ContentsPreface 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 Arbitrage1.3 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 Expectation2.
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 LÂ'evy-Khintchine Formula 2.11 Elliptically Contoured Distributions2.12 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 Stopping3.6 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 Measures4.2.1 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 Valuation4.5 The Cox-Ross-Rubinstein Model 4.5.1 Model Structure4.5.2 Risk-neutral Pricing 4.
5.3 Hedging 4.6 Binomial Approximations4.6.1 Model Structure4.6.2 The Black-Scholes Option Pricing Formula 4.6.
3 Further Limiting Models 4.7 American Options 4.7.1 Theory4.7.2 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 Motion5.3.4 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 Formula5.6 Stochastic Integrals; Ito Calculus 5.6.
1 Stochastic Integration5.6.2 Ito's Lemma 5.6.3 Geometric Brownian Motion 5.7 Stochastic Calculus for Black-Scholes Models5.8 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 Calculus5.10.3 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 IntegralsExercises 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 6.2 The Generalized Black-Scholes Model 6.2.1 The Model 6.2.
2 Pricing and Hedging Contingent Claims 6.2.3 The Greeks 6.2.4 Volatility 6.3 Further Contingent Claim Valuation 6.3.1 American Options 6.
3.2 Asian Options 6.3.3 Barrier Options 6.3.4 Lookback Options 6.3.5 Binary Options 6.
4 Discrete- versus Continuous-time Market Models 6.4.1 Discrete- to Continuous-timeConvergence Reconsidered 6.4.2 Finite Market Approximations 6.4.3 Examples of Finite Market Approximat.