List of Figures xix
List of Tables xxiii
Introduction 1
0.1 What is This Book? 1
0.2 Special Features in This Book 1
0.3 Who is This Book for and What Do You Learn? 2
0.4 Structure of This Book 2
0.5 C# Source Code 3
1 Global Overview of the Book 5
1.1 Introduction and Objectives 5
1.2 Comparing C# and C++ 5
1.3 Using This Book 6
2 C# Fundamentals 9
2.1 Introduction and Objectives 9
2.2 Background to C# 9
2.3 Value Types, Reference Types and Memory Management 10
2.4 Built-in Data Types in C# 10
2.5 Character and String Types 12
2.6 Operators 13
2.7 Console Input and Output 14
2.8 User-defined Structs 15
2.9 Mini Application: Option Pricing 16
2.10 Summary and Conclusions 21
2.11 Exercises and Projects 22
3 Classes in C# 25
3.1 Introduction and Objectives 25
3.2 The Structure of a Class: Methods and Data 25
3.3 The Keyword 'this' 28
3.4 Properties 28
3.5 Class Variables and Class Methods 30
3.6 Creating and Using Objects in C# 33
3.7 Example: European Option Price and Sensitivities 33
3.7.1 Supporting Mathematical Functions 34
3.7.2 Black-Scholes Formula 35
3.7.3 C# Implementation 36
3.7.4 Examples and Applications 39
3.8 Enumeration Types 40
3.9 Extension Methods 42
3.10 An Introduction to Inheritance in C# 44
3.11 Example: Two-factor Payoff Hierarchies and Interfaces 46
3.12 Exception Handling 50
3.13 Summary and Conclusions 50
3.14 Exercises and Projects 51
4 Classes and C# Advanced Features 53
4.1 Introduction and Objectives 53
4.2 Interfaces 53
4.3 Using Interfaces: Vasicek and Cox-Ingersoll-Ross (CIR) Bond and Option Pricing 54
4.3.1 Defining Standard Interfaces 55
4.3.2 Bond Models and Stochastic Differential Equations 55
4.3.3 Option Pricing and the Visitor Pattern 58
4.4 Interfaces in .NET and Some Advanced Features 61
4.4.1 Copying Objects 62
4.4.2 Interfaces and Properties 63
4.4.3 Comparing Abstract Classes and Interfaces 64
4.4.4 Explicit Interfaces 65
4.4.5 Casting an Object to an Interface 65
4.5 Combining Interfaces, Inheritance and Composition 67
4.5.1 Design Philosophy: Modular Programming 67
4.5.2 A Model Problem and Interfacing 68
4.5.3 Implementing the Interfaces 69
4.5.4 Examples and Testing 72
4.6 Introduction to Delegates and Lambda Functions 72
4.6.1 Comparing Delegates and Interfaces 74
4.7 Lambda Functions and Anonymous Methods 76
4.8 Other Features in C# 77
4.8.1 Static Constructors 77
4.8.2 Finalisers 78
4.8.3 Casting 79
4.8.4 The var Keyword 80
4.9 Advanced .NET Delegates 80
4.9.1 Provides and Requires Interfaces: Creating Plug-in Methods with Delegates 82
4.9.2 Multicast Delegates 85
4.9.3 Generic Delegate Types 86
4.9.4 Delegates versus Interfaces, Again 87
4.10 The Standard Event Pattern in .NET and the Observer Pattern 87
4.11 Summary and Conclusions 91
4.12 Exercises and Projects 92
5 Data Structures and Collections 97
5.1 Introduction and Objectives 97
5.2 Arrays 97
5.2.1 Rectangular and Jagged Arrays 98
5.2.2 Bounds Checking 101
5.3 Dates, Times and Time Zones 101
5.3.1 Creating and Modifying Dates 101
5.3.2 Formatting and Parsing Dates 103
5.3.3 Working with Dates 104
5.4 Enumeration and Iterators 105
5.5 Object-based Collections and Standard Collection Interfaces 107
5.6 The List Class 109
5.7 The Hashtable Class 110
5.8 The Dictionary Class 111
5.9 The HashSet Classes 112
5.10 BitArray: Dynamically Sized Boolean Lists 114
5.11 Other Data Structures 114
5.11.1 Stack 114
5.11.2 Queue 115
5.11.3 Sorted Dictionaries 116
5.12 Strings and StringBuilder 117
5.12.1 Methods in string 118
5.12.2 Manipulating Strings 119
5.13 Some new Features in .NET 4.0 120
