Intro-Maths-Fin-1
Financial Derivatives (A Brief Introduction )
Background This chapter deals with the two basic building blocks of financial derivatives:
1. Options
2. Forwards and futures.
We briefly introduce the third class of derivative: swap. We see how a complex swap can be decomposed into a number of forwards and options.
Definitions Derivatives securities are financial contracts that ‘derive’ their value from cash market instruments such as stocks, bonds, currencies and commodities.
At the time of the maturity of the derivative contract, denoted by T , the price F(T) of the derivative asset is completely determined by the market price of the underlying asset (S T ).
For instance, the value at maturity (T ) of a long position in a call option of strike (K) written on an asset (S T ) is:
Max [S T ?K ;0]
Also, the value of time T of a long position in a forward contract of forward price (F) written on an underlying asset worth (S(T) at time T is given by:
S (T )?F
Types of derivatives We group derivatives into three general headings:
1. Futures, Forwards, Repos, Reverse Repos and Flexible Repos (Basic building blocks )
2. Options and
3. Swaps
Many of these instruments will be discussed in other parts of the syllabus for the QF Exam.
The underlying asset
: We let (S t ) represent the price of the relevant cash instrument, which we call the underlying asset . The five main groups of underlying asset : We list five main groups of underlying assets:
1.Stocks (These are claims on “real” returns)
2.Currencies
3.Interest rates: Interest rate in not an asset, so we are referring to the direction of interest rates. The assets are Treasuries, bonds.
4.Indexes (S&P 500) and
https://www.doczj.com/doc/1910141960.html,modities: they are not financial assets either, they are goods in kind. There is another method for classifying the underlying asset:
1.The cash and carry markets and
2.The price discovery markets
Let us discuss these two markets
This new classification is important to us.
In the cash and carry market, one can borrow at risk-free rates, buy and store the product,
and insure it until the expiration date of any derivative contract.
Pure cash and carry market have one property: Information about demand and supplies
of the underlying instrument should not influence the spread between cash and
futures (forward) prices.
In the Pure cash and carry market, any relevant information concerning future supplies and
demands of the underlying instrument is expected to make the cash price and the future price change by the same amount (This is not so, in the price discovery market).
In the price discovery market, it is physically impossible to buy the underlying instrument
for cash and store it until some future expiration date. That strategy (of borrowing, buying and storing) is no longer applicable.
In the price discovery market, any information about the future supply and demand of the
underlying commodity cannot influence the corresponding cash price.
Expiration Date
At the expiration of the forward/futures contract, we expect:
At expiration,t?e Futures price=F(T)=T?e spot price of t?e underlying asset=S T But, during the life of the futures contract (t Forward1 and Futures Forwards and Futures are linear instruments (while options are nonlinear instruments). “Options are non-linear instruments because the derivative of the payoff function changes sign around the strike price. In fact, the payoff of an option is a convex function of the underlying asset” Definition of a forward contract A long forward contract is an obligation to buy an underlying asset at a specified forward price (or the strike price F) on a known date (the maturity T). The contract requires no initial premium (it costs nothing to enter into the contract). At expiration, the holder of the forward contract (the long position) purchases the asset at the forward price (agreed upon at contract inception)2. The long position in a forward contract makes money when the price at expiration of the underlying asset exceeds the agreed-upon forward price. Thus: Payoff of long forward position=S(T)?F Where: S(T)=T?e spot price of t?e underlying asset at t?e expiration of t?e contract(T) F=T?e forward price (agreed upon at contract inception) The short position profits only when prices fall, and thus: Payoff of s?ort forward position=F?S(T)=?Payoff of long position Graphically: 1 In Chapter 5 of Fixed Income Securities (FIS-5), we discuss forward contracts as they apply to fixed income instruments: The underlying asset will be (i) a ZCB and then (ii) a coupon-paying bond. 2From a risk management perspective, the long position (buyer of the forward contract) is The short position in the forward contract is graphically represented below3: Note the following points: Though the initial value of the forward contract is zero, the contract surely has value during its life. At any time (t) less than maturity (T), the contract is worth (S t?PV t(F)), where (PV t(F)) is the present value of the forward price calculated at time (t) and (S t) is the underlying asset spot price as of time t.4 If at expiration (T), the spot price of the underlying asset matches the agreed upon future price (F), then there is no profit to be made under the forward contract. The forward contract is a zero-sum game in a sense that the gain to one party is the loss to the other party. The short position in the forward contract is the party who wrote the contract and sold to the long position. The short position has an obligation/liability at maturity towards 3 The payoff clearly exhibits an unlimited loss when the underlying asset price (S T) exceeds the forward price (F). the long position only if (S(T)>F). However, if (S(T) diagram, the short position in the forward contract will benefit from the contract. The slope of the line is 1, and the forward contract is referred to as a ‘linear contract’. Futures and forwards are similar instruments. The major differences between them can be stated briefly as follows: 1.Futures are traded in organized exchanges and forwards are custom-made and traded over the counter. 