Kwok Yue-Kuen. Mathematical Models of Financial Derivatives

Springer, 2008. — 541 p. — ISBN 3540422889.An update of a classic in the field, the first edition gained a good reputation and was on of the earliest introductory textbooks in mathematical finance
Mathematical Models of Financial Derivatives is a textbook on the theory behind:
Modeling derivatives using the financial engineering approach, focussing on the martingale pricing principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are
Analyzed, emphasizing on the aspects of pricing, hedging and their risk management. Starting from the renowned Black-Scholes-Merton formulation of option pricing model, readers are guided through the text on the new advances on the state-of-the-art derivative pricing models and interest rate models. Both analytic techniques and numerical methods for solving various types of derivative pricing models are emphasized.
The second edition presents a substantial revision of the first edition. The continuous-time martingale pricing theory is motivated through analysis of the underlying financial economics principles within a discrete-time framework. A large collection of closed-form formulas of various forms of exotic equity and fixed income derivatives are documented. The most recent research results and methodologies are made accessible to readers through the extensive set of exercises at the end of each chapter.
Yue-Kuen Kwok is Professor of Mathematics at Hong Kong University of Science and Technology. He is the author of over 80 research papers and several books, including Applied Complex Variables. He is an associate editor of Journal of Economic Dynamics and Control and Asia-Pacific Financial Markets.Introduction to Derivative Instruments
Financial Options and Their Trading Strategies
Trading Strategies Involving Options
Rational Boundaries for Option Values
Effects of Dividend Payments
Put-Call Parity Relations
Foreign Currency Options
Forward and Futures Contracts
Values and Prices of Forward Contracts
Relation between Forward and Futures Prices
Swap Contracts
Interest Rate Swaps
Currency Swaps
Problems
Financial Economics and Stochastic Calculus
Single Period Securities Models
Dominant Trading Strategies and Linear Pricing Measures
Arbitrage Opportunities and Risk Neutral Probability
Measures
Valuation of Contingent Claims
Principles of Binomial Option Pricing Model
Filtrations, Martingales and Multiperiod Models
Information Structures and Filtrations
Conditional Expectations and Martingales
Stopping Times and Stopped Processes
Multiperiod Securities Models
Multiperiod Binomial Models
Asset Price Dynamics and Stochastic Processes
Random Walk Models
Brownian Processes
Stochastic Calculus: Ito’s Lemma and Girsanov’s Theorem
Stochastic Integrals
Ito’s Lemma and Stochastic Differentials
Ito’s Processes and Feynman–Kac Representation Formula
Change of Measure: Radon–Nikodym Derivative and
Girsanov’s Theorem
Problems
Option Pricing Models: Black–Scholes–Merton Formulation
Black–Scholes–Merton Formulation
Riskless Hedging Principle
Dynamic Replication Strategy
Risk Neutrality Argument
Martingale Pricing Theory
Equivalent Martingale Measure and Risk Neutral Valuation
Black–Scholes Model Revisited
Black–Scholes Pricing Formulas and Their Properties
Pricing Formulas for European Options
Comparative Statics
Extended Option Pricing Models
Options on a Dividend-Paying Asset
Futures Options
Chooser Options
Compound Options
Merton’s Model of Risky Debts
Exchange Options
Equity Options with Exchange Rate Risk Exposure
Beyond the Black–Scholes Pricing Framework
Transaction Costs Models
Jump-Diffusion Models
Implied and Local Volatilities
Stochastic Volatility Models
Problems
Path Dependent Options
Barrier Options
European Down-and-Out Call Options
Transition Density Function and First Passage Time Density
Options with Double Barriers
Discretely Monitored Barrier Options
Lookback Options
European Fixed Strike Lookback Options
European Floating Strike Lookback Options
More Exotic Forms of European Lookback Options
Differential Equation Formulation
Discretely Monitored Lookback Options
Asian Options
Partial Differential Equation Formulation
Continuously Monitored Geometric Averaging Options
Continuously Monitored Arithmetic Averaging Options
Put-Call Parity and Fixed-Floating Symmetry Relations
Fixed Strike Options with Discrete Geometric Averaging
Fixed Strike Options with Discrete Arithmetic Averaging
Problems
American Options
Characterization of the Optimal Exercise Boundaries
American Options on an Asset Paying Dividend Yield
Smooth Pasting Condition
Optimal Exercise Boundary for an American Call
Put-Call Symmetry Relations
American Call Options on an Asset Paying Single Dividend
One-Dividend and Multidividend American Put Options
Pricing Formulations of American Option Pricing Models
Linear Complementarity Formulation
Optimal Stopping Problem
Integral Representation of the Early Exercise Premium
American Barrier Options
American Lookback Options
Analytic Approximation Methods
Compound Option Approximation Method
Numerical Solution of the Integral Equation
Quadratic Approximation Method
Options with Voluntary Reset Rights
Valuation of the Shout Floor
Reset-Strike Put Options
Problems
Numerical Schemes for Pricing Options
Lattice Tree Methods
Binomial Model Revisited
Continuous Limits of the Binomial Model
Discrete Dividend Models
Early Exercise Feature and Callable Feature
Trinomial Schemes
Forward Shooting Grid Methods
Finite Difference Algorithms
Construction of Explicit Schemes
Implicit Schemes and Their Implementation Issues
Front Fixing Method and Point Relaxation Technique
Truncation Errors and Order of Convergence
Numerical Stability and Oscillation Phenomena
Numerical Approximation of Auxiliary Conditions
Monte Carlo Simulation
Variance Reduction Techniques
Low Discrepancy Sequences
Valuation of American Options
Problems
Interest Rate Models and Bond Pricing
Bond Prices and Interest Rates
Bond Prices and Yield Curves
Forward Rate Agreement, Bond Forward and Vanilla Swap
Forward Rates and Short Rates
Bond Prices under Deterministic Interest Rates
One-Factor Short Rate Models
Short Rate Models and Bond Prices
Vasicek Mean Reversion Model
Cox–Ingersoll–Ross Square Root Diffusion Model
Generalized One-Factor Short Rate Models
Calibration to Current Term Structures of Bond Prices
Multifactor Interest Rate Models
Short Rate/Long Rate Models
Stochastic Volatility Models
Affine Term Structure Models
Heath–Jarrow–Morton Framework
Forward Rate Drift Condition
Short Rate Processes and Their Markovian Characterization
Forward LIBOR Processes under Gaussian HJM Framework
Problems
Interest Rate Derivatives: Bond Options, LIBOR and Swap Products
Forward Measure and Dynamics of Forward Prices
ForwardMeasure
Pricing of Equity Options under Stochastic Interest Rates
Futures Process and Futures-Forward Price Spread
Bond Options and Range Notes
Options on Discount Bonds and Coupon-Bearing Bonds
Range Notes
Caps and LIBOR Market Models
Pricing of Caps under Gaussian HJM Framework
Black Formulas and LIBOR Market Models
Swap Products and Swaptions
Forward Swap Rates and Swap Measure
Approximate Pricing of Swaption under Lognormal LIBOR Market Model
Cross-Currency Swaps
ProblemsAuthor Index
Subject Index