5.13.1 Optional Parameters 120
5.13.2 Named Parameters 121
5.13.3 COM Interoperability in .NET 4.0 121
5.13.4 Dynamic Binding 122
5.14 Summary and Conclusions 123
5.15 Exercises and Projects 123
6 Creating User-defined Data Structures 125
6.1 Introduction and Objectives 125
6.2 Design Rationale and General Guidelines 125
6.2.1 An Introduction to C# Generics 125
6.2.2 Generic Methods and Generic Delegates 128
6.2.3 Generic Constraints 129
6.2.4 Generics, Interfaces and Inheritance 130
6.2.5 Other Remarks 130
6.3 Arrays and Matrices 131
6.4 Vectors and Numeric Matrices 135
6.5 Higher-dimensional Structures 139
6.6 Sets 140
6.7 Associative Arrays and Matrices 142
6.7.1 Associative Arrays 142
6.7.2 Associative Matrices 144
6.8 Standardisation: Interfaces and Constraints 145
6.9 Using Associative Arrays and Matrices to Model Lookup Tables 152
6.10 Tuples 155
6.11 Summary and Conclusions 156
6.12 Exercises and Projects 156
7 An Introduction to Bonds and Bond Pricing 159
7.1 Introduction and Objectives 159
7.2 Embedded Optionality 160
7.3 The Time Value of Money: Fundamentals 160
7.3.1 A Simple Bond Class 164
7.3.2 Testing the Bond Functionality 165
7.4 Measuring Yield 166
7.5 Macauley Duration and Convexity 167
7.6 Dates and Date Schedulers for Fixed Income Applications 168
7.6.1 Accrued Interest Calculations and Day Count Conventions 169
7.6.2 C# Classes for Dates 170
7.6.3 DateSchedule Class 174
7.7 Exporting Schedulers to Excel 176
7.8 Other Examples 177
7.9 Pricing Bonds: An Extended Design 178
7.10 Summary and Conclusions 181
7.10.1 Appendix: Risks Associated with Bonds 181
7.11 Exercises and Projects 181
8 Data Management and Data Lifecycle 185
8.1 Introduction and Objectives 185
8.2 Data Lifecycle in Trading Applications 185
8.2.1 Configuration Data and Calculated Data 186
8.2.2 Which Kinds of Data Storage Devices Can We Use? 186
8.3 An Introduction to Streams and I/O 186
8.3.1 Stream Architecture 186
8.3.2 Backing Store Streams Functionality 187
8.3.3 Stream Decorators 189
8.3.4 Stream Adapters 191
8.4 File and Directory Classes 195
8.4.1 The Class Hierarchy 196
8.4.2 FileInfo and DirectoryInfo Classes 198
8.5 Serialisation Engines in .NET 199
8.5.1 DataContractSerializer 199
8.5.2 NetDataContractSerializer 201
8.5.3 Formatters 201
8.5.4 Implicit and Explicit Serialisation 203
8.6 The Binary Serialiser 203
8.7 XML Serialisation 204
8.7.1 Subclasses and Child Objects 205
8.7.2 Serialisation of Collections 206
8.7.3 The IXmlSerializable Interface 207
8.8 Data Lifetime Management in Financial and Trading Applications 209
8.9 Summary and Conclusions 213
8.10 Exercises and Projects 213
9 Binomial Method, Design Patterns and Excel Output 215
9.1 Introduction and Objectives 215
9.2 Design of Binomial Method 216
9.3 Design Patterns and Classes 217
9.3.1 Creating Input Data: Factory Method Pattern 217
9.3.2 Binomial Parameters and the Strategy Pattern 219
9.3.3 The Complete Application Object and the Mediator Pattern 228
9.3.4 Lattice Presentation in Excel 230
9.4 Early Exercise Features 232
9.5 Computing Hedge Sensitivities 233
9.6 Multi-dimensional Binomial Method 233
9.7 Improving Performance Using Pade Rational Approximants 236
9.8 Summary and Conclusions 238
9.9 Projects and Exercises 238
10 Advanced Lattices and Finite Difference Methods 241
10.1 Introduction and Objectives 241
10.2 Trinomial Model of the Asset Price and Its C# Implementation 241
10.3 Stability and Convergence of the Trinomial Method 246
10.4 The Black-Scholes Partial Differential Equation and Explicit Schemes 246