2.Futures exchanges are cleared through exchanges clearing houses and there is a mechanism designed to reduce default risk. Forwards are not cleared and there is default risk. 3.Futures contracts are market to market. Every day, the contract is settled and a new contract is entered. 4.The security underlying the futures contract is standardized (the type of security is clearly specified and the timing and method of delivery as well). Forward contracts can be customized. 5.Because of the mark-to-market system in the futures contracts, they have less credit risk than forward contracts (same point as point 2). Repos, Reverse Repos, and Flexible Repos5 In a Repo (Repurchase agreement), one party sells securities to another party in return for cash, with an agreement to repurchase the securities (or equivalent) at a pre-agreed price (the repurchase price) and pre-agreed time (the maturity date). The long position in a repo (the buyer) acts as a lender of cash, and the short position (the seller) as a borrower. For the party selling the security and agreeing to repurchase it in the future, the transaction is a repo. For the party on the other end, the transaction is a reverse repo. The securities are used as collateral in this transaction. Profit from a repo Assume that a trader is entering into a repo transaction with a Repo Dealer as follows: P t=T?e price of t?e collateral asset at time t 5 At time t, the trader exchanges this underlying asset in return for cash received from the Repo Dealer. The Repo Dealer pays (P t )6 Amount borrowed from t?e Repo Dealer =P t . At maturity of the repo (time T ), the trader must repurchase the underlying asset from the Repo Dealer. This underlying asset worth is now worth (P T ). But under the repo transaction, both parties would have agreed upon a repurchase price (reflecting the interest earned on the repo transaction). Let: X T =T?e agreed upon repurc?ase price of t?e collateral We have: X T =P t ×[1+Repo rate ] At time T, the trader repurchases the security at price (X T ) and sells it back in the market for (P T ). Uses of repos Repos are used to raise short term capital and are classified as money market instruments as a consequence. Categories of repos There are three broad categories of repos: 1) Overnight repos: A one day maturity repo transaction. 2) Term repos: This is a repo with a specified maturity. 3) Open repo: This repo has no end date. A flexible repo is a repo with a flexible withdrawal schedule. Therefore, the party holding the collateral can sell it in parts before or at the maturity of the repo. There are two types of flexible repos: 1) Secured : The municipality/customer receives collateral in the form of Treasury bonds, GNMA bonds, agency MBS/CMO. 2) Unsecured : The customer does not receive collateral. The deal commands a higher spread. Differences between flexible repos and traditional repos : They are four major differences with a traditional repo: 1) Convexity due to cash withdrawals, 2) Formal written auction like trade, 3) Enhanced documentation, 4) Counterparties are usually municipal bond issuers. Options 6 Forwards and futures obligate the holder to deliver or accept the delivery of the underlying instrument at expiration. Options, on the other hand give the owner the right (not the obligation) to purchase or sell an asset. Call option Consider an investor who purchases a call option written on an underlying asset 7As such, the payoff of the long call option (the call option buyer) is: . The initial spot price of the asset is (S 0). The investor pays a premium (c ) to be able to take advantage of the flexibility offered in the option contract. The option matures at time (T ), when the underlying asset has a spot price of (S T ). The future spot price is unknown to all market participants when entering into the option initially (t=0). The option gives the investor the right (but not the obligation) to purchase the asset at time T , for a pre-agreed price of K (or X, or Strike), called the strike price. Long call option maturity payoff =?S T ?K if S T >K 0 if S T ≤K To put words into the mathematics, we say this: If at maturity of the option (T ), the underlying asset ( S T ) is worth less than the strike (K ), the option buyer will not exercise his/her option. The instrument ends worthless. If at maturity of the option (T ), the underlying asset (S T ) is worth more Long call option maturity payoff =Max (S T ?K ;0) than the strike (K ), the option buyer will exercise his/her option, and the payoff is the excess of the asset’s value over the strike (S T ?K ). Thus, we also write: The payoff of the short position (the call option writer) is the opposite of the long position as follows: Short call option maturity payoff =? ?