约强度过程{λt}(t≥0)与标的资产价格,企业价值的过程两两相关的情况下,承诺到期支付为XT=(ST-K)+,违约补偿率为cVTD的欧式期权在远期测度下的定价公式为(这里为了简化计算,初始时间为0 时刻):其中的表达式如前所述.证明在高斯利率框架下,用远期中性测度推导含信用风险的期权的价格.含信用风险的期权在到期T时的价值为:其中第一部分为企业没有违约时的到期支付,第二部分为违约发生时的补偿支付.根据鞅定价原理,该期权在初始时刻的价值为这里用到P(T,T)=1.由引理,将(4)和I(τ>0)=1带入上式得,为方便起见,令EF[·]=EF[·|F0], 同时将上式拆分成四项X0=E1-E2+E3-E4,其中下面分别计算E1,E2,E3和E4.E1的计算.将式(1),(3)以及S(0,T)代入E1得由,故令,则有). 而对于SF(T,T)≥K,由(1),可以得到≥.通过简单的计算,可以得到下式: 定义x,令y=x,则其中n(·,·)是2维联合正态分布N(0,0,1,1;ρ)的密度函数,n(·),N(·)分别表示标准正态分布的密度函数和分布函数.第一个等号的成立运用N(b1)=1-N(-b1)这一结论.因此有其中类似E1的计算,同理可以得到E2的表达式如下:E3的计算.计算如下式子其中将式(1)和(2)以及S(0,T)代入得类似于(6)式的计算方法,得到对于的计算如下所示定义其中,则). 令,则有其中n(y1;Σ)表示三维正态分布N(0,0,0,1,1,1;Σ)的密度函数.综上,E3为类似E3的计算,同理可以得到E4的表达式如下:综合(6-9),即可得到式(5),证毕.本文采用混合定价模型,给出了考虑信用风险下,利率为随机利率时的欧式期权的价格.在传统模型的基础上,假定利率遵从高斯利率过程,违约强度函数遵从重Poisson 随机过程,且它与标的资产和企业价值都相关,这与传统模型相比更为接近实际情况,用此模型来定价含信用风险的欧式期权所得到的定价方程更为合理.本文建模过程中涉及到两种不同类型的不确定,一种不确定性来源于标的资产和公司资产价格,另一种则是来源于违约时间的不确定,而且这两种不确定存在相关关系.应用Nicole El Karoui给出的相关结论,通过计算最后给出了简化之后的期权价格如定理所示.可以从以下几个方面来扩展我们的研究,可以放宽假设,如公司的债务D可以考虑随机过程,同时可以把此方法用于含信用风险的多资产期权的定价问题,与传统方法相比,用该方法得到的解更为简化.【相关文献】[1] Black Fischer,Myron Scholes. The pricing of options and corporate liabilities[J]. The journal of political economy,1973,81(3): 637-654.[2] Merton Robert C. On the pricing of corporate debt: The risk structure of interestrates[J]. The Journal of Finance,1974,29(2): 449-470.[3] Ammann Manuel. Credit risk valuation: methods, models, and applications[M]. New York:Springer, 2001:194-200.[4] Johnson Herb, Rene Stulz. The pricing of options with default risk[J]. The journal of finance, 1987,42(2): 267-280.[5] Klein Peter, Michae lInglis. Pricing vulnerable European options when the option’s payoff can increase the risk of financial distress[J]. Journal of banking and finance, 2001,25(5):993-1012.[6] Jarrow Robert, Yu Fan. Counterparty risk and the pricing of defaultable securities[J]. The Journal of Finance, 2001,56(5):1765-1799.[7] Leung Kwai Sun, Kwok Yue Kuen. Counterparty risk for credit default swaps: Markov chain interacting intensities model with stochastic intensity[J]. Asia-Pacific Financial Markets, 2009,16(3): 169-181.[8] Guo Xin, Jarrow Robert, Yan Zeng. Modeling the recovery rate in a reduced form model[J]. Mathematical Finance, 2009,19(1): 73-97.[9] Duffie Darrell, Pan Jun, Kenneth Singleton. Transform analysis and asset pricing for affine jump-diffusions[J]. Econometrica, 2000,68(6): 1343-1376.[10] Kloeden Peter E.,Eckhard Platen. Numerical solution of stochastic differential equations[M]. New York: Springer,1992:253-266.[11] Fouque Jean-Pierre, George Papanicolaou, Ronnie Sircar. K. Mean-reverting stochastic volatility[J].International Journal of Theoretical and Applied Finance,2000,3(1):101-142.[12] 宋丽平,李时银. 违约风险定价模型的推广与应用[J].厦门大学学报:自然科学版,2005,44(5):616-620.[13] Blanchet Scalliet, Christophette, Nicole El Karoui, etc. Dynamic asset pricing theory with uncertain time-horizon[J]. Journal of Economic Dynamics and Control, 2005,29(10): 1737-1764.[14] Su Xiaonan, Wang Wensheng. Pricing options with credit risk in a reduced form model[J]. Journal of the Korean Statistical Society, 2012,41(4):437-444.。
CFA衍生工具(Derivatives)考点解析对于很多想参加CFA考试的同学来说,对于CFA的考试内容还不是很了解。
我就为大家分享一下CFA考试的考试科目:1、道德与职业行为标准(Ethics and Professional Standards)2、定量分析(Quantitative)3、经济学(Economics)4、财务报表分析(Financial Statement Analysis)5、公司理财(Corporate Finance)6、权益投资(Equity Investments)7、固定收益投资(Fixed Income)8、衍生工具(Derivatives)9、其他类投资(Alternative Investments)10、投资组合管理(Portfolio Management)Derivatives(金融衍生品)很多CFA考生都认为一级里的Derivatives(金融衍生品)非常难,碰到这个章节就觉得十分头疼。
好在这个部分在考试中占比仅为5%,有些考生甚至采取了丢车保帅的做法。
提醒大家,不必对此产生畏难情绪。
CFA一级考试金融衍生品科目考试以前有一些计算,但现在以定性题目为主,要求考生能理解其中原由,难度有所下降。
随着国内逐渐开放衍生品市场,越来越需要有衍生品专业知识的人才。
这部分的衍生品主要介绍衍生品的一些基本知识,包括衍生品的种类及市场区分,4大类衍生品的基本定价原理,以及简单期权策略。
CFA一级考试的Derivatives(金融衍生品)具体的内容知识点包含1个study session,3个reading。
其中,Reading 57对衍生品市场进行了区别,并对4大类衍生品进行了基本定义;Reading 58讲衍生品的定价和估值的基本原理,并对4大类衍生品的基本定价做了介绍;Reading 59对期权做了进一步分析,介绍两种期权及两种期权策略的应用。
从CFA考试的重要度来看,Reading 58、Reading 59是最重要的,Reading 57其次,其他Reading重要性不大。
高三英语经济术语练习题50题1.The value of a currency is determined by many factors, including supply and demand. If the supply of a currency increases, its value is likely to _____.A.increaseB.decreaseC.remain unchangedD.fluctuate randomly答案:B。
