C# for Financial Markets (The Wiley Finance Series)

Description

A practice-oriented guide to using C# to design and program pricing and trading models In this step-by-step guide to software development for financial analysts, traders, developers and quants, the authors show both novice and experienced practitioners how to develop robust and accurate pricing models and employ them in real environments. Traders will learn how to design and implement applications for curve and surface modeling, fixed income products, hedging strategies, plain and exotic option modeling, interest rate options, structured bonds, unfunded structured products, and more. A unique mix of modern software technology and quantitative finance, this book is both timely and practical. The approach is thorough and comprehensive and the authors use a combination of C# language features, design patterns, mathematics and finance to produce efficient and maintainable software. Designed for quant developers, traders and MSc/MFE students, each chapter has numerous exercises and the book is accompanied by a dedicated companion website, http://www.datasimfinancial.com/forum/viewforum.php?f =196&sid=f30022095850dee48c7db5ff62192b34, providing all source code, alongside audio, support and discussion forums for readers to comment on the code and obtain new versions of the software. C# for Financial Markets Contents List of Figures List of Tables Introduction 0.1 What Is This Book? 0.2 Special Features in This Book 0.3 Who Is This Book for and What Do You Learn? 0.4 Structure of This Book 0.5 C# Source Code 1 Global Overview of the Book 1.1 Introduction and Objectives 1.2 Comparing C# and C++ 1.3 Using This Book 2 C# Fundamentals 2.1 Introduction and Objectives 2.2 Background to C# 2.3 Value Types, Reference Types and Memory Management 2.4 Built-in Data Types in C# 2.5 Character and String Types 2.6 Operators 2.7 Console Input and Output 2.8 User-defined Structs 2.9 Mini Application: Option Pricing 2.10 Summary and Conclusions 2.11 Exercises and Projects 3 Classes in C# 3.1 Introduction and Objectives 3.2 The Structure of a Class: Methods and Data 3.3 The Keyword ‘this’ 3.4 Properties 3.5 Class Variables and Class Methods 3.6 Creating and Using Objects in C# 3.7 Example: European Option Price and Sensitivities 3.7.1 Supporting Mathematical Functions 3.7.2 Black-Scholes Formula 3.7.3 C# Implementation 3.7.4 Examples and Applications 3.8 Enumeration Types 3.9 Extension Methods 3.10 An Introduction to Inheritance in C# 3.11 Example: Two-factor Payoff Hierarchies and Interfaces 3.12 Exception Handling 3.13 Summary and Conclusions 3.14 Exercises and Projects 4 Classes and C# Advanced Features 4.1 Introduction and Objectives 4.2 Interfaces 4.3 Using Interfaces: Vasicek and Cox-Ingersoll-Ross (CIR) Bond and Option Pricing 4.3.1 Defining Standard Interfaces 4.3.2 Bond Models and Stochastic Differential Equations 4.3.3 Option Pricing and the Visitor Pattern 4.4 Interfaces in .NET and Some Advanced Features 4.4.1 Copying Objects 4.4.2 Interfaces and Properties 4.4.3 Comparing Abstract Classes and Interfaces 4.4.4 Explicit Interfaces 4.4.5 Casting an Object to an Interface 4.5 Combining Interfaces, Inheritance and Composition 4.5.1 Design Philosophy: Modular Programming 4.5.2 A Model Problem and Interfacing 4.5.3 Implementing the Interfaces 4.5.4 Examples and Testing 4.6 Introduction to Delegates and