Handbook of Financial Risk Management

Transcription

1 Handbook of Financial Risk Management Simulations and Case Studies N.H. Chan H.Y. Wong The Chinese University of Hong Kong WILEY

2 Contents Preface xi 1 An Introduction to Excel VBA How to Start Excel VBA / Introduction / Visual Basic Editor / The Macro Recorder / Insert a Command Button / VBA Programming Fundamentals / Declaration of Variables / Types of Variables / Multivariable Declaration / Declaration of Constants /, Operators / User-Defined Data Types / Arrays and Matrices / Data Input and Output / Conditional Statements / Loops / 16

3 VI CONTENTS 1.3 Linking VBA to C++ / Sub Procedures and Function Procedures / VBA Built-in Functions / Multiple Linear Regression / Random Number Generation / Inverse Transform / Acceptance-Rejection Method / List of Functions Defined in the Book / Constants / 28 v Types / General Functions / Asset Path Simulation Functions / Other Functions / Remarks / 32 2 Background A Brief Review of Martingales and Ito's Calculus / Martingales / Brownian Motion / Ito's Process and Ito's Lemma / Discretization Methods / The Black-Scholes Equation and Risk-Neutral Valuation / Change of Measures / Volatility / Mark to Market and Calibration / Marking to Market / Calculation of MTM Values / Calibration / Variance Reduction Techniques / A Brief Review of Variance Reduction Techniques / Pricing a Call Option / 68 3 Structured Products When Is Simulation Unnecessary? / Portfolio Replication Pricing / Equity-Linked Notes / Simulation of Black-Scholes Model and European Options / 73

4 CONTENTS VII 3.3 American Options / Empirical Martingale Correction / Range Accrual Notes / Possible Design and Sample Term Sheet / Closed-Form Solution for European RAN Under Black-Scholes Model / Callable and American Features / FX Accumulator: The Case of Citic Pacific LTD / Event Playback / Structure of an Accumulator / Accumulator Valuation / Sensitivity Analysis / Life Insurance Contracts / Introduction / Typical Contract Structures / Simulation Algorithms / Multi-Asset Instruments / Multi-Asset Range Accrual Equity-Linked Notes / Currency-Translated Products / Volatility Modeling Local Volatility Models: Simulation and Binomial Tree / Calibration of Local Volatility Function and Dupire Equation / Implied Binomial Tree / The Heston Stochastic Volatility Model / The Heston Model and Option Pricing / Model Calibration and Implementation / Calibration to European Options: Differential Evolution 1 / Simulation of Exotic Option Prices under Heston Model / Heston Stochastic Volatility Model Simulation Methods: Quadratic-Exponential Discretization Scheme / QE Discretization Scheme for V(i) I QE Discretization Scheme for S(0 / Performance Analysis of the QE Scheme / CITIC Case Study Revisited / The GARCH Option Pricing Model / Estimation of Model Parameters / 157

5 Vlll CONTENTS Identification of the Risk-Neutral Process / Pricing Exotics / Jump-Diffusion Model / Simulation of Asset Price Paths and Product Valuation / Estimation of Jump-Diffusion / Fixed-Income Derivatives I: Short-Rate Models Yield Curve Building / Building the Forward Rate Curve / The Hull-White Model / Calibration of the Hull-White Model / Pricing Interest Rate Products Using the Direction Simulation Approach / Target Redemption Notes / Interest Rate Range Accrual Notes / Pricing Interest Rate Products Using the Trinomial Tree Approach / Bond Price / Generalized Hull-White Model: The Tree Approach / Simulation Using the Trinomial Tree / Pricing Target Redemption Notes / Pricing Interest Rate Range Accrual Notes / Fixed-Income Derivatives II: LIBOR Market Models LIBOR Market Models / Pricing Formula for Caplets/Caps / Swaption Formula / Calibration to Caps and Swaptions / Simulation Across Different Forward Measures / Bermudan Swaptions in a Three-Factor Model / Epilogue / Credit Derivatives and Counterparty Credit Risk Structural Models of Credit Risk / The Merton Model / First Passage Time Model / The Vasicek Single-Factor Model / Credit Portfolio Management / Pricing Collateralized Debt Obligations / 266

6 CONTENTS IX 7.3 Copula Approach to Credit Derivative Pricing / Basic Concepts of Copulas / The Gaussian Copula and f-copula / Modeling Joint Default Times with Copulas / Pricing Basket Default Swaps / Counterparty Credit Risk / Exposure in Trading Derivatives with a Counterparty / Counterparty-Level Exposure / Collateral Modeling for Margined Portfolios / Credit Value Adjustment / Independence of Probability of Default and Exposure / Modeling Right-Way and Wrong-Way Risks / Value-at-Risk and Related Risk Measures Value-at-Risk / Parametric VaR / Two-Asset Case / Heavy-Tailed Distribution / Holding Period Adjustment / Portfolio VaR / Delta-Normal Approximation / Option VaR / Fixed-Income VaR / Delta-Gamma Approximation / Option VaR / Fixed-Income VaR / VaR Simulation Methods / Historical Simulation / Advantages and Disadvantages / Monte Carlo Simulation / Gibbs Sampling and Multivariate Normal Distribution / Advantages and Disadvantages / VaR-Related Risk Measures / Conditional Value-at-Risk / CVaR Distribution / Marginal, Incremental, and Component VaRs / VaR and CVaR in Local Volatility Models / 337

7 X CONTENTS 8.7 VaR Back-Testing / Back-Testing of VaR Models / The Greeks Black-Scholes Greeks / Greeks in a Binomial Tree / Finite Difference Approximation / Likelihood Ratio Method / Pathwise Derivative Estimates / Application to European Options / Application to Multi-Asset Derivatives / Application to Interest Rate Derivatives in LIBOR Market Model / Problem with the Adjoint Method / Greek Calculation with Discontinuous Payoffs / Functional Approximation for Digital Options / Vibrato Method for Digital Options / Multivariate Generalization / 379 Appendix 381 References 401 Author Index 405 Subject Index 407