解析:当一种货币的供应量增加时,根据供求关系,供大于求会导致其价值下降。
选项A 增加错误;选项C 保持不变错误;选项D 随机波动不准确,一般供应量增加价值倾向于下降。
2.In international trade, the exchange rate between two currencies can affect the price of imported and exported goods. If the exchange rate of a country's currency appreciates, the price of its exports is likely to _____.A.increaseB.decreaseC.remain unchangedD.depend on other factors答案:A。
解析:如果一个国家的货币汇率升值,那么其出口商品的价格会上升,因为同样的商品以本币计价不变,但换算成外币价格升高。
选项B 下降错误;选项C 保持不变错误;选项D 不准确,汇率升值出口价格通常会上升。
3.Different forms of money include cash and digital currency. Which of the following is an advantage of digital currency over cash?A.It is more widely accepted.B.It is easier to counterfeit.C.It offers more privacy.D.It is more convenient for online transactions.答案:D。
Counterparty Risk and the Pricing of Defaultable SecuritiesRobert A.Jarrow and Fan Yu∗∗Jarrow is from the Johnson Graduate School of Management,Cornell University and Kamakura Corporation, and Yu is from the Graduate School of Management,University of California at Irvine.A previous version of this paper appeared as Chapter1of Yu’s doctoral dissertation at Cornell University.We thank Warren Bailey,Richard Green(the editor),Haitao Li,Robert Masson,George Oldfield,George Pennacchi,an anonymous referee,and seminar participants at Baruch College,Boston University,the College of William and Mary,Cornell University,the Federal Reserve Bank of New York,Georgetown University,McGill University,Rice University,the University of British Columbia,the University of California at Irvine,the University of Illinois at Urbana-Champaign,the University of Iowa,the University of Wyoming,the2000Derivatives Securities Conference at Boston University,and the1999 Frank Batten Young Scholars Conference at the College of William and Mary for useful comments.Yu acknowledges the support of a Sage Graduate Fellowship from Cornell University while part of this research was completed.Counterparty Risk and the Pricing of Defaultable SecuritiesAbstractMotivated by recentfinancial crises in East Asia and the U.S.where the downfall of a small number offirms had an economy-wide impact,this paper generalizes existing reduced-form models to include default intensities dependent on the default of a counterparty.In this model,firms have correlated defaults due not only to an exposure to common risk factors,but also tofirm-specific risks that are termed“counterparty risks.”Numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps.It has been well documented in Moody’s reports on historical default rates of corporate bond issuers that the number of defaults,the number of credit rating downgrades,and credit spreads are all strongly correlated with the business cycle.This has motivated reduced-form models such as Duffie and Singleton(1999)and Lando(1994,1998),which assume that the intensity of default is a stochastic process that derives its randomness from a set of state variables such as the short-term interest rate.This approach has the convenient features that conditioning on the state variables, defaults become independent events,and default correlation arises due to the common influence of these state variables.On the other hand,a default intensity that depends linearly on a set of smoothly varying macroeconomic variables is unlikely to account for the clustering of defaults around an economic recession.This is evident from a casual inspection of the exhibits in the latest Moody’s report(see Keenan(2000)).Within the usual affine framework,one can model the state variables as jump diffusions(see Duffie,Pan and Singleton(1999)).But presently there is no evidence whether the magnitude of jumps needed to justify the clustering of defaults is consistent with well-defined,observable macroeconomic variables.1This paper complements the current literature on default risk modeling by introducing the concept of counterparty risk.In our model,eachfirm has a unique(firm-specific)counterparty structure that arises from its relation with otherfirms in