Lambda Functions 4.6.1 Comparing Delegates and Interfaces 4.7 Lambda Functions and Anonymous Methods 4.8 Other Features in C# 4.8.1 Static Constructors 4.8.2 Finalisers 4.8.3 Casting 4.8.4 The var Keyword 4.9 Advanced .NET Delegates 4.9.1 Provides and Requires Interfaces: Creating Plug-in Methods with Delegates 4.9.2 Multicast Delegates 4.9.3 Generic Delegate Types 4.9.4 Delegates versus Interfaces, Again 4.10 The Standard Event Pattern in .NET and the Observer Pattern 4.11 Summary and Conclusions 4.12 Exercises and Projects 5 Data Structures and Collections 5.1 Introduction and Objectives 5.2 Arrays 5.2.1 Rectangular and Jagged Arrays 5.2.2 Bounds Checking 5.3 Dates, Times and Time Zones 5.3.1 Creating and Modifying Dates 5.3.2 Formatting and Parsing Dates 5.3.3 Working with Dates 5.4 Enumeration and Iterators 5.5 Object-based Collections and Standard Collection Interfaces 5.6 The List Class 5.7 The Hashtable Class 5.8 The Dictionary Class 5.9 The HashSet Classes 5.10 BitArray: Dynamically Sized Boolean Lists 5.11 Other Data Structures 5.11.1 Stack 5.11.2 Queue 5.11.3 Sorted Dictionaries 5.12 Strings and StringBuilder 5.12.1 Methods in string 5.12.2 Manipulating Strings 5.13 Some new Features in .NET 4.0 5.13.1 Optional Parameters 5.13.2 Named Parameters 5.13.3 COM Interoperability in .NET 4.0 5.13.4 Dynamic Binding 5.14 Summary and Conclusions 5.15 Exercises and Projects 6 Creating User-defined Data Structures 6.1 Introduction and Objectives 6.2 Design Rationale and General Guidelines 6.2.1 An Introduction to C# Generics 6.2.2 Generic Methods and Generic Delegates 6.2.3 Generic Constraints 6.2.4 Generics, Interfaces and Inheritance 6.2.5 Other Remarks 6.3 Arrays and Matrices 6.4 Vectors and Numeric Matrices 6.5 Higher-dimensional Structures 6.6 Sets 6.7 Associative Arrays and Matrices 6.7.1 Associative Arrays 6.7.2 Associative Matrices 6.8 Standardisation: Interfaces and Constraints 6.9 Using Associative Arrays and Matrices to Model Lookup Tables 6.10 Tuples 6.11 Summary and Conclusions 6.12 Exercises and Projects 7 An Introduction to Bonds and Bond Pricing 7.1 Introduction and Objectives 7.2 Embedded Optionality 7.3 The Time Value of Money: Fundamentals 7.3.1 A Simple Bond Class 7.3.2 Testing the Bond Functionality 7.4 Measuring Yield 7.5 Macauley Duration and Convexity 7.6 Dates and Date Schedulers for Fixed Income Applications 7.6.1 Accrued Interest Calculations and Day Count Conventions 7.6.2 C# Classes for Dates 7.6.3 DateSchedule Class 7.7 Exporting Schedulers to Excel 7.8 Other Examples 7.9 Pricing Bonds: An Extended Design 7.10 Summary and Conclusions 7.10.1 Appendix: Risks Associated with Bonds 7.11 Exercises and Projects 8 Data Management and Data Lifecycle 8.1 Introduction and Objectives 8.2 Data Lifecycle in Trading Applications 8.2.1 Configuration Data and Calculated Data 8.2.2 Which Kinds of Data Storage Devices Can We Use? 8.3 An Introduction to Streams and I/O 8.3.1 Stream Architecture 8.3.2 Backing Store Streams Functionality 8.3.3 Stream Decorators 8.3.4 Stream Adapters 8.4 File and Directory Classes 8.4.1 The Class Hierarchy 8.4.2 FileInfo and DirectoryInfo Classes 8.5 Serialisation Engines in .NET 8.5.1 DataContractSerializer 8.5.2 NetDataContractSerializer 8.5.3 Formatters 8.5.4 Implicit and Explicit Serialisation 8.6 The Binary Serialiser 8.7 XML Serialisation 8.7.1 Subclasses and Child Objects 8.7.2 Serialisation of