8. Hull modelling

金融工程经典书籍1.Futures, Options and other derivatives--John Hull这本书被称为“华尔街圣经”,不管是找工作还是senior quant都会用到。

John Hull 非常厉害,各个方面都有开创性的成果。

2.Arbitrage theory in continuous time--Tomas Bjork这本书非常适合数学/物理背景的人读,注重数学理论的培养。

3.Financial Calculus--Martin Baxter& Rennie非常薄但是elegant的一本书,1996年,算是比较早了,但是和Hull的书齐名。

4.Financial calculus for finance I II--ShreveShreve的书,非常elegant,非常仔细,适合有数学背景的人读。

I是讲离散模型,II是讲连续模型。

5.Martingale methods in Financial modelling--Musiela & Rutkovski6. Brownian motion and stochastic calculus--Shreve& Karasatz7.Stochastic differential equations--Oksendal8.Stochastic integration and differential equations--Protter9.Numerical analysisJunior quant:10.Concepts and practice of Mathematical Finance--Mark Joshi非常适合刚入行的quant,对于学生不推荐。

非常实用,作者非常聪明。

11. C++ design patterns and derivatives pricing--Mark Joshi对于懂得C++基础的人来说很重要,更重要的是教你学会Monte Carlo。

An Introduction to SIMUL8 Release NineJim Shalliker amp Chris Ricketts School of Mathematics amp Statistics University of PlymouthThe contents of this introduction to Simul8 Release Nine may be copied or modifiedand incorporated into other teaching material wholly or in part on paper or in electronicformat for use by staff and students of any educational establishment having a sitelicence for the software provided that the source continues to be st update 10 Oct 2002CONTENTS1. BUILDING A SIMPLE SIMULATION MODEL WITH SIMUL8 RELEASE 9 1 1.1 An introduction to building simulation models 1 1.1.1 What is SIMUL8 1 1.1.2 The Building Blocks 2 1.1.3 Starting SIMUL8 3 1.2 Building your own model 5 1.3 Gear manufacturing - deterministic simulation 6 1.4 Travel Times 13 1.5 Stochastic effects 14 1.6 Adding more operations - polishing and inspecting 15 1.7 Using Quickview 172. CONTROLLING THE SIMULATION EXPERIMENT 19 2.1 The warm-up period 20 2.2 Variation between runs 21 2.3 Obtaining confidence limits 24 2.4 Conducting a trial multiple simulation runs automatically 26 2.5 Variation between work items 28 2.6 Using Excel to analyse results 30 2.7 Variation in simulation experiments: summary 323. ADVANCED MODELLING TECHNIQUES 33 3.1 Controlling the graphical appearance of your simulation model. 33 3.1.1 Changing the icons 33 3.1.2 Zooming in and out 35 3.1.3 Grouping several icons into a single icon 36 3.1.4 Changing the appearance of icons to reflect their current status 37 3.1.5 Changing the appearance of work items to reflect their current status 37 3.1.6 Multiple identical work centres 38 3.2 Interruptions scheduled and unexpected 39 3.2.1 Scheduled stoppages for maintenance 39 3.2.2 Unscheduled stoppages due to breakdowns 41 3.3 Other methods of defining distributions 43 3.3.1 Sampling from empirical distributions 43 3.3.2 Time dependent distributions 48 3.4 Processes Prioritising and Routing 51 3.4.1 Prioritising the work centres 52 3.4.2 Sending to scrap 53 3.4.3 Sending back to a preceding work centre with priority treatment 54 3.4.4 Routing back to the same work centre 56 3.5 Resources 58 3.5.1 Using an operator at the grinders 58 3.5.2 Improving the model 61 3.6 Labels 63 3.6.1 Using a numeric label to prioritise work 63 3.6.2 Using a text label to specify different timing distributions 67 3.6.3 Using labels to control the appearance of work items 70 3.7 Visual Logic 74 3.7.1 Prioritising work centres 75 3.7.2 Using an extra grinding machine when there is high demand 80An Introduction to SIMUL8 Release Nine Page 11. BUILDING A SIMPLE SIMULATION MODEL WITH SIMUL8 RELEASE 91.1 An introduction to building simulation models1.1.1 What is SIMUL8 SIMUL8 is a computer package for Discrete Event Simulation. It allows the user tocreate a visual model of the system being investigated by drawing objects directly onthe screen. Typical objects may be queues or service points. The characteristics ofthe objects can be defined in terms of for example capacity or speed.When the system has been modelled then a simulation can be undertaken. The flowof work items around the system is shown by animation on the screen so that theappropriateness of the model can be assessed.When the structure of the model has been confirmed then a number of trials can be runand the performance of the system described statistically. Statistics of interest may beaverage waiting times utilisation of work centres or resources etc.Visual Thinking International have produced a number of plug-ins. These are auxiliarysoftware packages which enhance the facilities if SIMUL8 in a number of specific areas.The instructions in this workbook make no reference to the use of plug-ins and they areequally valid whether or not plug-ins are present. 