the economy.Counterparty risk is the risk that the default of afirm’s counterparty might affect its own default probability.This approach has two benefits.First,to the extent that the public is aware of the counterparty relations,the prices of marketed securities will reflect the market’s assessment of the importance of counterparty risk.Relying on the notion of market efficiency,our model allows the extraction of this information, which is potentially important for the pricing of defaultable bonds and credit derivatives,as we demonstrate below.Second,the additional default correlation introduced by counterparty relations makes it straightforward to account for the observed clustering of defaults.For instance,a group offirms can be so highly interdependent that a single default can trigger a cascade of defaults. Because the likelihood of default is higher for allfirms during a recession,this cascading effect is much more likely to be observed then.This has important implications for the management of credit risk portfolios,where default correlation needs to be explicitly modeled.Our concept of counterparty risk has been motivated by a series of recent events in which firm-specific risksfigure prominently.Several such examples are given below:•The South Korean banking crisis was commonly attributed to non-performing loans made toa handful of chaebols(industrial conglomerates).•Long Term Capital Management’s potential default had implications for the likelihood of default of other major investment banks.This was the given reason for the rescue effort led by the Federal Reserve Bank of New York in September1998.•Bankers Trust revealed its$350million position in Russian assets on August31,1998.A month later,Standard and Poor’s downgraded its senior debt.•Goldman Sachs committed$2billion in bridge loan to United Pan-Europe Communications on March22,2000.Two months later,UPC’s stock price was down69percent and Goldman Sachs was unable tofind a buyer for this loan.•First Boston extended a$457million bridge loan to the purchaser of Ohio Mattress in1989.It ended up owning Ohio Mattress and could not recover its loan.This resulted in a takeover by Credit Suisse.While there are numerous stories like these in thefinancial press,a common thread is that a firm will face significant counterparty risk when its portfolio is concentrated in just a few positions. As these positions change,often unexpectedly,thefirm is likely to run intofinancial difficulties. The rational anticipation of these future events implies that there should be a response in the term structure of credit spreads today.It is this discernible shift that reveals the relevant information.In this context,traditional structural or reduced-form approaches are inadequate because they ignore thisfirm-specific source of risk.The concept of counterparty risk,however,is not limited to the portfolio perspective.With the adoption of just-in-time manufacturing processes,firms are increasingly reliant on the smooth operation of otherfirms upstream,and a broken link is likely to have an impact on afirm’s likelihood of bankruptcy.A case in point is the heavy loss suffered by GM when its Delphi plant went on strike in1998.Our model can capture this sort of industrial organization interdependencies in default intensities.Similarly,in the study of mortgage prepayment behavior,one could specify an empirical prepayment function that incorporates not only macroeconomic factors such as interest rates,but also regional demographic and economic variables that could affect prepayment.Forexample,the default of a key local industry could increase the likelihood of prepayment in the related locality as unemployed workers relocate tofind new opportunities.These are but a few of the potential applications of our framework.The modeling of counterparty risk is achieved through an extension of the existing reduced-form models.2In our model,the intensity of default is influenced not only by a set of economy-wide state variables,but also by a collection of counterparty-specific jump terms capturing inter-firm linkages. This