10.5 Implementing Explicit Schemes in C# 247
10.5.1 Using the Explicit Finite Difference Method 251
10.6 Stability of the Explicit Finite Difference Scheme 252
10.7 An Introduction to the Alternating Direction Explicit Method (ADE) 255
10.7.1 ADE in a Nutshell: The One-factor Diffusion Equation 255
10.7.2 ADE for Equity Pricing Problems 256
10.8 Implementing ADE for the Black-Scholes PDE 258
10.9 Testing the ADE Method 262
10.10 Advantages of the ADE Method 263
10.11 Summary and Conclusions 263
10.12 Appendix: ADE Numerical Experiments 263
10.13 Exercises and Projects 268
11 Interoperability: Namespaces, Assemblies and C++/CLI 271
11.1 Introduction and Objectives 271
11.2 Namespaces 271
11.2.1 Applications of Namespaces 272
11.3 An Introduction to Assemblies 273
11.3.1 Assembly Types 274
11.3.2 Specifying Assembly Attributes in AssemblyInfo.cs 275
11.3.3 The Relationship between Namespaces and Assemblies 276
11.4 Reflection and Metadata 276
11.4.1 Other Classes in the Reflection Namespace 281
11.4.2 Dynamic Method Invocation 283
11.4.3 Dynamic Object Creation 283
11.4.4 Dynamic Assembly Loading 284
11.4.5 Attributes and Reflection 284
11.4.6 Custom Attributes 286
11.5 C# and Native C++ Interoperability: How is That Possible? 289
11.5.1 Using Native C++ from C# 289
11.6 Using C# from C++ 293
11.7 Code Generation Using the Reflection API 298
11.7.1 The DynamicMethod Class 299
11.7.2 The Evaluation Stack and Argument Passing to Dynamic Methods 300
11.7.3 The Case in Hand: Operator Overloading for Generic Vectors and Matrices 301
11.8 Application Domains 304
11.8.1 Creating and Destroying Application Domains 304
11.8.2 Multiple Application Domains 305
11.8.3 Sharing Data between Domains 307
11.8.4 When to Use Application Domains 308
11.9 Summary and Conclusions 309
11.10 Exercises and Projects 309
12 Bond Pricing: Design, Implementation and Excel Interfacing 311
12.1 Introduction and Objectives 311
12.2 High-level Design of Bond Pricing Problem 311
12.3 Bond Scheduling 312
12.4 Bond Functionality and Class Hierarchies 313
12.5 Calculating Price, Yield and Discount Factors: MathTools 317
12.6 Data Presentation and Excel Interop 319
12.7 Bond Data Management 321
12.7.1 Data into Memory 321
12.7.2 Serialisation and Deserialisation 322
12.8 Using the Excel Files 324
12.9 Summary and Conclusions 328
12.10 Exercises and Projects 328
1 Code Integration: Handling Bond Details 328
2 Spread on Benchmark 330
3 Floating Rate Bond and Other Structured Notes 331
4 Class Hierarchy Integration 333
13 Interpolation Methods in Interest Rate Applications 335
13.1 Introduction and Objectives 335
13.2 Interpolation and Curve Building: Basic Formula for Interpolator Tests 335
13.3 Types of Curve Shape 337
13.4 An Overview of Interpolators 338
13.5 Background to Interpolation 339
13.6 Approximation of Function Derivatives 341
13.7 Linear and Cubic Spline Interpolation 342
13.8 Positivity-preserving Cubic Interpolations: Dougherty/Hyman and Hussein 344
13.9 The Akima Method 348
13.10 Hagan-West Approach 349
13.11 Global Interpolation 350
13.11.1 Polynomial Interpolation 351
13.11.2 Rational Interpolation 352
13.12 Bilinear Interpolation 352
13.13 Some General Guidelines, Hints and Tips 355
13.14 Using the Interpolators and Test Examples 357
13.14.1 The 101 Example, from A to Z 357
13.14.2 Some Financial Formulae 360
13.14.3 Cubic Spline Interpolation: an Application Example 361
13.14.4 A Bilinear Interpolation Simple Example 364
13.15 Summary and Conclusions 367
13.16 Exercises and Projects 367
14 Short Term Interest Rate (STIR) Futures and Options 369