Collections 8.7.3 The IXmlSerializable Interface 8.8 Data Lifetime Management in Financial and Trading Applications 8.9 Summary and Conclusions 8.10 Exercises and Projects 9 Binomial Method, Design Patterns and Excel Output 9.1 Introduction and Objectives 9.2 Design of Binomial Method 9.3 Design Patterns and Classes 9.3.1 Creating Input Data: Factory Method Pattern 9.3.2 Binomial Parameters and the Strategy Pattern 9.3.3 The Complete Application Object and the Mediator Pattern 9.3.4 Lattice Presentation in Excel 9.4 Early Exercise Features 9.5 Computing Hedge Sensitivities 9.6 Multi-dimensional Binomial Method 9.7 Improving Performance Using Padé Rational Approximants 9.8 Summary and Conclusions 9.9 Projects and Exercises 10 Advanced Lattices and Finite Difference Methods 10.1 Introduction and Objectives 10.2 Trinomial Model of the Asset Price and Its C# Implementation 10.3 Stability and Convergence of the Trinomial Method 10.4 The Black-Scholes Partial Differential Equation and Explicit Schemes 10.5 Implementing Explicit Schemes in C# 10.5.1 Using the Explicit Finite Difference Method 10.6 Stability of the Explicit Finite Difference Scheme 10.7 An Introduction to the Alternating Direction Explicit Method (ADE) 10.7.1 ADE in a Nutshell: The One-factor Diffusion Equation 10.7.2 ADE for Equity Pricing Problems 10.8 Implementing ADE for the Black-Scholes PDE 10.9 Testing the ADE Method 10.10 Advantages of the ADE Method 10.11 Summary and Conclusions 10.12 Appendix: ADE Numerical Experiments 10.13 Exercises and Projects 11 Interoperability: Namespaces, Assemblies and C++/CLI 11.1 Introduction and Objectives 11.2 Namespaces 11.2.1 Applications of Namespaces 11.3 An Introduction to Assemblies 11.3.1 Assembly Types 11.3.2 Specifying Assembly Attributes in AssemblyInfo.cs 11.3.3 The Relationship between Namespaces and Assemblies 11.4 Reflection and Metadata 11.4.1 Other Classes in the Reflection Namespace 11.4.2 Dynamic Method Invocation 11.4.3 Dynamic Object Creation 11.4.4 Dynamic Assembly Loading 11.4.5 Attributes and Reflection 11.4.6 Custom Attributes 11.5 C# and Native C++ Interoperability: How Is That Possible? 11.5.1 Using Native C++ from C# 11.6 Using C# from C++ 11.7 Code Generation Using the Reflection API 11.7.1 The DynamicMethod Class 11.7.2 The Evaluation Stack and Argument Passing to Dynamic Methods 11.7.3 The Case in Hand: Operator Overloading for Generic Vectors and Matrices 11.8 Application Domains 11.8.1 Creating and Destroying Application Domains 11.8.2 Multiple Application Domains 11.8.3 Sharing Data between Domains 11.8.4 When to Use Application Domains 11.9 Summary and Conclusions 11.10 Exercises and Projects 12 Bond Pricing: Design, Implementation and Excel Interfacing 12.1 Introduction and Objectives 12.2 High-level Design of Bond Pricing Problem 12.3 Bond Scheduling 12.4 Bond Functionality and Class Hierarchies 12.5 Calculating Price, Yield and Discount Factors: MathTools 12.6 Data Presentation and Excel Interop 12.7 Bond Data Management 12.7.1 Data into Memory 12.7.2 Serialisation and Deserialisation 12.8 Using the Excel Files 12.9 Summary and Conclusions 12.10 Exercises and Projects 1 Code Integration: Handling Bond Details 2 Spread on Benchmark 3 Floating Rate Bond and Other Structured Notes 4 Class Hierarchy Integration 13 Interpolation Methods in Interest Rate Applications 13.1 Introduction and Objectives 13.2 Interpolation and