setup allows us to maintain the simplicity of a reduced-form model while incorporatingfirm-specific information provided by the market.3In the limit asfirms hold well-diversified credit risk portfolios,the counterparty risk part of their default intensities will disappear and our model reduces to a standard one.We start Section I by assuming the existence of a collection of doubly stochastic Poisson pro-cesses representing default.The default intensities could potentially depend on the status of all the otherfirms in the economy.Within this general framework,we provide a pricing formula for defaultable bonds that generalizes a key result in Lando(1994,1998).In Section II,we discuss the subtleties involved in the simultaneous construction of several default processes.Through a simple example,we show that the complexity of the model explodes whenever there exist“loops”in the counterparty structure.We then place a further restriction on the model to simplify subse-quent exposition.In Section III and IV we explore the implication of counterparty risk on bond pricing through several examples.These include simple ones where default is independent of the default-free term structure,and more realistic ones where the default intensity depends linearly on a Gaussian spot rate.In Section V we extend our model to the pricing of credit derivatives, focusing on default swaps and the importance of default correlation in pricing a default swap.We conclude with Section VI.All proofs and some detailed derivations are contained in the appendices.I.The ModelOur model generalizes Lando(1994,1998)to include counterparty default ndo’s(1994, 1998)reduced-form model allows for dependency between credit and market risk through the use of a doubly stochastic Poisson process(also called a“Cox process”).In a Cox process,the intensity of default,which measures the likelihood of default per unit time,is itself a stochastic process thatdepends on a set of economy-wide state ndo(1994,1998)models these state variables as continuously varying diffusion processes.Our innovation is the inclusion of jump processes in this set of state variables,thereby capturing the interdependence among several default processes. Because of this feature,the construction of the default processes becomes recursive,since a complete default history of all other interdependentfirms is needed to construct the default process for a givenfirm.This added complexity is fully analyzed below.As the primary goal of this section is to extend Lando’s(1994,1998)defaultable bond pricing formula to include interdependent default risk,we initially assume the existence of these default processes and defer their construction to Section II.In the following,we outline the three ingredients of our model:the default process,the recovery mechanism,and the pricing formula.A.Default ProcessLet the uncertainty in the economy be described by thefiltered probability space ³Ω,F,{F t}T∗t=0,P´,where F=F T∗and P is an equivalent martingale measure under which discounted bond prices are martingales.We assume the existence and uniqueness of P,so that bond markets are complete and priced by arbitrage,4as shown in discrete time by Harrison and Kreps(1979)and in continuous time by Harrison and Pliska(1981).Subsequent specifications of the model are all under the equivalent martingale measure P.On this probability space there is an R d-valued process X t,which represents d economy-wide state variables.There are also I point processes,N i,i=1,···,I,initialized at0.These represent the default processes of the Ifirms in the economy such that the default of the i thfirm occurs when N i jumps from0to1.The properties satisfied by these point processes will be specified shortly.Thefiltration is generated collectively by the information contained in the state variables and the default processes:5F t=F X t∨F1t∨···∨F I t,(1) whereF X t=σ(X s,0≤s≤t)and F i t=σ¡N i s,0≤s≤t¢(2) are thefiltrations generated by X t and N i t,respectively.Define a newfiltration G i t as follows.First,we let thefiltration generated by the default processes of allfirms other than that of the i th be denoted byF−i t=F1t∨···∨F i−1t∨F i+1t∨···∨F I t.