(S T ?K ) if S T >K 0 if S T ≤K The premium (c)8 Profit for t?e long position =(Maturity Payoff of t?e long position )?FV (Premium ) must be adjusted from the payoff in order to get the net profit for each position: And Profit for t?e s?ort position =(Maturity Payoff of t?e short position )+FV (Premium ) Or: Profit for t?e s?ort position =FV (Premium )?(Maturity Payoff of t?e long position ) 7 We assume that the underlying asset pays no dividends during the life of the option. 8 This premium represents the compensation the seller accepts for the right granted to the buyer. option . Graphically: Put option Consider an investor who purchases a put option written on an underlying asset. The initial spot price of the asset is (S 0) at contract inception. The investor pays a premium (p) for the put option. The option matures at time (T ), when the underlying asset has a spot price (S T ). The future spot price (S T ) is unknown to both parties at the inception of the put contract. At maturity of the contract, the long position will decide on whether to exercise his/her option to sell the asset for the strike price (K ): If at maturity of the option (T ), the underlying asset (S T ) is worth less than the strike (K ), the put option buyer (the long position in the put option) has the ability to sell at price (K ), an asset that is worth less than (K ). He/she will exercise his/her option. The payoff from exercising this option is clearly equaled to (K ?S T ). If at maturity of the option (T ), the underlying asset (S T ) is worth more than the strike (K ), the put option buyer (the long position in the put option) has the ability to sell at price (K ), an asset that is worth more Long put option maturity payoff =? K ?S T if S T than (K ). He/she will not exercise his/her option. Thus, the instrument ends worthless. Thus, the maturity payoff of the long put option is: Or also: Max (K ?S T ;0) The payoff of the short position (the option writer) is the mirror image as follows: Short put option maturity payoff =? ?(K ?S T ) if S T Note : From the perspective of the buyer, it is interesting to buy the put option when you think that the underlying asset ‘might’ decrease below the strike price. You can also purchase the put option if option + asset) is comparable to owning an insurance contract9 on an asset (subject to damage in value). Graphically the payoff/profit of a call option (long/short) are plotted below: Also, the payoff/profit of a put option (long/short) are plotted below: Let us consider other reasons why would a trader may consider buying options: Reasons why traders may want to calculate the arbitrage-free price of a call option 1.New contract: before the option is first issued, a trader may want to know the price that the option will trade at. 2.Mispricing: A trader may want to calculate the arbitrage free value of an option to determine if the option is mispriced in the market. 9 In fact, in the financial economics literature, the portfolio containing the stock and the put option written on the stock is called a protective put. Likewise, the writer (seller) of the call might want to protect himself from a huge increase in the stock index, as such, he/she would buy the underlying 7.1). The profit at maturity (T ) of the derivative to the long Profit (Long position )=Payoff of the Long Position (T )?FV (Premium ) position is calculated as: Where FV (Premium )=T?e Future Value of t?e Premium paid at inception by t?e long position Also, the profit at maturity (T ) of the derivative to the short Profit (Short position )=FV (Premium )?Liability of the Short Position (T ) position is calculated as: Where Liability of t?e S?ort Position (T )=Payoff of t?e Long Position (T ) We build the cash flows table as follows: As already explained: The long position in a stock is purchasing the stock price today (a negative cash flow) to receive the proceeds from the sale of the stock at maturity (a positive cash flow). The short position in a stock receives money from selling the stock today (a positive cash flow) and has to redeem the stock at maturity (negative cash flow). The long stock and the short stock are in a zero-sum game. The long position in a ZCB of redemption value K has to pay for the ZCB today. The price of which is the PV of the redemption amount. Because this is a purchase, it is a negative cash flow. At maturity though, the long position receives the redemption value of the bond K, a positive cash flow. The long position in any derivative has to pay a premium for entering into the derivative transaction at time t=0 (negative cash flow). At maturity, this long position is entitled to a payoff. The short position in any derivative receives the premium from the long position (positive cash flow) and at maturity; the short position is responsible for paying off the payoff arising to the long position. Because this payoff is a liability, it is a negative cash flow. 10 Though not directly discussed in Neftci-1, the concept here is discussed in FIS-6 and frankly the A swap is an agreement between two counterparties for selling and purchasing