Contents. Part I Introduction to Option Pricing

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1 Part I Introduction to Option Pricing 1 Asset Pricing Basics Fundamental Concepts State Prices in a One-Period Binomial Model Probabilities and Numeraires Asset Pricing with a Continuum of States Introduction to Option Pricing An Incomplete Markets Example Problems Continuous-Time Models Simulating a Brownian Motion Quadratic Variation ItôProcesses Itô sformula Multiple Itô Processes Examples of Itô s Formula Reinvesting Dividends Geometric Brownian Motion Numeraires and Probabilities Tail Probabilities of Geometric Brownian Motions Volatilities Problems Black-Scholes Digital Options Share Digitals Puts and Calls Greeks DeltaHedging... 55

2 XII 3.6 Gamma Hedging Implied Volatilities Term Structure of Volatility Smiles and Smirks Calculations in VBA Problems Estimating and Modelling Volatility Statistics Review Estimating a Constant Volatility and Mean Estimating a Changing Volatility GARCHModels Stochastic Volatility Models Smiles and Smirks Again Hedging and Market Completeness Problems Introduction to Monte Carlo and Binomial Models Introduction to Monte Carlo Introduction to Binomial Models Binomial Models for American Options Binomial Parameters Binomial Greeks Monte Carlo Greeks I: Difference Ratios Monte Carlo Greeks II: Pathwise Estimates Calculations in VBA Problems Part II Advanced Option Pricing 6 Foreign Exchange Currency Options Options on Foreign Assets Struck in Foreign Currency Options on Foreign Assets Struck in Domestic Currency Currency Forwards and Futures Quantos Replicating Quantos QuantoForwards Quanto Options ReturnSwaps Uncovered Interest Parity Problems...125

3 XIII 7 Forward, Futures, and Exchange Options Margrabe sformula Black sformula Merton sformula Deferred Exchange Options Calculations in VBA GreeksandHedging The Relation of Futures Prices to Forward Prices Futures Options Time-Varying Volatility Hedging with Forwards and Futures Market Completeness Problems Exotic Options Forward-Start Options Compound Options American Calls with Discrete Dividends Choosers Options on the Max or Min Barrier Options Lookbacks Basket and Spread Options Asian Options Calculations in VBA Problems More on Monte Carlo and Binomial Valuation Monte Carlo Models for Path-Dependent Options Binomial Valuation of Basket and Spread Options Monte Carlo Valuation of Basket and Spread Options Antithetic Variates in Monte Carlo Control Variates in Monte Carlo Accelerating Binomial Convergence Calculations in VBA Problems Finite Difference Methods Fundamental PDE Discretizing the PDE Explicit and Implicit Methods Crank-Nicolson European Options American Options Barrier Options

4 XIV 10.8 Calculations in VBA Problems Part III Fixed Income 11 Fixed Income Concepts The Yield Curve LIBOR Swaps Yield to Maturity, Duration, and Convexity Principal Components Hedging Principal Components Problems Introduction to Fixed Income Derivatives Caps and Floors Forward Rates Portfolios that Pay Spot Rates The Market Model for Caps and Floors The Market Model for European Swaptions A Comment on Consistency Caplets as Puts on Discount Bonds Swaptions as Options on Coupon Bonds Calculations in VBA Problems Valuing Derivatives in the Extended Vasicek Model The Short Rate and Discount Bond Prices The Vasicek Model Estimating the Vasicek Model Hedging in the Vasicek Model Extensions of the Vasicek Model Fitting Discount Bond Prices and Forward Rates Discount Bond Options, Caps and Floors Coupon Bond Options and Swaptions Captions and Floortions Yields and Yield Volatilities The General Hull-White Model Calculations in VBA Problems...293

5 XV 14 A Brief Survey of Term Structure Models Ho-Lee Black-Derman-Toy Black-Karasinski Cox-Ingersoll-Ross Longstaff-Schwartz Heath-Jarrow-Morton Market Models Again Problems Appendices A Programming in VBA A.1 VBA Editor and Modules A.2 Subroutines and Functions A.3 Message Box and Input Box A.4 Writing to and Reading from Cells A.5 VariablesandAssignments A.6 Mathematical Operations A.7 RandomNumbers A.8 ForLoops A.9 While Loops and Logical Expressions A.10 If, Else, and ElseIf Statements A.11 Variable Declarations A.12 VariablePassing A.13 Arrays A.14 Debugging B Miscellaneous Facts about Continuous-Time Models B.1 Girsanov stheorem B.2 The Minimum of a Geometric Brownian Motion B.3 BesselSquaredProcessesandtheCIRModel List of Programs List of Symbols References Index...353

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