(3) Then,letG i t=F i t∨F X T∗∨F−i T∗.(4) Since F i0is the trivialσ-field,G i0=F X T∗∨F−i T∗.We note that G i0contains complete information on the state variables and the default processes of allfirms other than that of the i th,all the way up to time T∗.Conditioning upon G i0is equivalent to conditioning upon the state of the macro economy and the default status of all the remainingfirms.In a world that evolves according to thefiltration G i t, it is possible to select,at time0,a complete history of a processλi t,nonnegative,G i0-measurable and satisfying R t0λi s ds<∞,P-a.s.for all t∈[0,T∗],so that an inhomogeneous Poisson process N i can be defined,using the realized history of the processλi t as its intensity function.This will be the point process governing default forfirm i,since it has an intensity process that depends on state variables as well as the default status of all the otherfirms.This two-step randomization procedure,in fact,provides the intuition behind a formal definition of a doubly stochastic Poisson process in Brémaud(1981).Letτi denote thefirst jump time of N i.Then the conditional and unconditional distributions ofτi are given byP¡τi>t|G i0¢=expµ−Z t0λi s ds¶,t∈[0,T∗],(5)and P¡τi>t¢=E expµ−Z t0λi s ds¶,t∈[0,T∗].(6) This completes our specification of the default process.We note that the computation of bond prices with counterparty risk generally requires the joint distribution of severalfirst jump times.Due to the presence of counterparty risk,thesefirst jump times may no longer be assumed independent conditional on the complete history of the state variables.We again defer the discussion to Section II.B.Recovery RateThe second ingredient in the modeling of defaultable bonds is the recovery rate.Our specifica-tion of the recovery rate is as follows.Let p(t,T)denote the time-t price of a default-free zero-coupon bond that pays one dollar at time T where0≤t≤T≤T∗.Let v i(t,T)denote the time-t price of a zero-coupon bond maturing at time T,issued byfirm i where i=1,···,I.These corporate bonds are subject to default.When firm i defaults,a unit of its bond will pay an exogenously specified constant fractionδi∈[0,1)of a dollar at maturity,so that the value of the bond after default is given byδi times the price of a default-free bond.6This is the“recovery of Treasury”assumption in Jarrow and Turnbull(1995) and Jarrow,Lando,and Turnbull(1997).An alternative to the above is the“recovery of market value”where a fraction of pre-default market value is recovered immediately upon default.However,with this alternative assumption, only the loss rateλ(1−δ)can be recovered from zero-coupon bond prices.7To estimate the default intensity and the recovery rate simultaneously,one would have to resort to either the prices of credit derivatives,as suggested by Duffie and Singleton(1999),or the prices of equity or equity options, as suggested by Jarrow(1999).C.PricingWe now derive a pricing formula for defaultable bonds.First,let r t denote the spot rate process adapted to F X t.8The spot rate process could come from any arbitrage-free default-free term structure model,such as Heath,Jarrow,and Morton(1992,HJM hereafter).Since P is an equivalent martingale measure,the money market account and bond prices are given byB(t)=expµZ t0r s ds¶,(7)p(t,T)=E tµB(t)¶,(8)and v i(t,T)=E tµB(t)¡δi1{τi≤T}+1{τi>T}¢¶,(9) where E t(·)denotes the expectation conditional on time-t information F t.The following proposition expresses equation(9)in terms of the default intensity.Proposition1:The defaultable bond price is given byv i(t,T)=δi p(t,T)+1{τi>t}(1−δi)E t expµ−Z T t¡r s+λi s¢ds¶,T≥t.