cash flows involving various currencies, interest rates and a number of other financial assets. The counterparties borrow in sectors where they have an advantage and then exchange the interest payments. In a simple IRS, at the end, both counterparties secure a lower rates and the swap dealer will earn a fee. The simple IRS example This contract allows parties to exchange payments between two differently indexed legs, starting from a future time instant (Tα). At every time (T i), the fixed leg pays out the amount: Notional×τi×K Where: τi=T?e year fraction between T i?1and T i K=T?e fixed rate of interest for t?e fixed payments of t?e IRS swap Notional=T?e notional amount of t?e swap Whereas the floating leg pays out the amount: Notional×τi×L(T i?1,T i) Where: L(T i?1,T i) =T?e floating rate t?at resets at t?e previous time (T i?1) and is used t?e payment at time (T i) Graphically, we have: A counter-party in this plan vanilla swap may be able to close out the transaction by paying the net present value (NPV) of future swap payments. Pricing swaps11 One method for pricing swaps and swaptions is to decompose them into forwards and options. The forwards can then be priced separately, and the corresponding value of the swap can be determined from these numbers. Two examples of swaps 1)The simple IRS (Interest Rate Swap): Each counter-party borrows in the market (fixed rate and floating rate market) where it has an advantage and they both exchange the payments. 2)The Cancelable Swaps: In this swap, each party has the option to cancel the transaction before maturity and extinguish the obligation to pay the PV of future payments. They come in two flavors: Callable swaps and Puttable swaps. Some properties of Cancelable swaps Popular among institutions with an obligation in which they are to repay principal before maturity. The embedded option on the swap can be exercised to honor such liabilities. They can be used as hedge instruments. They allow institutions to mitigate maturity mismatch between assets and liabilities due to prepayments options or early surrenders. Past exams SOA Spring 2015 QFIC Q11 on Repo (Must Read) SOA Spring 2013 APM Q3 (Must Read) PAK Practice questions Question 1 a)List the differences between forwards and futures: Question 2 Assume that the S&P 500 index is at 100. For a single premium of $100, a life insurance company had sold the following type of products: Contract 1: promising to pay 100 at maturity of the contract in 5 years plus any excess of the S&P 500 over its initial value of 100. Contract 2: The Company promises to pay the excess of two quantities: 90% of the initial premium accumulated at 2% per annum and The proceeds from the investment of the initial premium into a fund that performs exactly For each contract, determine the following quantities: 1.The maturity of the contract 2.The type of derivative embedded in the liability and the underlying asset. 3.Identify the payoff of the liability, and the strike amount Question 3 a)Describe the bull call spread option Question 4 a)Show the payoff of a cap portfolio (short stock + long call): In mathematical terms and the plot. b)What is the net profit of the cap portfolio? c)Show that the ca portfolio can be viewed as a long put position. Solution Question 1: Differences between futures and forward contracts There are important differences between these two contracts: Forward contracts are settled at expiration while futures contracts are settled daily. At the end of each trading day, the clearinghouse adjusts the margin accounts to reflect the daily gain/loss to each counterparty of the transaction. This is called mark-to-market. Forward contracts are settled at the agreed-upon forward price while futures contracts are settled at the settlement price determined on the last trading date. In a forward contract, there are no cash flows until expiration whereas for a futures contract, there are daily cash flows to reflect the gain and loss to each counterparty. Futures contracts are more liquid than forward contracts. Futures contracts can be offset any day by entering into an opposite transaction. Because of the daily mark-to-market accounting, futures contracts have lower (if any) credit risk than forward contracts. There are typically daily price limits in future markets. Such limits are market moves that trigger a temporary halt in trading. Question 2: Life insurance index contract 1. Contract 1 has a maturity of 5 years and contract 2 has a maturity of 10 years. 2 and 3. Embedded derivative in Contract 1: A call option on the S&P 500 of maturity 5 and strike 100. Embedded derivative in contract 2: Payoff is: Max (0.9×100×(1.02)10;F 10) Where: F 10=t?e terminal value of t?e fund t?at mimics t?e S &P 500 The payoff is equal to: Max (109.7;F 10)=F 10+Max (0;109.7?F 10)=F 10+Payoff of a put option Thus, the embedded derivative is a put option on the underlying fund of strike 109.7 and maturity 10 years . Question 3: The Bull spread 12 Bull Call Spread Option (Neftci practice problem 6 on page 11) A bull spread call is a strategy that involves purchasing call options at a specific strike price while also selling the same number of calls of the same asset and expiration date but at a higher strike. A bull call spread is used when a moderate rise in the price of the underlying asset is expected. The maximum profit in this strategy is the difference between the strike prices of the long and short options, less the net cost of options. Question 4: The cap portfolio The combination (short asset and long call option on the asset) is called a cap 13 . Let us now look at the mathematics of the cap (c-S ). The payoff table is captured below: Note the following about the payoff of the cap position: Max (0; S (T )?K )?S (T )=? If S (T ) 12 More of this type of strategies in QFIQ-120-19 section 4. 