In this second edition of their popular text, the authors take into account recent developments in the field, and changes in their own thinking and teaching.

The chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on:

· Infinite divisibility and Lévy processes
· Lévy-based models in incomplete markets

Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.

Contents
Preface to the Second Edition
Preface to the First Edition
1. Derivative Background
1.1 Financial Markets and Instruments
1.1.1 Derivative Instruments
1.1.2 Underlying Securities
1.1.3 Markets
1.1.4 Types of Traders
1.1.5 Modeling Assumptions
1.2 Arbitrage
1.3 Arbitrage Relationships
1.3.1 Fundamental Determinants of Option Values
1.3.2 Arbitrage Bounds
1.4 Single-period Market Models
1.4.1 A Fundamental Example
1.4.2 A Single-period Model
1.4.3 A Few Financial-economic Considerations
Exercises 2. Probability Background
2.1 Measure
2.2 Integral
2.3 Probability
2.4 Equivalent Measures and Radon-Nikodym Derivatives
2.5 Conditional Expectation
2.6 Modes of Convergence
2.7 Convolution and Characteristic Functions
2.8 The Central Limit Theorem
2.9 Asset Return Distributions
2.10 In.nite Divisibility and the L¿evy-Khintchine Formula
2.11 Elliptically Contoured Distributions
2.12 Hyberbolic Distributions
Exercises 3. Stochastic Processes in Discrete Time
3.1 Information and Filtrations
3.2 Discrete-parameter Stochastic Processes
3.3 De.nition and Basic Properties of Martingales
3.4 Martingale Transforms
3.5 Stopping Times and Optional Stopping
3.6 The Snell Envelope and Optimal Stopping
3.7 Spaces of Martingales
3.8 Markov Chains
Exercises 4. Mathematical Finance in Discrete Time
4.1 The Model
4.2 Existence of Equivalent Martingale Measures
4.2.1 The No-arbitrage Condition
4.2.2 Risk-Neutral Pricing
4.3 Complete Markets: Uniqueness of EMMs
4.4 The Fundamental Theorem of Asset Pricing: Risk-Neutral Valuation
4.5 The Cox-Ross-Rubinstein Model
4.5.1 Model Structure
4.5.2 Risk-neutral Pricing
4.5.3 Hedging
4.6 Binomial Approximations
4.6.1 Model Structure
4.6.2 The Black-Scholes Option Pricing Formula
4.6.3 Further Limiting Models
4.7 American Options
4.7.1 Theory
4.7.2 American Options in the CRR Model
4.8 Further Contingent Claim Valuation in Discrete Time
4.8.1 Barrier Options
4.8.2 Lookback Options
4.8.3 A Three-period Example
4.9 Multifactor Models
4.9.1 Extended Binomial Model
4.9.2 Multinomial Models
Exercises 5. Stochastic Processes in Continuous Time
5.1 Filtrations; Finite-dimensional Distributions
5.2 Classes of Processes
5.2.1 Martingales
5.2.2 Gaussian Processes
5.2.3 Markov Processes
5.2.4 Diffusions
5.3 Brownian Motion
5.3.1 Definition and Existence
5.3.2 Quadratic Variation of Brownian Motion
5.3.3 Properties of Brownian Motion
5.3.4 Brownian Motion in Stochastic Modeling
5.4 Point Processes
5.4.1 Exponential Distribution
5.4.2 The Poisson Process
5.4.3 Compound Poisson Processes
5.4.4 Renewal Processes
5.5 Levy Processes
5.5.1 Distributions
5.5.2 Levy Processes
5.5.3 Levy Processes and the Levy-Khintchine Formula
5.6 Stochastic Integrals; Ito Calculus
5.6.1 Stochastic Integration
5.6.2 Itös Lemma
5.6.3 Geometric Brownian Motion
5.7 Stochastic Calculus for Black-Scholes Models
5.8 Stochastic Differential Equations
5.9 Likelihood Estimation for Diffusions
5.10 Martingales, Local Martingales and Semi-martingales
5.10.1 Definitions
5.10.2 Semi-martingale Calculus
5.10.3 Stochastic Exponentials
5.10.4 Semi-martingale Characteristics
5.11 Weak Convergence of Stochastic Processes
5.11.1 The Spaces Cd and Dd
5.11.2 Definition and Motivation
5.11.3 Basic Theorems of Weak Convergence
5.11.4 Weak Convergence Results for Stochastic Integrals
Exercises 6. Mathematical Finance in Continuous Time
6.1 Continuous-time Financial Market Models
6.1.1 The Financial Market Model
6.1.2 Equivalent Martingale Measures
6.1.3 Risk-neutral Pricing
6.1.4 Changes of Numeraire