(10)Proof:This is an extension of Lando(1994,Proposition3.3.1).Details are in Appendix A.Equation(10)is very intuitive.It states that the risky bond’s price can be divided into two components.Thefirst component is the recovery rateδi that is received for sure,discounted to time t.The second component is the residual1−δi in the event of no default,also discounted to time t.The second term reflects the default risk since it is discounted with an adjusted spot rate. Pricing under the equivalent martingale measure thus depends critically on the evaluation of the expectation in equation(10).II.Construction of Default ProcessesThe previous section assumes the existence of a collection of doubly stochastic Poisson processes, whose intensities satisfy a special measurability ing this and only this knowledge, the distribution of thefirst jump times can be derived.The bond price of afirm whose default probability is affected only by macroeconomic conditions and not by the default of otherfirms can be easily calculated using equation(10).For afirm,A,whose default probability is strongly affected by the default offirm B,the calculation of its bond price entails knowing the distribution of the default time for B.However,if B holds a significant amount of debt issued by A,the distribution of the default time for B would then depend on that of A.In general,whenever such a relationship forms a loop,the calculation of bond prices is a difficult task.In the following,wefirst use a simple example to illustrate the complexity involved when looping default is introduced into the model. We then impose a restriction on the structure of our model in order to eliminate looping default.A.Looping DefaultConsider the case where eachfirm holds the otherfirm’s debt,so that when A defaults,B’s default probability will jump,and vice versa.Specifically,the default intensities can be describedbyλA t=a1+a21{t≥τB},(11)andλB t=b1+b21{t≥τA},(12) where a1,a2,b1and b2are positive constants.The pricing of these bonds requires knowledge of the distribution of thefirst jump timesτA and τB.However,these distributions are defined recursively through each other and can be obtained explicitly only in special cases.In a full-fledged model of looping default among threefirms,the calculation of bond prices would require joint distributions of pairs of default times,and among fourfirms,triples of default times,etc.Working out these distributions is more difficult,and it is why only twofirms are used in this illustration.Let F(t)=P¡τA≤t¢and G(t)=P¡τB≤t¢be the marginal distribution functions forτA andτB.By equations(6)and(11),P¡τA>t¢=E expµ−Z t0³a1+a21{s≥τB}´ds¶=E expµ−Z t0(a1+a2)ds+Z t0a21{s<τB}ds¶=e−(a1+a2)t E e a2min(τB,t).(13) Hence1−F(t)=e−(a1+a2)tµZ t0ds g(s)e a2s+Z∞t ds g(s)e a2t¶,(14) where g(s)=dG(s)/ds.Multiplying both sides by e(a1+a2)t,we obtaine(a1+a2)t(1−F(t))=Z t0ds g(s)e a2s+e a2t(1−G(t)).(15) Differentiating the above,we arrive at an ordinary differential equation for F in terms of G and a similar equation for G in terms of F:(a1+a2)(1−F)−f=a2e−a1t(1−G),(16)and(b1+b2)(1−G)−g=b2e−b1t(1−F),(17) where f(t)=dF(t)/dt.In general,equations(16)and(17)must be solved with numerical methods.But when thefirms have identical default intensities,they can be solved analytically.Let a1=b1=a and a2=b2=b, then F=G and they are given byF(t)=1−e−(a+b)t+b a(1−e−at).(18) Once the distribution functions are derived,bond prices are calculated using numerical integration.Equation(18)shows how counterparty risk(b>0)increases the probability of default prior to time t in contrast to the no counterparty risk case(b=0).The change is generally nonlinear as illustrated here.B.Primary-Secondary FrameworkAlthough looping default generates an interesting complexity in our model,it is unlikely to occur in practical applications of our model.In a typical application one considers the default probability of a commercial bank.If bank A holds a significant amount of productionfirm B’s debt,it is unlikely that B is also holding bank A’s debt or equity,let alone amounts large enough to influence B’s default probability.Thus we impose the following restriction.Assumption1:Let I be the set offirms in the economy.A subset S1⊂I contains primaryfirms whose default intensities depend only on F X t.Its complement,S2⊂I,contains secondaryfirms whose default intensities depend only on F X t and the status of the primaryfirms.This assumption splitsfirms into one of two mutually exclusive types:primaryfirms