Curve Building: Basic Formula for Interpolator Tests 13.3 Types of Curve Shape 13.4 An Overview of Interpolators 13.5 Background to Interpolation 13.6 Approximation of Function Derivatives 13.7 Linear and Cubic Spline Interpolation 13.8 Positivity-preserving Cubic Interpolations: Dougherty/Hyman and Hussein 13.9 The Akima Method 13.10 Hagan-West Approach 13.11 Global Interpolation 13.11.1 Polynomial Interpolation 13.11.2 Rational Interpolation 13.12 Bilinear Interpolation 13.13 Some General Guidelines, Hints and Tips 13.14 Using the Interpolators and Test Examples 13.14.1 The 101 Example, from A to Z 13.14.2 Some Financial Formulae 13.14.3 Cubic Spline Interpolation: an Application Example 13.14.4 A Bilinear Interpolation Simple Example 13.15 Summary and Conclusions 13.16 Exercises and Projects 14 Short Term Interest Rate (STIR) Futures and Options 14.1 Introduction and Objectives 14.2 An Overview of Cash Money Markets 14.3 Sources of Risk in Money Market Transactions 14.4 Reference Rate and Fixings 14.5 STIR Futures 14.6 Pricing STIR Options 14.7 Generating International Monetary Market (IMM) Dates 14.7.1 Modelling Option Delta and Sensitivity Analysis 14.7.2 Listed Instruments and Contracts 14.8 List STIR Futures and STIR Futures Options 14.9 Putting It All Together: STIR versus OTC from a Trader’s Perspective 14.10 Summary and Conclusions 14.11 Exercises and Projects 15 Single-curve Building 15.1 Introduction and Objectives 15.2 Starting Definitions and Overview of Curve Building Process 15.3 Building Blocks 15.3.1 Unsecured Deposit 15.3.2 Forward Rate Agreements (FRA) 15.3.3 Future Implied Rate 15.3.4 Interest Rate Swap (IRS) 15.4 Introduction to Interest Rate Swap 15.4.1 IRS Cash Flow 15.4.2 The Use of Interest Rate Swaps 15.4.3 Contract Specification and Practical Aspects 15.4.4 Traditional Swap Valuation 15.4.5 Overnight Index Swap (OIS) 15.5 The Curve Construction Mechanism 15.5.1 Traditional Bootstrapping Method 15.5.2 Best Fit Method 15.5.3 The Key Role of Interpolation 15.6 Code Design and Implementation 15.6.1 Process Design 15.6.2 ISingleRateCurve Interface 15.6.3 RateSet Class and BuildingBlock Class 15.6.4 Interpolator and Adapters 15.6.5 The Generic Base Class SingleCurveBuilder 15.6.6 Derived Class for Traditional Bootstrapping Method 15.6.7 Derived Class for Global Method with Interpolation 15.6.8 Derived Class for Global Method with Smoothness Condition 15.7 Console Examples 15.7.1 Calculating Present Value (PV) of the Floating Leg of a Swap 15.7.2 Checking If the Curve is Calibrated 15.7.3 Calculate the Time Taken to Instantiate a SingleCurveBuilder 15.7.4 Visualise Forward Rates in Excel 15.7.5 Computing Forward Start Swap 15.7.6 Computing Sensitivities: An Initial Example 15.7.7 More on Sensitivities 15.8 Summary and Conclusions 15.9 Exercises and Projects 15.10 Appendix: Types of Swaps 16 Multi-curve Building 16.1 Introduction and Objectives 16.2 The Consequences of the Crisis on Interest Rate Derivatives Valuation 16.2.1 The Growing Importance of Overnight Indexed Swap 16.2.2 Collateralisation under a CSA 16.2.3 The Role of OIS Discounting: One Curve Is Not Enough 16.2.4 Basis 16.2.5 The Par Swap Rate Formulae 16.3 Impact of Using OIS Discounting 16.3.1 Effect on Forward Rates 16.3.2 Effect on Mark-to-Market 16.3.3 Risk Effect 16.4 The Bootstrapping Process Using Two Curves: Description of the Mechanism 16.5 Sensitivities 