14.1 Introduction and Objectives 369
14.2 An Overview of Cash Money Markets 370
14.3 Sources of Risk in Money Market Transactions 370
14.4 Reference Rate and Fixings 371
14.5 STIR Futures 371
14.6 Pricing STIR Options 374
14.7 Generating International Monetary Market (IMM) Dates 378
14.7.1 Modelling Option Delta and Sensitivity Analysis 380
14.7.2 Listed Instruments and Contracts 383
14.8 List STIR Futures and STIR Futures Options 384
14.9 Putting It All Together: STIR versus OTC from a Trader's Perspective 387
14.10 Summary and Conclusions 389
14.11 Exercises and Projects 389
15 Single-curve Building 393
15.1 Introduction and Objectives 393
15.2 Starting Definitions and Overview of Curve Building Process 393
15.3 Building Blocks 395
15.3.1 Unsecured Deposit 395
15.3.2 Forward Rate Agreements (FRA) 396
15.3.3 Future Implied Rate 397
15.3.4 Interest Rate Swap (IRS) 397
15.4 Introduction to Interest Rate Swap 397
15.4.1 IRS Cash Flow 398
15.4.2 The Use of Interest Rate Swaps 399
15.4.3 Contract Specification and Practical Aspects 399
15.4.4 Traditional Swap Valuation 402
15.4.5 Overnight Index Swap (OIS) 403
15.5 The Curve Construction Mechanism 403
15.5.1 Traditional Bootstrapping Method 404
15.5.2 Best Fit Method 405
15.5.3 The Key Role of Interpolation 405
15.6 Code Design and Implementation 406
15.6.1 Process Design 406
15.6.2 ISingleRateCurve Interface 406
15.6.3 RateSet Class and BuildingBlock Class 407
15.6.4 Interpolator and Adapters 409
15.6.5 The Generic Base Class SingleCurveBuilder 410
15.6.6 Derived Class for Traditional Bootstrapping Method 412
15.6.7 Derived Class for Global Method with Interpolation 413
15.6.8 Derived Class for Global Method with Smoothness Condition 415
15.7 Console Examples 418
15.7.1 Calculating Present Value (PV) of the Floating Leg of a Swap 418
15.7.2 Checking If the Curve is Calibrated 418
15.7.3 Calculate the Time Taken to Instantiate a SingleCurveBuilder 418
15.7.4 Visualise Forward Rates in Excel 419
15.7.5 Computing Forward Start Swap 421
15.7.6 Computing Sensitivities: An Initial Example 421
15.7.7 More on Sensitivities 422
15.8 Summary and Conclusions 426
15.9 Exercises and Projects 427
15.10 Appendix: Types of Swaps 429
16 Multi-curve Building 431
16.1 Introduction and Objectives 431
16.2 The Consequences of the Crisis on Interest Rate Derivatives Valuation 431
16.2.1 The Growing Importance of Overnight Indexed Swap 432
16.2.2 Collateralisation under a CSA 432
16.2.3 The Role of OIS Discounting: One Curve is Not Enough 433
16.2.4 Basis 433
16.2.5 The Par Swap Rate Formulae 434
16.3 Impact of Using OIS Discounting 436
16.3.1 Effect on Forward Rates 436
16.3.2 Effect on Mark-to-Market 436
16.3.3 Risk Effect 436
16.4 The Bootstrapping Process Using Two Curves: Description of the Mechanism 437
16.5 Sensitivities 438
16.6 How to Organise the Code: A Possible Solution 439
16.6.1 IRateCurve Base Interface and Derived Interfaces 439
16.6.2 The class MultiCurveBuilder 441
16.7 Putting it Together, Working Examples 445
16.7.1 Calibration Consistency 445
16.7.2 Print Forward Rates and Discount Factors on Excel 446
16.7.3 Sensitivities on Console 446
16.7.4 Forward Swap Matrix 447
16.7.5 Mark-to-Market Differences 448
16.7.6 Comparing Two Versions of the MultiCurveBuilder 450
16.7.7 Input Data, Interpolation and Forward Rates 452
16.7.8 Comparing Discount Factor 453
16.8 Summary and Conclusions 453
16.9 Exercises and Projects 453
16.10 Appendix: Par Asset Swap Spread and Zero Volatility Spread 455
17 Swaption, Cap and Floor 459