2002 Jim Shalliker amp Chris Ricketts University ofPlymouthAn Introduction to SIMUL8 Release Nine Page 21.1.2 The Building BlocksIn any simulation there are four main building blocks which are listed below.1. Work Entry Point This is where work items be they jobs customers or parts arrive in the system. The pattern of arrival of work items can be controlled - to follow a scheduled arrival patternor a particular probability distribution - to arrive singly or in batches. There can be more than one Work Entry Point as more than one type of raw material may be required and they may enter at any stage of the process.2. Storage Area This is where work is held while waiting to be processed. Storage areas are equivalent to buffers or queues. There can be no user control over times in buffers as this is dictated by the performance of the work centres. However the user can control - the capacity of the queue - the shelf life of work in a queue - the queue discipline.3. Work Centre This is where work is performed by a machine or server. The length of time the work takes can be controlled to follow a particular probability distribution and the output can be routed to other objects in a variety of ways.4. Work Exit Point This is where work leaves the system. There can be more than one Work Exit Point. For example a process may produce - satisfactory product which will be dispatched at the end of processing - scrap which may leave the system at any stage of the process.There are two other important elements in a simulation.1. Work Items These are the objects that are processed by the system and are automatically generated at work entry points.2. Resources These are only necessary when processes at work stations compete for resources such as when there is only one operator for several machines. 2002 Jim Shalliker amp Chris Ricketts University of PlymouthAn Introduction to SIMUL8 Release Nine Page 31.1.3 Starting SIMUL8Start upSIMUL8.How you do this will depend on how the package has been installed on your system.In the Simul8 Release Nine dialogue box which appears click on - either Create a new blank simulation - or GoIn Simul8 Release 9 the menu-bar and toolbar look like this. Run the mouse pointer overthe toolbar to find out what each button means and label the buttons in the space below. Show/Hide Routing Arrows 2002 Jim Shalliker amp Chris Ricketts University of PlymouthAn Introduction to SIMUL8 Release Nine Page4Depending on how Simul8 has beeninstalled on your network or stand-alone computer you may find thatthere is wide blank area to the rightof the screen like this.If so then click on Objects in the menu bar then in thedrop-down Objects menu click on item Quickview.This will prevent Simul8 from showing Quickview whenyou are building and running your simulation model.Repeating this would put Quickview backagain.Quickview is a facility that enables more experiencedusers to work more efficiently. You will learn aboutQuickview later.Your Simul8 screen should now looklike this with more room to displayyour Simul8 model.Conventions used in these notes In the following instructions the notation / Objects / Quickview will be used to refer to items selected from the menu bar for example meaning to click on Objects on the menu bar then click on Quickview in the File menu. When referring to buttons on the toolbar items in dialogue boxes etc key words will be highlighted. Key words will also be highlighted for other actions that you have to take for example selecting options in a dialogue box. Lines beginning with a symbol are computer instructions requiring an actio n from you. Anything else is an explanation not requiring an action from you. 2002 Jim Shalliker amp Chris Ricketts University of PlymouthAn Introduction to SIMUL8 Release Nine Page 51.2 Building your own modelYou will now start to build a model to simulate the operation of a factory thatmanufactures gears from raw mouldings.In your initialsimulation of a simple factory as shown below i gear mouldings arrive in batches ii they enter a storage area while waiting for processing iii the gear