16.6 How to Organise the Code: A Possible Solution 16.6.1 IRateCurve Base Interface and Derived Interfaces 16.6.2 The class MultiCurveBuilder 16.7 Putting it Together, Working Examples 16.7.1 Calibration Consistency 16.7.2 Print Forward Rates and Discount Factors on Excel 16.7.3 Sensitivities on Console 16.7.4 Forward Swap Matrix 16.7.5 Mark-to-Market Differences 16.7.6 Comparing Two Versions of the MultiCurveBuilder 16.7.7 Input Data, Interpolation and Forward Rates 16.7.8 Comparing Discount Factor 16.8 Summary and Conclusions 16.9 Exercises and Projects 16.10 Appendix: Par Asset Swap Spread and Zero Volatility Spread 17 Swaption, Cap and Floor 17.1 Introduction and Objectives: A Closed Formula World 17.2 Description of Instruments and Formulae 17.2.1 Cap and Floor: Description and Formulae 17.2.2 Cap and Floor at the money Strike 17.2.3 Cap Volatility and Caplet Volatility 17.2.4 Implied Volatility 17.2.5 Multi-strike and Amortising Cap and Floor 17.2.6 Swaption: Mechanism and Closed Pricing Formulae 17.2.7 Call Put Parity for Cap, Floor and Swaption 17.3 Multi-curve Framework on Cap, Floor and Swaption 17.4 Bootstrapping Volatility for Cap and Floor 17.4.1 Cap Stripping 17.4.2 Missing Data, Volatility Models and Interpolation 17.5 How to Organise the Code in C#: A Possible Solution 17.5.1 Ready to Use Formula 17.5.2 Cap Stripping Code 17.5.3 Calculating Mono-strike Caplet Volatilities 17.5.4 Managing More Mono-strike Caplet Volatilities 17.6 Console and Excel Working Examples 17.6.1 Simple Caplet Price 17.6.2 Cap As a Sum of Caplets 17.6.3 Simple Cap Volatility Bootstrapping: First Unknown Volatility 17.6.4 ATM Strike and Recursive Bootstrapping 17.6.5 Sparse Data from the Market: Volatility Optimisation and Input Interpolation 17.7 Summary and Conclusions 17.8 Exercise and Discussion 18 Software Architectures and Patterns for Pricing Applications 18.1 Introduction and Objectives 18.2 An Overview of the GOF Pattern 18.3 Creational Patterns 18.4 Builder Pattern 18.5 Structural Patterns 18.5.1 Facade Pattern 18.5.2 Layers Pattern 18.6 Behavioural Patterns 18.6.1 Visitor Pattern 18.6.2 Strategy and Template Method Patterns 18.7 Builder Application Example: Calibration Algorithms for Cap and Floor 18.7.1 Example Caplet Volatility Matrix 18.7.2 Volatility Matrix with Multiple Strikes 18.8 A PDE/FDM Patterns-based Framework for Equity Options 18.8.1 High-level Design 18.8.2 Generalisations and Extensions 18.9 Using Delegates to Implement Behavioural Design Patterns 18.10 A System Design for Monte Carlo Applications 18.10.1 A Universal System Design Methodology 18.11 Dynamic Programming in .NET 18.11.1 Numeric Type Unification 18.11.2 Implementing Dynamic Objects 18.12 Summary and Conclusions 18.13 Exercises and Projects 19 LINQ (Language Integrated Query) and Fixed Income Applications 19.1 Introduction and Objectives 19.2 Scope of Chapter and Prerequisites 19.3 LINQ Query Operators 19.3.1 Collection as Input, Collection as Output 19.3.2 Collection as Input, Noncollection as Output 19.3.3 Noncollection to Collection 19.4 LINQ Queries and Initial Examples 19.4.1 Lambda Queries and Composition 19.4.2 Comprehension Queries 19.4.3 Deferred Execution 19.5 Advanced Queries 19.5.1 Subqueries 19.5.2 Composition Strategies 19.5.3 Interpreted Queries 19.6 A Numerical Example 19.6.1 Basic Functionality 19.6.2 User-defined Aggregation Methods 19.6.3 Set Operations 