13 The insight here is that without the call option, the short position in the asset has an obligation/liability of amount (S(T)) at maturity time T . However, with the long call option added to exceed that strike level . Note: That is why in the table, the final payoff for the position is simply (Max(?S(T);?K)). It is also very important to realize that the expression (Max(?S(T);?K)) is not the same as (?Max(S(T);K))14. Graphically, the maturity payoff of (the sum of the short stock + the long call option) yields a liability (opposite payoff) that cannot exceed a certain cap (the opposite of the strike level) as can be depicted below: Where we clearly see that when (S(T) The net profit of the cap As explained earlier on also, the profit at maturity (T) of the derivative to the short position is always calculated as: Profit(Short position)=FV(Premium)+Liability of the Short Position(T) Where Liability of t?e S?ort Position(T)=?Payoff of t?e Long Position(T) Thus, the net profit from the cap is calculated as: Max??K;?S(T)?+FV[S(0)?c] Thus: 14For instance, (Max(?3;?10)=?3) while (?Max(3;10)=?10). These are two different Profit from the cap portfolio=Max??K;?S(T)?+[S(0)?c]×(1+r)T The cap can be viewed as a long put We are claiming that the net profit of the cap is equal to the net profit of a long put. How so? Once again, we make use of the put call parity identity: c?S(0)=p?K×(1+r)?T Multiplying this line by the accumulation factor (?(1+r)T), we get: [S(0)?c]×(1+r)T=?p×(1+r)T+K By substitution of the FV of the premium ([S(0)?c](1+r)T) into the net profit for the cap, we get: Profit from the cap portfolio=Max??K,?S(T)??p×(1+r)T+K By allowing K to enter into the Max-term, we get: Profit from the cap portfolio=Max?K?K;K?S(T)??p×(1+r)T Thus: Profit from the cap portfolio=Max?0;K?S(T)??p×(1+r)T =Profit for a long put option 中国精算师资格考试体系简介 中国精算师资格考试体系简介中国精算师资格考试体系简介建立中国保险精算制度的基本思路是在其保险精算监管系统中实行首席精算师签字的精算报告制度，制度本身包括两个方面的内容：中国精算师认可制度和保险公司的精算报告制度。 1、中国精算师认可制度 认可制度中国保险业的精算师认可制度是实行考试认可制度。考生通过保险监管部门要求的全部课程考试，可取得中国精算师考试合格证书。 纵观世界各国，大体有两种精算师认可制度。一是考试认可制度，即设定一系列考试课，无论什么教育背景，只要通过全部考试，即可获得精算师资格。这以北美精算师协会和英国精算师协会的考试最为典型，属于这种类型的国家有英、美、加、澳、日本等国家。二是学历认可制度，通常在大学设立精算专业，类似于准精算师和精算师水平，分本科和研究生两个阶段，精算专业研究生毕业，即可获得精算师资格。属于这种类型的有德、法、意、瑞士、西班牙、荷兰、巴西、墨西哥等国家。这两种制度也有其共同点，一是对保险公司的指定精算师或首席精算师，除要求精算师资格外，还要求最低的精算专业从业年限，强调精算工作业绩。 中国精算教育始于1988年南开大学招收第一届中美联合培养 的精算研究生，至今，国内已有近20所院校招收精算专业本科生、研究生，精算教育目前还有迅速发展的趋向。但这些院校师资力量、教学水平差别很大，又没有统一的课程设置标准，如采用学历认可制度，很难控制精算师的质量。有鉴于此，借鉴英、美等国经验，建立中国精算师资格考试制度是符合中国现状的。 中国精算师的职业制度基本思路在考试认可制度下，取得精算师考试合格证书仅是精算师职业制度的开端：①取得中国精算师资格证书者，若以精算师名义在商业保险机构执业，还需向中国保监会申请注册，在取得精算师执业证书后，方可执业：②执业的精算师应加入精算师的专业团体中国精算师协会，每年需参加中国精算师协会规定的职业培训，接受其监督管理；③保险公司聘请一名执业精算师作为公司的首席精算师，并报中国保监会备案(首席精算师需经中国保监会的资格审查认可)；④首席精算师离职应当报中国保险监督管理委员会备案。保险公司解除其首席精算师的职务，应当向中国保险监督管理委员会陈述理由，并报中国保险监督管理委员会备案。 2、保险公司精算报告制度 配合中国保险业精算监管系统的建立和完善，中国保监会将逐步建立保险公司的精算报告制度。在每一经营年度完了，保险公司除应向保险监管部门提交精算财务报告外，还必须提供由公司首席精算师签署的有关精算报告，其基本内容是(1)提供各项准备金评估时所采用的精算假设、计算方法、并列明各项准备金结果等；(2)公司偿付能力、财务稳定性分析：(3)模拟、测算不同运营环境下，公司现金 Intro-Maths-Fin-1 Financial Derivatives (A Brief Introduction ) Background This chapter deals with the two basic building blocks of financial derivatives: 1. Options 2. Forwards and futures. We briefly introduce the third class of derivative: swap. We see how a complex swap can be decomposed into a number of forwards and options. Definitions Derivatives securities are financial contracts that ‘derive’ their value from cash market instruments such as stocks, bonds, currencies and commodities. At the time of the maturity of the derivative contract, denoted by T , the price F(T) of the derivative asset is completely determined by the market price of the underlying asset (S T ). For instance, the value at maturity (T ) of a long position in a call option of strike (K) written on an asset (S T ) is: Max [S T ?K ;0] Also, the value of time T of a long position in a forward contract of forward price (F) written on an underlying asset worth (S(T) at time T is given by: S (T )?F Types of derivatives We group derivatives into three general headings: 1. Futures, Forwards, Repos, Reverse Repos and Flexible Repos (Basic building blocks ) 2. Options and 3. Swaps Many of these instruments will be discussed in other parts of the syllabus for the QF Exam. The underlying asset : We let (S t ) represent the price of the relevant cash instrument, which we call the underlying asset . The five main groups of underlying asset : We list five main groups of underlying assets: 我用这个秘诀，快速搞定北美精算师考试FM 科目…… 宏景4月传捷报， 北美精算师考试看宏景。 宏景国际教育在北美精算师SOA考试 2018年3月期的Exam FM通过率再创辉煌！ 近日，2018年3月的北美精算师考试Exam FM科目考试成绩公布，宏景学员ZHUOFU LI、XIAOFENG YAN、YIDAN CAO、CHONGPU LIU、LAN LIU、JINPENG GAO、JING LIANG等又一批学员在准精算师ASA阶段考试中，Exam FM 考试内容合格。 接下来，让我们来一睹学员Exam FM 考试合格成绩截图（因涉及信息保护，只展示部分学员成绩截图）★ 有点小激动，这是有史以来第一次，我们SOA学员Exam FM考试通过人数最多的一次；这是有史以来我们学员Exam FM科目通过率最高的一次……对，你没有看错！！ 