mouldings are gro und into gears at three grinders working in parallel iv the ground gears go directly for washing v the washed gears leave the factory.You will start with a system in which arrivals and processing times are deterministicfixed with no uncertainty so that the operation of the system is clear. You will specifythe pattern of arrivals the capacity of the storage area and the service time at eachwork centre.You will then convert the system to have stochastic arrivals and processing timesvariable subject to some uncertainty.Finally you will extend the factory so that the washed gears are polished and inspectedbefore leaving the factory.In later sections you will then extend this simple model to include more complexbehaviour such as scrapping and reprocessing of faulty items and prioritising work. 2002 Jim Shalliker amp Chris Ricketts University of PlymouthAn Introduction to SIMUL8 Release Nine Page 61.3 Gear manufacturing - deterministic simulationCreate the Layout working from left to right across the screen. Create a Work Entry Point by clicking on the Create Work Entry Point tool then clicking somewhere in the topleft-hand corner of the Simulation Window Create a Storage Area Queue for the incoming work items using the Create Storage Area tool in the same way Create a single Work Centre Activity for grinding using the Create Work Centre tool Create a second single Work Centre for washing again using the Create Work Centre tool Create a Work Exit Point using the Create Work Exit Point tool Save the model as Gear1 The number at the end of each filename will refer to the section in your workbook.Your model should look similar to this:Note that if you make a mistake you can edit the model. If you create the wrong type of object you can double click on it then in the dialogue box that appears click on the Erase button If you need to move an icon you can click and drag it to another location 2002 Jim Shalliker amp Chris Ricketts University of PlymouthAn Introduction to SIMUL8 Release Nine Page 7If you make no mistakes then all the routing arrows will be put in for you correctly.If you need to modify the routing arrows then there are two methods.Try each method by removing and replacing a routing arrow if you have madeno mistakes. Method 1 - To remove an existing link or create a new one hold down the Shift key then click and drag from the source object to the destination object Method 2 - To remove an existing link or create a new one click on the Route Drawing Mode button not the Show/Hide Route Arrows button which is on its right then click and drag from the source object to the destination objectIt is good practice to define a Work Item Type so that the name is meaningful.In this case you will use the name Gear. Use / Objects / Work Item Type ie click on Objects in the menu bar then click on Work Item Type in the Objects menu In the Work Item Types dialogue box change the name from Main Work Item Type to Gear Click on OK to close the dialogue boxDefine Arrivals to have a batch of 15 gear mouldings arrive every 60 minutes. Double click on the Work Entry Point icon in the layout In the Work Entry Point Properties dialogue box change its name to Deliveries but don’t press the Enter key and make sure the Input Work Item Type is Gear At the bottom of the Inter-arrival times options box click on the Distribution selector arrow and select the Fixed distribution which you will find near the top of the list Change the Fixed Value to 60 but don’t press the Enter key By default Simul8 assumes that the units are minutes. You will look at this in more detail later. Click on the Batching button and in the Batching dialogue box select a Fixed distribution and change the Fixed Value to 15 items Click on OK to go back to the Work Entry Point Properties dialogue boxClick on the Graphics button and in the Graphics dialogue box click on the Title button In the Simul8 Object Title dialogue box select Show Title on Simulation Window then OK back to the model 2002 Jim Shalliker amp Chris Ricketts University of PlymouthAn Introduction to SIMUL8 Release Nine Page 8Define the characteristics of the Storage Area queue or buffer to have a capacity of25 gear mouldings. This means that if there are more than ten raw mouldings in thestorage area when a scheduled delivery of 15 raw mouldings is made then the n.。