and sec-ondaryfirms.Primaryfirms’default processes only depend on macro-variables.Secondaryfirms’default processes depend on macro-variables and the default processes of the primaryfirms.This assumption makes it easy to construct the doubly stochastic Poisson processes used in Section I.To achieve this,consider the state variables X t that describe the evolution of the default-free term structure.For instance,X t could be the independent Brownian motions generating the HJM model.One could also add to X t additional factors thought to be important determinants of the default process,such as GNP indices.The probability space on which X t is defined is then enlarged to accommodate a set of indepen-dent unit exponential random variables,which are also independent of X t.If we call these variables©E i,1≤i≤S1ª,9then the default times of the set of S1primaryfirms can be defined asτi=inf½t:Z t0λi s ds≥E i¾,1≤i≤S1,(19) where the intensityλi t is adapted to F X t.Since E i is independent of X t,the distribution ofτi is given by:P¡τi>t|F X T∗¢=expµ−Z t0λi s ds¶,t∈[0,T∗].(20) Then,for each i,define N i t=1{τi≤t}asfirm i’s default process and F i t=σ¡N i s,0≤s≤t¢as the information set generated by the default process offirm i.Thisfirst step of our construction is directly from Lando(1994).In the second step,we construct the secondary default processes.We enlarge the probability space further by introducing another set of independent unit exponential random variables,which are independent of both X t and©τi,1≤i≤S1ª.If we call them©E j,S1+1≤j≤Iª,then the default times of the set of S2secondaryfirms can be similarly defined asτj=inf½t:Z t0λj s ds≥E j¾,S1+1≤j≤I,(21) where the intensityλj t is adapted to F X t∨F1t∨···∨F S1t.Since E j is independent of both X t and the set of primary default times,the distribution ofτj is given by:P³τj>t|F X T∗∨F1T∗∨···∨F S1T∗´=expµ−Z t0λj s ds¶,t∈[0,T∗].(22) For secondaryfirms,we assume that their default intensities have the following form:λj t=a j0,t+S1X k=1a j k,t1{t≥τk},S1+1≤j≤I.(23)We assume thatfirm j holds only the assets of primaryfirms,and that a jk,tis adapted to F X t forall k.Depending upon the sign of a jk,t ,the default offirm k increases(a jk,t>0)the probabilitythatfirm j defaults or decreases(a jk,t<0)it.10This is not the most general form of secondary firm default intensity.In particular,it can be made more general by including interactions among the indicator functions.Its linear form could also be generalized.Under the above assumption,the joint distribution of primary default times conditional on the history of the state variables,which is required in order to calculate secondary bond prices,simplybecomes the product of the conditional distribution of the individual primary default times.This is a result of the definition of a primaryfirm.Without the primary-secondary structure,the point processes governing default are defined recursively(through their intensities)and there is no simple procedure for either their construction or the derivation of the joint distribution of thefirst jump times.III.Bond Pricing When Default Is Independent of the Default-Free Term StructureIn this and the next section,we use the primary-secondary framework developed in Section II to study examples of bond pricing in which explicit pricing formulas can be derived.The examples, although simple,capture the qualitative impact of counterparty risk on default and the pricing of bonds.In this section,we assume that the point processes governing default are independent of the risk-free spot interest rate.We also assume that the risk-free spot rate is the only state variable,and as such,default is not influenced by any state variables.These simplifying assumptions allow the effects of counterparty risk to be studied separately from those of interest rate risk,and therefore provide a good starting point for the analysis.A.Single CounterpartyThe simplest and perhaps most relevant case in which counterparty risk occurs is where one firm’s position in anotherfirm constitutes a significant fraction of its total assets.Considerfirms