这些喜人成绩的取得与宏景国际教育有口碑的SOA教学质量是分不开的。宏景国际教育北美精算师特训营，提供从考试申请、考位预定、课程培训，到牌照申请等一站式服务，让你有更多的时间和精力去准备考试。全职海归组成的教师团队采用单对单教学模式传授SOA考试金牌秘籍；全球最权威、最经典SOA ASM教 材让你的学习事半功倍……在课堂教学和报考服务、工作推荐等工作上形成一套特色体系，使人才培养质量达到更高的水平。 在此，我们对在此次考试中取得优异成绩的学员表示祝贺。同时，希望他们再接再厉，在新的起点上，奋发图强，坚持不懈，争取更大的辉煌。也希望其他学员能够学习总结师兄师姐成功经验、锲而不舍，在自己的SOA考试中取得优秀的成绩。 来源：宏景AICPA 原创分享，转载请联系授权，未经授权禁止转载。文中图片部分来自于网络，版权归原作所有，如有侵权行为请联系删除。 中国精算师资格考试体系简介 建立中国保险精算制度的基本思路是在其保险精算监管系统中实行首席精算师签字的精算报告制度，制度本身包括两个方面的内容：中国精算师认可制度和保险公司的精算报告制度。 1、中国精算师认可制度 认可制度中国保险业的精算师认可制度是实行考试认可制度。考生通过保险监管部门要求的全部课程考试，可取得中国精算师考试合格证书。 纵观世界各国，大体有两种精算师认可制度。一是考试认可制度，即设定一系列考试课，无论什么教育背景，只要通过全部考试，即可获得精算师资格。这以北美精算师协会和英国精算师协会的考试最为典型，属于这种类型的国家有英、美、加、澳、日本等国家。二是学历认可制度，通常在大学设立精算专业，类似于准精算师和精算师水平，分本科和研究生两个阶段，精算专业研究生毕业，即可获得精算师资格。属于这种类型的有德、法、意、瑞士、西班牙、荷兰、巴西、墨西哥等国家。这两种制度也有其共同点，一是对保险公司的指定精算师或首席精算师，除要求精算师资格外，还要求最低的精算专业从业年限，强调精算工作业绩。 中国精算教育始于1988年南开大学招收第一届中美联合培养的精算研究生，至今，国内已有近20所院校招收精算专业本科生、研究生，精算教育目前还有迅速发展的趋向。但这些院校师资力量、教学水平差别很大，又没有统一的课程设置标准，如采用学历认可制度，很难控制精算师的质量。有鉴于此，借鉴英、美等国经验，建立中国精算师资格考试制度是符合中国现状的。 中国精算师的职业制度基本思路在考试认可制度下，取得精算师考试合格证书仅是精算师职业制度的开端：①取得中国精算师资格证书者，若以精算师名义在商业保险机构执业，还需向中国保监会申请注册，在取得精算师执业证书后，方可执业：②执业的精算师应加入精算师的专业团体中国精算师协会，每年需参加中国精算师协会规定的职业培训，接受其监督管理；③保险公司聘请一名执业精算师作为公司的首席精算师，并报中国保监会备案 (首席精算师需经中国保监会的资格审查认可)；④首席精算师离职应当报中国保险监督管理委员 北美精算师ASA如何申请 1.哪些人适合申请精算？ 这里所说的适合包含两层含义，一层是自己觉得适合，另一层是自己具备一定条件有把握收到ADMISSION或OFFER. 先说第一层，何为自己觉得适合？这里需要考虑几个问题。第一个问题是你选择专业的指导思想是什么？兴趣，热门，高薪……? 如果你选的是第一个答案那你继续往下看。第二个问题是你是否对数学感兴趣，你是否有很强的分析能力和business sense, 你是否愿意一辈子和模型打交道？这个问题的思考不仅有助于你的PS写作,而且对你今后的CAREER有指导意义，因为有些人选了精算专业，工作后才发现虽然年薪很高，可是自己事业上却有点力不从心。 第二层，你申请的胜算有多少？ 首先，我们把申请人群作个区分。申请人大致可分为在中国的和在美国的。这个区分相当重要，因为他们的录取机会相差很大。明确了自己属于哪个申请群，你就知道自己的竞争对手和应该怎样使你的申请材料超越对手。 如果你在美国，那恭喜你。只要你有足够的MONEY，录取不是件很难的事。不管你以前是学什么专业的，你都有机会被录取。 计算机，机械，环境，英语，文学，教育……NO PROBLEM! 美国的高等教育很普及，大学只要你有钱都能上。有些人可能想不通，为 什么念英语的也能念精算？但是，这就是事实。在这念精算的中国人很多，背景五花八门，不过大家都念得很好。 如果你在中国，那也恭喜你，因为你受到了挑战。人生有什么比受到挑战更快乐的了？它使你超越别人和自我。拿破仑说过：我感谢困难，因为它像篱笆，把不如我的都挡在了后面。 挑战之一来自你的专业，因为你属于这个申请群，所以你的专业必须和精算有联系。这包括数学，统计，金融（保险，投资，银行），会计等等。 挑战之二来自你的背景。因为国内的申请人数庞大，所以你必须脱颖而出。你的竞争对手很强，你必须比他们更强。 挑战之三来自你的签证。美国签证很难，精算签证尤胜。 看到这有些人垂头丧气，有些人手舞足蹈。前者对生活抱悲观态度，后者则用乐观向上的精神指引人生。你属于哪种？你希望自己是哪种？要不要改变？申请的过程是痛苦的，每个人都会有软弱的时候，你必须有一个强大的精神支柱！ 2、材料的准备 所有申请材料中两样东西最重要，成绩单和PS。成绩单是死的，PS是活的。 如果你是大一大二或者大三，那你的成绩单也是活的，趁着在校多修修很精算有关的课程。 以下着重阐述PS写作。 北美精算师考试制度分为二个阶段：第一阶段是准精算师（ＡＳＡ）。目前对准精算师的考试要求为300学分。除了100系列的11门课程（复利数学、精算数学等）外，还须通过200系列的4门课程（经济保障计划、精算实务等）。每门课在10至30学分不等。 学员在获得300学分后即成为ASA，之后可继续考FSA课程。ASAl00系列的11门课程的考试均采用英文试卷，选择题形式，考试时间分别为1个半小时至4个小时不等；200系列采用英语书写答题形式。考生是否通过某一门课程考试以及所获得的分数，是到该课程全部试卷批完后，按成绩顺序排列后确定的。 第二阶段是精算师（ＦＳＡ）。考生在取得准精算师资格证书后方可参加ＦＳＡ课程考试。目前把精算师的考试课程分为财务、团体与健康保险、个人人寿与健康保险、养老金、投资五个方向，每个方向又分若干门课，每门课学分在10至30分不等。要取得ＦＳＡ资格必须通过以上一个方向的所有课程考试，以及再选择以上方向的其他课程，使学分达到150分，即学分总计要达到450分。当ＦＳＡ要素的课程考试全部通过后，考生还要参加最后一门课程：正式精算师认可课程（ＦＡＣ），其内容主要是职业道德和案例，时间为二天半，一般只要自始至终参加，在结束后的晚宴上会获得ＦＳＡ证书。 北美精算师协会的考点分布在全世界各个国家和地区，考试每年5月和11月举行两次，考试时间由北美精算师协会确定，世界各地统一，考卷由北美精算师协会提供。 报名及考试地点：南开大学、湖南财经学院、复旦大学、中国人民大学、中山大学、中国科技大学、陕西财经学院、平安总公司 北美精算学会考试课程 准精算师考试： 100系列课程：100微积分和线性代数、110概率论和数理统计、120应用统计、130运筹学、135数值分析、140复利数学、150精算数学、151风险理论、160生存模型和生命表编制、161人口数学、165匀修数学 200系列课程：200经济保障计划概论、210精算实务概论、220资产管理和公司财务概论、230资产和负债管理原理 正精算师的考试课程分为五个方向： 一财务 包括科目：财务管理、公司财务等 二团体和健康保险 包括科目：团体和个人健康保险的设计和销售等 三个人人寿和年金保险 包括科目：个人人寿和年金保险的精算实务调查、人寿保险法和税收等 四养老金 Financial Mathematics Exam—December 2015 The Financial Mathematics exam is three-hour exam that consists of 35 multiple-choice questions and is administered as a computer-based test. For additional details, please refer to Exam Rules The goal of the syllabus for this examination is to provide an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. The candidate will also be given an introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics. The Financial Mathematics Exam assumes a basic knowledge of calculus and an introductory knowledge of probability. The following learning objectives are presented with the understanding that candidates are allowed to use specified calculators on the exam. The education and examination of candidates reflects that fact. In particular, such calculators eliminate the need for candidates to learn and be examined on certain mathematical methods of approximation. Please check the Updates section on this exam's home page for any changes to the exam or syllabus. Each multiple-choice problem includes five answer choices identified by the letters A, B, C, D, and E, only one of which is correct. Candidates must indicate responses to each question on the computer. Candidates will be given three hours to complete the exam. As part of the computer-based testing process, a few pilot questions will be randomly placed in the exam (paper and pencil and computer-based forms). These pilot questions are included to judge their effectiveness for future exams, but they will NOT be used in the scoring of this exam. All other questions will be considered in the scoring. All unanswered questions are scored incorrect. Therefore, candidates should answer every question on the exam. There is no set requirement for the distribution of correct answers for the multiple-choice preliminary examinations. It is possible that a particular answer choice could appear many times on an examination or not at all. Candidates are advised to answer each question to the best of their ability, independently from how they have answered other questions on the examination. Since the CBT exam will be offered over a period of a few days, each candidate will receive a test form composed of questions selected from a pool of questions. Statistical scaling methods are used to ensure within reasonable and practical limits that, during the same testing period of a few days, all forms of the test are comparable in content and passing criteria. The methodology that has been adopted is used by many credentialing programs that give multiple forms of an exam. The ranges of weights shown in the Learning Objectives below are intended to apply to the large majority of exams administered. On occasion, the weights of topics on an individual exam may fall outside the published range. Candidates should also recognize that some questions may cover multiple learning objectives. 