Preface
1 Introduction to Derivative Instruments
1.1Financial Options and Their Trading Strategies
1.1.1Trading Strategies Involving Options
1.2Rational Boundaries for Option Values
1.2.1Effects of Dividend Payments
1.2.2Put-Call Parity Relations
1.2.3Foreign Currency Options
1.3Forward and Futures Contracts
1.3.1Values and Prices of Forward Contracts
1.3.2Relation between Forward and Futures Prices
1.4Swap Contracts
1.4.1Interest Rate Swaps
1.4.2Currency Swaps
1.5Problems
2 Financial Economics and Stochastic Calculus
2.1Single Period Securities Models
2.1.1Dominant Trading Strategies and Linear Pricing Measures
2.1.2Arbitrage Opportunities and Risk Neutral Probability Measures
2.1.3Valuation of Contingent Claims
2.1.4Principles of Binomial Option Pricing Model
2.2Filtrations, Martingales and Multiperiod Models
2.2.1Information Structures and Filtrations
2.2.2Conditional Expectations and Martingales
2.2.3Stopping Times and Stopped Processes
2.2.4Multiperiod Securities Models
2.2.5Multiperiod Binomial Models
2.3Asset Price Dynamics and Stochastic Processes
2.3.1Random Walk Models
2.3.2Brownian Processes
2.4Stochastic Calculus: Ito’’s Lemma and Girsanov’’s Theorem
2.4.1Stochastic Integrals
2.4.2Ito’’s Lemma and Stochastic Differentials
2.4.3Ito’’s Processes and Feynman-Kac Representation Formula
2.4.4Change of Measure: Radon-Nikodym Derivative and Girsanov’’s Theorem.
2.5Problems
3 Option Pricing Models: Blaek-Scholes-Merton Formulation
3.1Black-Scholes-Merton Formulation
3.1.1Riskless Hedging Principle
3.1.2Dynamic Replication Strategy
3.1.3Risk Neutrality Argument
3.2Martingale Pricing Theory
3.2.1Equivalent Martingale Measure and Risk Neutral Valuation
3.2.2Black-Scholes Model Revisited
3.3Black-Scholes Pricing Formulas and Their Properties
3.3.1Pricing Formulas for European Options
3.3.2Comparative Statics
3.4Extended Option Pricing Models
3.4.1Options on a Dividend-Paying Asset
3.4.2Futures Options
3.4.3Chooser Options
3.4.4Compound Options
3.4.5Merton’’s Model of Risky Debts
3.4.6Exchange Options
3.4.7Equity Options with Exchange Rate Risk Exposure
3.5Beyond the Black-Scholes Pricing Framework
3.5.1Transaction Costs Models
3.5.2Jump-Diffusion Models
3.5.3Implied and Local Volatilities
3.5.4Stochastic Volatility Models
3.6Problems
4 Path Dependent Options
4.1Barrier Options
4.1.1European Down-and-Out Call Options
4.1.2Transition Density Function and First Passage Time Density
4.1.3Options with Double Barriers
4.1.4Discretely Monitored Barrier Options
4.2Lookback Options
4.2.1European Fixed Strike Lookback Options
4.2.2European Floating Strike Lookback Options
4.2.3More Exotic Forms of European Lookback Options
4.2.4Differential Equation Formulation
4.2.5Discretely Monitored Lookback Options
4.3Asian Options.
4.3.1Partial Differential Equation Formulation
4.3.2Continuously Monitored Geometric Averaging Options
4.3.3Continuously Monitored Arithmetic Averaging Options
4.3.4Put-Call Parity and Fixed-Floating Symmetry Relations
4.3.5Fixed Strike Options with Discrete Geometric Averaging
4.3.6Fixed Strike Options with Discrete Arithmetic Averaging
4.4Problems
5 American Options
5.1Characterization of the Optimal Exercise Boundaries
5.1.1American Options on an Asset Paying Dividend Yield
5.1.2Smooth Pasting Condition.
5.1.3Optimal Exercise Boundary for an American Call
5.1.4Put-Call Symmetry Relations.
5.1.5American Call Options on an Asset Paying Single Dividend
5.1.6One-Dividend and Multidividend American Put Options
5.2Pricing Formulations of American Option Pricing Models
5.2.1Linear Complementarity Formulation
5.2.2Optimal Stopping Problem
5.2.3Integral Representation of the Early Exercise Premium
5.2.4American Barrier Options
5.2.5American Lookback Options
5.3Analytic Approximation Methods
5.3.1Compound Option Approximation Method
5.3.2Numerical Solution of the Integral Equation
5.3.3Quadratic Approximation Method
5.4 Options with Voluntary Reset Rights
5.4.1Valuation of the Shout Floor
5.4.2Reset-Strike Put Options
5.5Problems
6 Numerical Schemes for Pricing Options
7 Interest Rate Models and Bond Pricing
8 Interest Rate Derivatives: Bond Options, LIBOR and Swap Products
References
Author Index
Subject Index
