內容簡介

Books are written for use，and the best compliment that the community in the field could have paid to the first edition of 1998 was to buy out the printrun，and that of the corrected printing，as happened. Meanwhile，the fast-developing field of mathematical finance had moved on，as had our thinking，and it seemed better to recognize this and undertake a thorough-going re-write for the second edition than to tinker with the existing text.
 

目錄

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 Infinite Divisibility and the Levy-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 Definition 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
6.Mathematical Finance in Continuous Time
7.Incomplete Markets
8.Interest Rate Theory
9.Credit Risk
A.Hilbert Space
B.Projections and Conditional Expectations
C.The Separating Hyperplane Theorem
Bibliograpy
Index
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