关于北美精算师，你必须知道的入门级知识——Exam P 成为一名北美准精算师（ASA）必须要经历五门SOA的准精算师考试，而其中最简单也是大部分人最先开始学习准备的就是Exam P，即probability。顾名思义，Exam P考察的就是最基本的数理统计与概率问题。下面我们就来了解一下Exam P的考试形式与内容。 考试目的 考生可以掌握用于定量评估风险的基本的概率方法，并着重于用这些方法应用解决精算学中遇到的问题。参加这门考试的考生应具有一定的微积分基础，并了解基本的概率、保险和风险管理的概念。 考试形式 Exam P采用机考的形式，总共30道单项选择题，考试时间为3个小时。每道选择题共有5个选项，其中只有一个正确选项。 与SAT考试不同的是，Exam P考试答错并不会额外扣分，也就是说考生一定不要空任何一道题。Exam P中会随机分布几道“pilot question”，这些题目是主办方用来分析从而改进将来的考试而出现的，它们的正确与否并不会影响到考生的实际分数。但是由于考生并无法分辨出这些题目，所以对每一道题目，考生都要同样认真地对待。 考试内容 概率（占总分10%－20%） 最基本的事件概率计算问题。包括集合方程与表示（sat functions）、互斥事件（mutually exclusive events）、事件独立性（independence of events）、组合概率（Combinatorial probability）、条件概率（Conditional probability）以及贝叶斯定理（Bayes theorem）等。 拥有单因素概率分布的随机变量（占总分35%－45%） 连续分布或离散分布的单因素随机变量的研究。包括PDF&CDF（Probability density functions and Cumulative distribution functions）、独立随机事件的和的分布、众数（Mode）、中位数（Median）、百分位数（Percentile）、动差（Moment）、方差（Variance）以及变形等问题。 拥有多因素概率分布的随机变量（占总分35%－45%） 包括联合PDF&CDF、中心极限定理（central limit theorem）、条件与边缘概率分布与动差（Conditional and marginal probability distributions and moments）、条件与边缘概率分布的方差、协方差与概率系数（Covariance and correlation coefficients）以及变换与顺序统计（Transformation and order statistics）等。 提醒：众所周知，2018年7月1日起，SOA新课程体系将正式生效，其中Exam P科目不变，考试大纲有变动，具体有那些变化？？？后台回复“Exam P”免费获取Exam P最新考试大纲。 考试时间 November 2001 Course 2 Interest Theory, Economics and Finance Society of Actuaries/Casualty Actuarial Society 1.Ernie makes deposits of 100 at time 0, and X at time 3 . The fund grows at a force of interest 2 100 t t δ=, t > 0 . The amount of interest earned from time 3 to time 6 is X. Calculate X. (A)385 (B)485 (C)585 (D)685 (E)785 2.The production of a good requires two inputs, labor and capital. At its current level of daily output, a competitive firm employs 100 machine hours of capital and 200 labor hours. The marginal product of machine hours is 10 units. The marginal product of labor hours is 5 units. The rental rate, or “price,” of capital is 20 per machine hour. If the firm minimizes its costs, what is the hourly wage rate? (A) 2.5 (B) 5.0 (C)10.0 (D)20.0 (E)40.0 精算学大学排名及专业介绍 一精算业 精算是依据经济学的基本原理，利用现代数学方法，对各种经济活动未来的财务风险进行分析、估价和管理的一门综合性的应用科学。精算方法和精算技术是现代保险、金融、投资科学管理的有效工具。其一直是被广泛应用于保险及其它金融行业、寿险业务、年金市场、财务运营、资金运作和预测未来等多个领域甚至退休保障等社会福利中。从社会保障标准的计算、财政收支计划的测算以及投资活动的分析，到人寿保险业中对于人生老病死等随机事件的把握，都离不开精算师周密、科学的分析和运算。 二精算师 精算师(Actuary，拉丁语意思"经营")是一种处理金融风险的商业性职业,是运用精算方法和技术解决经济问题的专业人士，是评估经济活动未来财务风险的专家。精算师更被国际社会形象地比喻为协调和平衡社会经济运作的"第一小提琴手"。 精算师采用数学、经济、财政和统计工具,在商业保险业,投资和经济预测领域从事产品开发、责任准备金核算、利源分析及动态偿付能力测试等重要工作，确保保险监管机关的监管决策、保险公司的经营决策建立在科学基础之上和为保险公司作风险评估及制定投资方针，并定期作出检讨及跟进。 精算师也会在咨询公司(主要的客户是规模较细的保险公司及银行)、养老金投资公司、医疗保险公司及投资公司工作。 三成为精算师的条件 要想成为精算师，首先必需掌握一些基础课程，如微积分、线性代数、概率论与数理统计、保险学和风险管理等。不仅如此，由于精算师所从事的是经济领域的职业，因而他们还必需有较高的经济学修养，掌握会计、金融、经济学和计算机等科学。这样，精算师才能对经济环境的变化有较强的反应能力。此外，精算师的职业还要求掌握语言表达、商业写作、哲学等科学知识取得精算师资格必需通过一些科目的严格考试，并获得精算组织的认可。例如，在美国和加拿大，作为一名合格的精算师，必需取得美国灾害保险精算学会 (Casuality Actuarial Society)或北美精算学会(Society of Actuaries) 的正式会员资格。北美精算学会是在人寿保险、健康保险和年金保险领域从事研究、考试和接受会员的国际组织，它负责从吸收非正式会员到正式会员的一系列考试。 四精算师的职业优势 1. 有较高的社会地位. 精算师是一份有着重要作用的职业,有时甚至是公司发展的关键所在.有着较高的社会地位.有人说,按英国标准来讲,中国只有两个精算师,而按美国精算师学会的名单,中国尚不存在一个合格的精算师。 2. 职业空缺 Probability Exam The Probability Exam is a three-hour multiple choice examination and is referred to as Exam P by the SOA and Exam 1 by the CAS. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA). The Probability Exam is administered as a computer-based test. For additional details, Please refer to “Computer-Based Testing Rules and Procedures”. The purpose of the syllabus for this examination is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed. A table of values for the normal distribution is available below for candidates to download and will be included with the examination. Since the table will be included with the examination, candidates will not be allowed to bring copies of the table into the examination room. Check the Updates section on this exam’s home page for any changes to the exam or syllabus. LEARNING OUTCOMES Candidates should be able to use and apply the following concepts in a risk management context: 1. General Probability ?Set functions including set notation and basic elements of probability ?Mutually exclusive events ?Addition and multiplication rules ?Independence of events ?Combinatori a l probability ?Conditional probability ?Bayes Theorem / Law of total probability 2. Univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, and normal) ?Probability functions and probability density functions ?Cumulative distribution functions ?Mode, median, percentiles, and moments ?Variance and measures of dispersion ?Moment generating functions ?Transformations 3. Multivariate probability distributions (including the bivariate normal) ?Joint probability functions and joint probability density functions ?Joint cumulative distribution functions ?Central Limit Theorem ?Conditional and marginal probability distributions ?Moments for joint, conditional, and marginal probability distributions 金融行业简介 一、行业简介 定义：简单来说，金融就是资金的融通。