19.7 Join and GroupJoin 19.8 Examples in Fixed Income Applications 19.8.1 Using Conversion Operators 19.8.2 Discount Factors 19.8.3 Bonds 19.8.4 Scenarios 19.8.5 Cash Flow Aggregation 19.8.6 Ordering Collections 19.8.7 Eonia Rates Replication 19.9 LINQ and Excel Interoperability 19.9.1 Applications in Computational Finance 19.10 Summary and Conclusions 19.11 Exercises and Projects 20 Introduction to C# and Excel Integration 20.1 Introduction and Objectives 20.2 Excel Object Model 20.3 Using COM Technology in .NET 20.4 Primary Interop Assemblies (PIA) 20.5 Standalone Applications 20.5.1 Standalone Application: Workbook and Worksheets 20.5.2 Charts 20.5.3 Using Excel with C++/CLI 20.6 Types of Excel Add-ins 20.6.1 XLL 20.6.2 XLA 20.6.3 COM 20.6.4 Automation 20.6.5 VSTO 20.7 The IDTExtensibility2 Interface and COM/.NET Interoperability 20.8 Data Visualisation in Excel 20.8.1 Excel Driver 20.8.2 Data Structures 20.8.3 ExcelMechanisms and Exception Handling 20.8.4 Examples and Applications 20.9 Conclusion and Summary 20.10 Exercises and Projects 21 Excel Automation Add-ins 21.1 Introduction and Objectives 21.2 COM Overview 21.3 Creating Automation Add-ins: The Steps 21.4 Example: Creating a Calculator, Version 1 21.5 Example: Creating a Calculator, Version 2 21.6 Versioning 21.7 Working with Ranges 21.8 Volatile Methods 21.9 Optional Parameters 21.10 Using VBA with Automation Add-ins 21.11 Summary and Conclusions 21.12 Exercises and Projects 22 C# and Excel Integration COM Add-ins 22.1 Introduction and Objectives 22.2 Preparations for COM Add-ins 22.3 The Interface IDTExtensibility2 22.4 Creating COM Add-ins: The Steps 22.5 Utility Code and Classes 22.6 Using Windows Forms 22.7 Example: Creating a COM Add-in 22.8 Debugging and Troubleshooting 22.9 An Introduction to Excel-DNA 22.9.1 Example 001: Hello World 22.9.2 Example 101: Simple Option Pricer 22.9.3 Excel-DNA and Rate Curves 22.9.4 Registration and Loading 22.9.5 What Is Inside ExcelDna.Integration.dll? 22.10 Excel COM Interoperability and Rate Multi-curve 22.11 Conclusion and Summary 22.12 Exercises and Projects 23 Real-time Data (RTD) Server 23.1 Introduction and Objectives 23.2 Real-time Data in Excel: Overview 23.3 Real-time Data Function 23.4 Example 23.5 The Topic Class and Data 23.6 Creating an RTD Server 23.7 Using the RTD Server 23.8 Testing and Troubleshooting the RTD Server 23.9 Conclusion and Summary 23.10 Exercises and Projects 24 Introduction to Multi-threading in C# 24.1 Introduction and Objectives 24.2 Processes 24.3 Using ProcessStartInfo to Redirect Process I/O 24.4 An Introduction to Threads in C# 24.4.1 The Differences between Processes and Threads 24.5 Passing Data to a Thread and between Threads 24.6 Thread States and Thread Lifecycle 24.6.1 Sleep 24.6.2 Thread Joining 24.6.3 Thread Interrupt and Abort 24.7 Thread Priority 24.8 Thread Pooling 24.9 Atomic Operations and the Interlocked Class 24.10 Exception Handling 24.11 Multi-threaded Data Structures 24.11.1 Extended Producer–Consumer Pattern 24.12 A Simple Example of Traditional Multi-threading 24.13 Summary and Conclusions 24.14 Exercises and Projects 25 Advanced Multi-threading in C# 25.1 Introduction and Objectives 25.2 Thread Safety 25.3 Locking Mechanisms for Objects and Classes 25.3.1 Locking a Class 25.3.2 Nested Locking 25.4 Mutex and Semaphore 25.5 Notification and Signalling 25.5.1 Thread Notification and the