17.1 Introduction and Objectives: A Closed Formula World 459
17.2 Description of Instruments and Formulae 459
17.2.1 Cap and Floor: Description and Formulae 459
17.2.2 Cap and Floor at the money Strike 461
17.2.3 Cap Volatility and Caplet Volatility 462
17.2.4 Implied Volatility 463
17.2.5 Multi-strike and Amortising Cap and Floor 463
17.2.6 Swaption: Mechanism and Closed Pricing Formulae 464
17.2.7 Call Put Parity for Cap, Floor and Swaption 466
17.3 Multi-curve Framework on Cap, Floor and Swaption 467
17.4 Bootstrapping Volatility for Cap and Floor 469
17.4.1 Cap Stripping 469
17.4.2 Missing Data, Volatility Models and Interpolation 473
17.5 How to Organise the Code in C#: A Possible Solution 474
17.5.1 Ready to Use Formula 474
17.5.2 Cap Stripping Code 476
17.5.3 Calculating Mono-strike Caplet Volatilities 476
17.5.4 Managing More Mono-strike Caplet Volatilities 479
17.6 Console and Excel Working Examples 481
17.6.1 Simple Caplet Price 481
17.6.2 Cap As a Sum of Caplets 482
17.6.3 Simple Cap Volatility Bootstrapping: First Unknown Volatility 483
17.6.4 ATM Strike and Recursive Bootstrapping 485
17.6.5 Sparse Data from the Market: Volatility Optimisation and Input Interpolation 487
17.7 Summary and Conclusions 490
17.8 Exercise and Discussion 491
18 Software Architectures and Patterns for Pricing Applications 493
18.1 Introduction and Objectives 493
18.2 An Overview of the GOF Pattern 494
18.3 Creational Patterns 496
18.4 Builder Pattern 496
18.5 Structural Patterns 499
18.5.1 Facade Pattern 499
18.5.2 Layers Pattern 499
18.6 Behavioural Patterns 500
18.6.1 Visitor Pattern 501
18.6.2 Strategy and Template Method Patterns 501
18.7 Builder Application Example: Calibration Algorithms for Cap and Floor 502
18.7.1 Example Caplet Volatility Matrix 502
18.7.2 Volatility Matrix with Multiple Strikes 503
18.8 A PDE/FDM Patterns-based Framework for Equity Options 504
18.8.1 High-level Design 506
18.8.2 Generalisations and Extensions 508
18.9 Using Delegates to Implement Behavioural Design Patterns 509
18.10 A System Design for Monte Carlo Applications 510
18.10.1 A Universal System Design Methodology 511
18.11 Dynamic Programming in .NET 513
18.11.1 Numeric Type Unification 514
18.11.2 Implementing Dynamic Objects 516
18.12 Summary and Conclusions 516
18.13 Exercises and Projects 517
19 LINQ (Language Integrated Query) and Fixed Income Applications 523
19.1 Introduction and Objectives 523
19.2 Scope of Chapter and Prerequisites 523
19.3 LINQ Query Operators 524
19.3.1 Collection as Input, Collection as Output 524
19.3.2 Collection as Input, Noncollection as Output 525
19.3.3 Noncollection to Collection 526
19.4 LINQ Queries and Initial Examples 526
19.4.1 Lambda Queries and Composition 527
19.4.2 Comprehension Queries 528
19.4.3 Deferred Execution 529
19.5 Advanced Queries 531
19.5.1 Subqueries 531
19.5.2 Composition Strategies 532
19.5.3 Interpreted Queries 533
19.6 A Numerical Example 533
19.6.1 Basic Functionality 533
19.6.2 User-defined Aggregation Methods 534
19.6.3 Set Operations 535
19.7 Join and GroupJoin 535
19.8 Examples in Fixed Income Applications 540
19.8.1 Using Conversion Operators 540
19.8.2 Discount Factors 540
19.8.3 Bonds 542
19.8.4 Scenarios 543
19.8.5 Cash Flow Aggregation 545
19.8.6 Ordering Collections 546
19.8.7 Eonia Rates Replication 547
19.9 LINQ and Excel Interoperability 549
19.9.1 Applications in Computational Finance 557
19.10 Summary and Conclusions 557
19.11 Exercises and Projects 557
20 Introduction to C# and Excel Integration 561
20.1 Introduction and Objectives 561