金融是货币流通和信用活动以及与之相联系的经济活动的总称，广义的金融泛指一切与信用货币的发行、保管、兑换、结算，融通有关的经济活动，甚至包括金银的买卖，狭义的金融专指信用货币的融通。 核心：金融的核心是跨时间、跨空间的价值交换，所有涉及到价值或者收入在不同时间、不同空间之间进行配置的交易都是金融交易，金融学就是研究跨时间、跨空间的价值交换为什么会出现、如何发生、怎样发展，等等。 金融在国民经济中具有举足轻重的地位和作用，是社会资金运动的中枢神经系统。现代市场经济条件下，以货币流通和社会信用总和为内容的金融在社会资金的筹措和分配中所占的比重越来越大。因此，金融作为一国社会资金流通系统的基本组成部分，对经济的增长和发展起着十分重要的调节控制作用。 金融的构成要素有5点： 1、金融对象：货币（资金）。由货币制度所规范的货币流通具有垫支性、周转性和增值性。 2、金融方式：以借贷为主的信用方式为代表。金融市场上交易的对象，一般是信用关系的书面证明、债权债务的契约文书等，包括直接融资：无中介机构介入；间接融资：通过中介结构的媒介作用来实现的金融 3、金融机构：通常区分为银行和非银行金融机构 4、金融场所：即金融市场，包括资本市场、货币市场、外汇市场，保险市场，衍生性金融工具市场，等等； 5、制度和调控机制：对金融活动进行监督和调控等。 各要素间关系：金融活动一般以信用工具为载体，并通过信用工具的交易，在金融市场中发挥作用来实现货币资金使用权的转移，金融制度和调控机制在其中发挥监督和调控作用。 二、金融机构 金融机构，是指专门从事货币信用活动的中介组织。我国的金融机构，按地位和功能可分为四大类： 第一类，中央银行，即中国人民银行。 第二类，银行。包括政策性银行、商业银行。 北美精算师考试内容及考试制度 北美精算师考试内容及考试制度北美精算师考试内容及考试制度 北美精算师考试制度分为二个阶段：第一阶段是准精算师（ａｓａ）。目前对准精算师的考试要求为300学分。除了100系列的11门课程（复利数学、精算数学等）外，还须通过200系列的4门课程（经济保障计划、精算实务等）。每门课在10至30学分不等。 学员在获得300学分后即成为asa，之后可继续考fsa课程。asal00系列的11门课程的考试均采用英文试卷，选择题形式，考试时间分别为1个半小时至4个小时不等；200系列采用英语书写答题形式。考生是否通过某一门课程考试以及所获得的分数，是到该课程全部试卷批完后，按成绩顺序排列后确定的。 第二阶段是精算师（ｆｓａ）。考生在取得准精算师资格证书后方可参加ｆｓａ课程考试。目前把精算师的考试课程分为财务、团体与健康保险、个人人寿与健康保险、养老金、投资五个方向，每个方向又分若干门课，每门课学分在10至30分不等。要取得ｆｓａ资格必须通过以上一个方向的所有课程考试，以及再选择以上方向的其他课程，使学分达到150分，即学分总计要达到450分。当ｆｓａ要素的课程考试全部通过后，考生还要参加最后一门课程：正式精算师认可课程（ｆａｃ），其内容主要是职业道德和案例，时间为二天 半，一般只要自始至终参加，在结束后的晚宴上会获得ｆｓａ证书。 北美精算师协会的考点分布在全世界各个国家和地区，考试每年5月和11月举行两次，考试时间由北美精算师协会确定，世界各地统一，考卷由北美精算师协会提供。 报名及考试地点：南开大学、湖南财经学院、复旦大学、中国人民大学、中山大学、中国科技大学、陕西财经学院、平安总公司北美精算学会考试课程 准精算师考试： 100系列课程：100微积分和线性代数、110概率论和数理统计、120应用统计、130运筹学、135数值分析、140复利数学、150精算数学、151风险理论、160生存模型和生命表编制、161人口数学、165匀修数学 200系列课程：200经济保障计划概论、210精算实务概论、220资产管理和公司财务概论、230资产和负债管理原理正精算师的考试课程分为五个方向： 一财务包括科目：财务管理、公司财务等 二团体和健康保险包括科目：团体和个人健康保险的设计和销售等 三个人人寿和年金保险包括科目：个人人寿和年金保险的精算实务调查、人寿保险法和税收等 四养老金包括科目：养老金估价原理i、退休计划设计等 Models for Financial Economics—April 2012 The Models for Financial Economics is called Exam MFE by the SOA and Exam 3F by the CAS. This three-hour exam consist of 30 multiple-choice questions. Also, a normal distribution calculator will be available during the test by clicking a link on the item screen. Details are available on the Prometric Web Site. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA). The purpose of the syllabus is to develop the candidate’s knowledge of the theoretical basis of certain actuarial models and the application of those models to insurance and other financial risks. A thorough knowledge of calculus, probability, interest theory and the earlier chapters of the McDonald textbook (which are in the syllabus of Exam FM/2) is assumed. Formulas are provided for the density and distribution functions for the standard normal and lognormal random variables. For paper and pencil examinations, tables of the standard normal distribution function are provided. Since the tables will be provided to the candidate at the examination, candidates will not be allowed to bring copies of the tables into the examination room. For CBT candidates, a normal distribution calculator is provided. See the link below for more information. Note: It is anticipated that candidates will have done the relevant exercises in the textbooks. Check the Updates section of the web site for any changes to the exam or syllabus. The ranges of weights shown are intended to apply to the large majority of exams administered. On occasion, the weights of topics on an individual exam may fall outside the published range. Candidates should also recognize that some questions may cover multiple learning outcomes. Each multiple-choice problem includes five answer choices identified by the letters A, B, C, D, and E, only one of which is correct. Candidates must indicate responses to each question on the computer. As part of the computer-based testing process, a few pilot questions will be randomly placed in the exam (paper and pencil and computer-based forms). These pilot questions are included to judge their effectiveness for future exams, but they will NOT be used in the scoring of this exam. All other questions will be considered in the scoring. All unanswered questions are scored incorrect. Therefore, candidates should answer every question on the exam. There is no set requirement for the distribution of correct answers for the SOA/CAS/CIA multiple-choice preliminary examinations. It is possible that a particular answer choice could appear many times on an examination or not at all. Candidates are advised to answer each question to the best of their ability, independently from how they have answered other questions on the examination. Since the CBT exam will be offered over a period of a few days, each candidate will receive a test form composed of questions selected from a pool of questions. Statistical scaling methods are used to ensure within reasonable and practical limits that, during the same testing period of a few days, all forms of the test are comparable in content and passing中国精算师资格考试体系简介
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