Monitor Class 25.6 Asynchronous Delegates 25.7 Synchronising Collections 25.8 Timers 25.9 Foreground and Background Threads 25.10 Executing Operations on Separate Threads: the BackgroundWorker Class 25.11 Parallel Programming in .NET 25.11.1 The Parallel Class 25.12 Task Parallel Library (TPL) 25.12.1 Creating and Starting Tasks 25.12.2 Continuations 25.13 Concurrent Data Structures 25.13.1 An Example: Producer Consumer Pattern and Random Number Generation 25.13.2 The Barrier Class 25.13.3 PLINQ 25.14 Exception Handling 25.15 Shifting Curves 25.16 Summary and Conclusions 25.17 Exercises and Projects 26 Creating Multi-threaded and Parallel Applications for Computational Finance 26.1 Introduction and Objectives 26.2 Multi-threaded and Parallel Applications for Computational Finance 26.3 Fork and Join Pattern 26.4 Geometric Decomposition 26.5 Shared Data and Reader/Writer Locks: Multiple Readers and Multiple Writers 26.5.1 Upgradeable Locks and Recursion 26.6 Monte Carlo Option Pricing and the Producer–Consumer Pattern 26.7 The StopWatch Class 26.8 Garbage Collection and Disposal 26.8.1 Disposal and the IDisposable Interface 26.8.2 Automatic Garbage Collection 26.8.3 Managed Memory Leaks 26.9 Summary and Conclusions 26.10 Exercises and Projects A1 Object-oriented Fundamentals A1.1 Introduction and Objectives A1.2 Object-oriented Paradigm A1.3 Generic Programming A1.4 Procedural Programming A1.5 Structural Relationships A1.5.1 Aggregation A1.5.2 Association A1.5.3 Generalisation/Specialisation (Gen/Spec Relationship) A1.6 An Introduction to Concept Modelling A1.6.1 The Defining Attribute View A1.6.2 The Prototype View A1.6.3 The Exemplar-based View A1.6.4 The Explanation-based View A1.7 Categorisation and Concept Levels A1.8 Whole–Part Pattern A1.8.1 Data Decomposition A1.9 Message-passing Concept versus Procedural Programming A2 Nonlinear Least-squares Minimisation A2.1 Introduction and Objectives A2.2 Nonlinear Programming and Multi-variable Optimisation A2.3 Nonlinear Least Squares A2.3.1 Nonlinear Regression A2.3.2 Simultaneous Nonlinear Equations A2.3.3 Derivatives of Sum-of-Squares Functions A2.4 Some Specific Methods A2.5 The ALGLIB Library A2.6 An Application to Curve Building A2.7 Rate Calibration Example A2.8 Exercises and Projects A3 The Mathematical Background to the Alternating Direction Explicit (ADE) Method A3.1 Introduction and Objectives A3.2 Background to ADE A3.3 Scoping the Problem: One-factor Problems A3.4 An Example: One-factor Black-Scholes PDE A3.5 Boundary Conditions A3.6 Example: Boundary Conditions for the One-factor Black-Scholes PDE A3.7 Motivating the ADE Method A3.8 The ADE Method Exposed A3.9 The Convection Term A3.10 Other Kinds of Boundary Conditions A3.11 Nonlinear Problems A3.12 ADE for PDEs in Conservative Form A3.13 Numerical Results and Guidelines A3.13.1 The Consequences of Conditional Consistency A3.13.2 Call Payoff Behaviour at the Far Field A3.13.3 General Formulation of the ADE Method A3.14 The Steps to Use when Implementing ADE A3.15 Summary and Conclusions A3.16 Exercises and Projects A4 Cap, Floor and Swaption Using Excel-DNA A4.1 Introduction A4.2 Different Ways of Stripping Cap Volatility A4.3 Comparing Caplet Volatility Surface A4.4 Call Put Parity A4.5 Cap Price Matrix A4.6 Multi-strike and Amortising A4.7 Simple Swaption Formula A4.8 Swaption Straddle A4.9 Exercises Bibliography Web References Index