20.2 Excel Object Model 561
20.3 Using COM Technology in .NET 561
20.4 Primary Interop Assemblies (PIA) 563
20.5 Standalone Applications 564
20.5.1 Standalone Application: Workbook and Worksheets 564
20.5.2 Charts 565
20.5.3 Using Excel with C++/CLI 565
20.6 Types of Excel Add-ins 566
20.6.1 XLL 567
20.6.2 XLA 567
20.6.3 COM 567
20.6.4 Automation 567
20.6.5 VSTO 568
20.7 The IDTExtensibility2 Interface and COM/.NET Interoperability 569
20.8 Data Visualisation in Excel 570
20.8.1 Excel Driver 570
20.8.2 Data Structures 572
20.8.3 ExcelMechanisms and Exception Handling 572
20.8.4 Examples and Applications 575
20.9 Conclusion and Summary 578
20.10 Exercises and Projects 579
21 Excel Automation Add-ins 581
21.1 Introduction and Objectives 581
21.2 COM Overview 581
21.3 Creating Automation Add-ins: The Steps 583
21.4 Example: Creating a Calculator, Version 1 585
21.5 Example: Creating a Calculator, Version 2 588
21.6 Versioning 590
21.7 Working with Ranges 590
21.8 Volatile Methods 590
21.9 Optional Parameters 591
21.10 Using VBA with Automation Add-ins 592
21.11 Summary and Conclusions 593
21.12 Exercises and Projects 594
22 C# and Excel Integration COM Add-ins 595
22.1 Introduction and Objectives 595
22.2 Preparations for COM Add-ins 595
22.3 The Interface IDTExtensibility2 596
22.4 Creating COM Add-ins: The Steps 596
22.5 Utility Code and Classes 597
22.6 Using Windows Forms 600
22.7 Example: Creating a COM Add-in 601
22.8 Debugging and Troubleshooting 603
22.9 An Introduction to Excel-DNA 603
22.9.1 Example 001: Hello World 604
22.9.2 Example 101: Simple Option Pricer 605
22.9.3 Excel-DNA and Rate Curves 608
22.9.4 Registration and Loading 613
22.9.5 What is Inside ExcelDna.Integration.dll? 614
22.10 Excel COM Interoperability and Rate Multi-curve 615
22.11 Conclusion and Summary 622
22.12 Exercises and Projects 622
23 Real-time Data (RTD) Server 625
23.1 Introduction and Objectives 625
23.2 Real-time Data in Excel: Overview 625
23.3 Real-time Data Function 626
23.4 Example 627
23.5 The Topic Class and Data 629
23.6 Creating an RTD Server 631
23.7 Using the RTD Server 631
23.8 Testing and Troubleshooting the RTD Server 632
23.9 Conclusion and Summary 632
23.10 Exercises and Projects 632
24 Introduction to Multi-threading in C# 635
24.1 Introduction and Objectives 635
24.2 Processes 636
24.3 Using ProcessStartInfo to Redirect Process I/O 637
24.4 An Introduction to Threads in C# 638
24.4.1 The Differences between Processes and Threads 641
24.5 Passing Data to a Thread and between Threads 641
24.6 Thread States and Thread Lifecycle 644
24.6.1 Sleep 645
24.6.2 Thread Joining 646
24.6.3 Thread Interrupt and Abort 648
24.7 Thread Priority 650
24.8 Thread Pooling 651
24.9 Atomic Operations and the Interlocked Class 652
24.10 Exception Handling 653
24.11 Multi-threaded Data Structures 654
24.11.1 Extended Producer-Consumer Pattern 657
24.12 A Simple Example of Traditional Multi-threading 659
24.13 Summary and Conclusions 661
24.14 Exercises and Projects 661
25 Advanced Multi-threading in C# 665
25.1 Introduction and Objectives 665
25.2 Thread Safety 666
25.3 Locking Mechanisms for Objects and Classes 667
25.3.1 Locking a Class 669
25.3.2 Nested Locking 669
25.4 Mutex and Semaphore 673
25.5 Notification and Signalling 676
25.5.1 Thread Notification and the Monitor Class 678
25.6 Asynchronous Delegates 679
25.7 Synchronising Collections 681
25.8 Timers 682
25.9 Foreground and Background Threads 684
25.10 Executing Operations on Separate Threads: the BackgroundWorker Class 685
25.11 Parallel Programming in .NET 687