A and B.Assume that the spot interest rate process r t is the result of an arbitrage-free default-free term structure model.Letfirm A represent the primaryfirm and B the secondaryfirm.Let the recovery rates beδA andδB,respectively.Since no state variable influences default,let A’s intensity of default beλA t=a>0.Assume that B’s intensity of default depends on whether A has defaulted in the past,perhaps because B holds a significant amount of A’s liabilities in its portfolio.Specifically,letλB t=b1+1{t≥τA}b2,(24) where b1>0and b2could be any value that preserves the positiveness of the intensity.11There are zero-coupon bonds issued by A and B.The time-t prices of zero-coupon bonds maturing at T≤T∗are given by the following proposition.Proposition2:The time-t prices of zero-coupon bonds issued by A and B with maturity T arev A(t,T)p(t,T)=δA+¡1−δA¢1{τA>t}e−a(T−t)(25) andv B(t,T) p(t,T)=(δB+¡1−δB¢1{τB>t}b2e−(a+b1)(T−t)−ae−(b1+b2)(T−t)b2−a if b2=aδB+¡1−δB¢1{τB>t}(a(T−t)+1)e−(a+b1)(T−t)if b2=a(26)iffirm A has not defaulted by time t,andv B(t,T)=δB+¡1−δB¢1{τB>t}e−(b1+b2)(T−t)(27) iffirm A has defaulted by time t.Proof:See Appendix B.To see the effect of counterparty risk onfirm B’s bond prices,we focus on the yield spread as a function of maturity.In a continuous-time context,the yield spread between defaultable bond v and default-free bond p is defined asy(t,T)=−1lnv(t,T).(28)To further simplify the matter,we assume that the recovery rate is zero.Viewed in this light, the yield spread onfirm B’s bond is simply B’s martingale default probability averaged over the time interval T−t.12In the absence of counterparty risk,b2is equal to0,and the yield spread is a constant b1that does not depend on maturity.When b2>0,firm B’s default is“accelerated”by firm A’s default,and its yield spread exhibits an increasing pattern.The opposite,a“deceleration,”holds when b2<0,so that the yield spread on B-bond is a decreasing function of maturity.For a set of reasonable parameters,these effects are illustrated in Figure1.It is interesting to note that,although completely different by source,these effects are graphically analogous to the credit spread curves in Jarrow,Lando,and Turnbull(1997,Figure2)when there is the possibility of credit downgrade or upgrade.[Figure1should be about here]B.Multiple CounterpartiesThe monotonic relation between yield spread and maturity exhibited in Figure1suggests that perhaps more interesting shapes can be attained when counterparty risk is not limited to a single party.An example with two counterparties is given below.Considerfirms A,B,and C.As in the last section,we assume that the spot interest rate is given by the process r t,recovery rates are constants,δA,δB,δC,respectively,and furthermore, that no state variables influence default.Let A and B be primaryfirms and C be a secondaryfirm.The default intensities of A and B areλA t=a andλB t=b,respectively.The default intensity of C isλC t=c0+1{t≥τA}c1+1{t≥τB}c2+1{t≥τA,t≥τB}c3,(29) where c0>0,c1>0and c2<0.The interpretation of equation(29)is thatfirm C holds a portfolio that contains a significant amount of long positions of A-bonds and short positions of B-bonds. Thus C’s default probability increases in the event A defaults and decreases in the event B defaults. Here we allow an interaction term,so that equation(29)is a generalization of the formulation in equation(23).The pricing of the primary A-and B-bonds is given by(25)in Section III-A.To price C-bonds, we assume that N A and N B are conditionally independent.This assumption says that each primary firm’s default is systematically influenced only by economy-wide state variables,that is,the residual default risk is idiosyncratic once the systematic part of default has been removed.It is consistent with the primary-secondary construction in Section II-B.Since the intensities are constants,this is equivalent to assuming unconditional independence between N A and N B.If it is assumed that neitherfirm A norfirm B has defaulted before time t,the price of a C-bond is given byv C(t,T)=δC+¡1−δC¢1{τC>t}E t expµ−Z T tλC s ds¶,(30)。