WILEY A John Wiley and Sons, Ltd., Publication

Transcription

1 Implementing Models of Financial Derivatives Object Oriented Applications with VBA Nick Webber WILEY A John Wiley and Sons, Ltd., Publication

2 Contents Preface xv PART I A PROCEDURAL MONTE CARLO METHOD IN VBA The Monte Carlo Method The Monte Carlo valuation method Issues with Monte Carlo Computational issues Summary Exercises Levels of Programming Sophistication 2.1 What makes a good application? 2.2 A high-level design 2.3 Progressing towards the ideal 2.4 Summary 2.5 Exercises Procedural Programming: Level Designing a Monte ^Carlo valuation application Deficiencies of the level 1 code Summary Exercises 36 Validation and Error Handling: Level Validation and error handling Encapsulating functionality The level 2 main () Summary Exercises 51

3 viii Contents PART II OBJECTS AND POLYMORPHISM 53 5 Introducing Objects: Level Objects in VBA An example: The stopwatch object Further helpful VBA features Objects in the Monte Carlo application 67,5.5 Summary 78 '5.6 Exercises v 78 6 Polymorphism and Interfaces: Level " Polymorphism Interfaces in VBA Implementing a polymorphic stopwatch Polymorphism and the Monte Carlo application Assessment of the polymorphic design Summary Exercises A Slice-Based Monte Carlo The revised Monte Carlo application object The option object The evolver object Summary Exercises An Embryonic Factory: Level Events The Level 5 Monte Carlo application The Factory object Output Summary, Exercises 133 PART HI USING FILES WITH VBA Input and Output to File in VBA File handling in VBA The TextStream and FileSystemObject objects Intrinsic VB language functions Example: Reading and writing to sequential and random files Summary Exercises Valuing a Book of Options Outline of the application Timings 174

4 Contents ix 10.3 Summary Exercises 176 PART IV POLYMORPHIC FACTORIES IN VBA The VBE Object Library and a Simple Polymorphic Factory Using the VBE object library A simple factory illustration 183 lf.3 Summary ' Exercises " A Fully Polymorphic Factory: Level Conceptual features The polymorphic factory Using the Factory object Summary Exercises A Semi-Polymorphic Factory: Meta-Classes The structure of the application Meta-class objects The semi-polymorphic factory Summary " Exercises 228 PART V PERFORMANCE ISSUES IN VBA Performance and Cost in VBA Arithmetic operations Procedure calls Data typing issues, Summary ' Exercises > Level and Performance Variations of the level 0 application Effect of level on times, Summary Exercises Evolution and Data Structures Data structures in VBA Using VBA containers Numerical comparisons Summary Exercises 277

5 x Contents PART VI VARIANCE REDUCTION IN THE MONTE CARLO METHOD Wiener Sample Paths and Antithetic Variates Generating Wiener sample paths Antithetic variates, Numerical assessment Summary 289,,17,5 Exercises The Wiener Process and Stratified Sampling :1 Stratified sampling " ' Jmplementing stratified sampling Numerical assessment Summary Exercises ' Low-Discrepancy Sampling Low-discrepancy sampling Implementing LD sampling Numerical assessment Summary Exercises Variance Reduction with Control Variates Control variates Examples of control variates Auxiliary model control variates Summary Exercises Implementing Control Variates A control variate application Numerical assessment ' Summary Exercises Extreme Options and Importance Sampling Importance Sampling Valuing an OTM digital option, Choices for the IS density Implementing importance sampling Numerical assessment Summary Exercises Combining Variance Reduction Methods Combining CV and IS Implementing variance reduction methods in combination 372 J

6 Contents 23.3 Numerical assessment Summary Exercises 386 PART VII THE MONTE CARLO METHOD: CONVERGENCE AND BIAS The Monte Carlo Method: Convergence and Bias Reducing bias s f2 Bias reduction methods ' * Bias and barrier options " Summary Exercises Discretization Methods Discretization and convergence Ito-Taylor discretization schemes, Schemes in 1-dimension > Predictor-corrector simulation Numerical assessment for benchmark processes Summary Exercises Applications to Models The CIR process Simulating discount factors Summary Exercises Valuation in the Heston Model Discretizing the Heston model Convergence in the Heston model Option valuation in the Heston model Summary \ Exercises 446 PART VIII VALUING AMERICAN OPTIONS BY SIMULATION Valuing American and Bermudan Options American options Monte Carlo and American options Summary Exercises Estimating the Early Exercise Boundary Approximating the continuation value function Choices for basis functions 463

7 xii Contents 29.3 The early exercise boundary Effect on valuation Summary Exercises The Plain LSLS Method Implementation in VBA Valuing the American put? Summary ^ Exercises., Control Variates and the LSLS Method Control variates and the American put Control variates and the EEB A two-pass LSLS Summary Exercises 511 Afterword 513 APPENDICES 515 A VBA and Excel 517 A.I Setting up Excel 517 A.2 Compiler problems in VBA 518 B Some Option Formulae 523 B.I Geometrically averaged average rate options 523 B.2 A quadratic payoff option 526 B.3 A Bermudan option 528 C The Utility Code Modules / 531 C.I The utility procedures 531 C.2 The complex number object 540 C.3 Quadrature 542 D Running DLLs from VBA 545 E Object-Oriented Programming 549 E.I Motivation for objects _ 549 E.2 Properties of objects 553 E.3 Implementing objects in VBA 556 E.4 Patterns of object use 559 E.5 Summary 565

8 Contents xiii F A Yukky Level 0 Monolithic Lattice Implementation 567 F.I Lattice methods 567 F.2 Implementing a level 0 lattice method 570 F.3 Summary 578 G A Level 1 Crank-Nicolson PDE Implementation 581 G.I PDE methods for derivative valuation 581 G.2 The Crank-Nicolson finite difference method 582 GV3 Implementing Crank-Nicolson ^ 585 G.4 Assessment of the design ' ' " G.5 ' Successive over-relaxation (SOR), 595 G.6 Summary 602 H Root-Finding and Minimization Algorithms 603 H.I Root finding algorithms 603 H.2 Minimization algorithms 610 H.3 Summary 612 VBA, Modelling, and Computing Glossary 613 Abbreviations 619 Coding, Notational, and Typographical Conventions Index to Code 623 Index to Spreadsheets 631 Index to Implementations 633 Index to Library Functions 637 Bibliography 641 Index - 645