25.11.1 The Parallel Class 687
25.12 Task Parallel Library (TPL) 691
25.12.1 Creating and Starting Tasks 692
25.12.2 Continuations 694
25.13 Concurrent Data Structures 694
25.13.1 An Example: Producer Consumer Pattern and Random Number Generation 695
25.13.2 The Barrier Class 698
25.13.3 PLINQ 699
25.14 Exception Handling 701
25.15 Shifting Curves 702
25.16 Summary and Conclusions 704
25.17 Exercises and Projects 704
26 Creating Multi-threaded and Parallel Applications for Computational Finance 707
26.1 Introduction and Objectives 707
26.2 Multi-threaded and Parallel Applications for Computational Finance 707
26.3 Fork and Join Pattern 709
26.4 Geometric Decomposition 711
26.5 Shared Data and Reader/Writer Locks: Multiple Readers and Multiple Writers 715
26.5.1 Upgradeable Locks and Recursion 718
26.6 Monte Carlo Option Pricing and the Producer-Consumer Pattern 719
26.7 The StopWatch Class 726
26.8 Garbage Collection and Disposal 727
26.8.1 Disposal and the IDisposable Interface 727
26.8.2 Automatic Garbage Collection 728
26.8.3 Managed Memory Leaks 730
26.9 Summary and Conclusions 730
26.10 Exercises and Projects 730
A1 Object-oriented Fundamentals 735
A1.1 Introduction and Objectives 735
A1.2 Object-oriented Paradigm 735
A1.3 Generic Programming 737
A1.4 Procedural Programming 738
A1.5 Structural Relationships 738
A1.5.1 Aggregation 739
A1.5.2 Association 740
A1.5.3 Generalisation/Specialisation (Gen/Spec Relationship) 742
A1.6 An Introduction to Concept Modelling 743
A1.6.1 The Defining Attribute View 743
A1.6.2 The Prototype View 744
A1.6.3 The Exemplar-based View 744
A1.6.4 The Explanation-based View 744
A1.7 Categorisation and Concept Levels 745
A1.8 Whole-Part Pattern 745
A1.8.1 Data Decomposition 746
A1.9 Message-passing Concept versus Procedural Programming 748
A2 Nonlinear Least-squares Minimisation 751
A2.1 Introduction and Objectives 751
A2.2 Nonlinear Programming and Multi-variable Optimisation 751
A2.3 Nonlinear Least Squares 753
A2.3.1 Nonlinear Regression 753
A2.3.2 Simultaneous Nonlinear Equations 754
A2.3.3 Derivatives of Sum-of-Squares Functions 754
A2.4 Some Specific Methods 755
A2.5 The ALGLIB Library 756
A2.6 An Application to Curve Building 758
A2.7 Rate Calibration Example 759
A2.8 Exercises and Projects 764
A3 The Mathematical Background to the Alternating Direction Explicit (ADE) Method 765
A3.1 Introduction and Objectives 765
A3.2 Background to ADE 765
A3.3 Scoping the Problem: One-factor Problems 766
A3.4 An Example: One-factor Black-Scholes PDE 768
A3.5 Boundary Conditions 769
A3.6 Example: Boundary Conditions for the One-factor Black-Scholes PDE 772
A3.7 Motivating the ADE Method 772
A3.8 The ADE Method Exposed 773
A3.9 The Convection Term 773
A3.10 Other Kinds of Boundary Conditions 774
A3.11 Nonlinear Problems 775
A3.12 ADE for PDEs in Conservative Form 775
A3.13 Numerical Results and Guidelines 776
A3.13.1 The Consequences of Conditional Consistency 776
A3.13.2 Call Payoff Behaviour at the Far Field 777
A3.13.3 General Formulation of the ADE Method 777
A3.14 The Steps to Use when Implementing ADE 778
A3.15 Summary and Conclusions 778
A3.16 Exercises and Projects 779
A4 Cap, Floor and Swaption Using Excel-DNA 789
A4.1 Introduction 789
A4.2 Different Ways of Stripping Cap Volatility 789
A4.3 Comparing Caplet Volatility Surface 792
A4.4 Call Put Parity 794
A4.5 Cap Price Matrix 795
A4.6 Multi-strike and Amortising 797
A4.7 Simple Swaption Formula 798
A4.8 Swaption Straddle 800
A4.9 Exercises 804
Bibliography 805
Web References 812
Index 815
