內容簡介

本書旨在講述研究現代金融市場衍生證券，如期權、期貨和交換業務等所需的數學知識。建立在著名的Black-Scholes理論基礎上的理想化連續時間模型需要對現代微積分有較深的了解。然而，書中許多潛在的知識點完全可以在離散時間的框架內理解。本書是在第1版的基礎上做了較多增補，使得連續時間理論應用范圍更加廣泛，更加詳細地介紹Black-Scholes模型及其推廣、期限結構和消費投資問題。增加的內容有：一致性風險測度及其在對沖中的應用；一般離散市場模型中資產估價的第一基本定理；不完全離散市場的套利區間；完全離散市場的特征；Black-Scholes模型中的風險、回報和靈敏度。本書內容安排相當謹慎、詳細，而不是泛泛羅列所有盡可能多的內容，對期權的處理相當精辟。通過本書的學習，讀者也可以了解更多的科研動態。目次：套利定價；鞅測度；第一基本定理；完全市場；離散時間美國期權；連續時間隨機計算；美國賣方期權；債券和期限結構；消費投資策略；風險度量。

讀者對象：數學專業的研究生、科研人員以及具有一定數學背景的金融愛好者。
 

目錄

Preface
Preface to the Second Edition
1 Prlcing by Arbitrage
1.1 Introduction: Pricing and Hedging
1.2 Single-Period Option Pricing Models
1.3 A General Single-Period Model
1.4 A Single-Period Binomial Model
1.5 Multi-period Binomial Models
1.6 Bounds on Option Prices
2 Martingale Measures
2.1 A General Discrete-Time Market Model
2.2 Trading Strategies
2.3 Martingales and Risk-Neutral Pricing
2.4 Arbitrage Pricing: Martingale Measures
2.5 Strategies Using Contingent Claims
2.6 Example: The Binomial Model
2.7 From CRR to Blaek-Scholes
3 The First Fundamental Theorem
3.1 The Separating Hyperplane Theorem in Rn
3.2 Construction of Martingale Measures
3.3 Pathwise Description
3.4 Examples
3.5 General Discrete Models
4 Complete Markets
4.1 Completeness and Martingale Representation
4.2 Completeness for Finite Market Models
4.3 The CRR Model
4.4 The Splitting Index and Completeness
4.5 Incomplete Models: The Arbitrage Interval
4.6 Characterisation of Complete Models
5 Discrete-time American Options
5.1 Hedging American Claims
5.2 Stopping Times and Stopped Processes
5.3 Uniformly Integrable Martingales
5.4 Optimal Stopping: The Snell Envelope
5.5 Pricing and Hedging American Options
5.6 Consumption-Investment Strategies
6 Continuous-Time Stochastic Calculus
6.1 Continuous-Time Processes
6.2 Martingales
6.3 Stochastic Integrals
6.4 The It8 Calculus
6.5 Stochastic Differential Equations
6.6 Markov Property of Solutions of SDEs
7 Continuous-Time European Options
7.1 Dynamics
7.2 Girsanov’’s Theorem
7.3 Martingale Representation
7.4 Self-Financing Strategies
7.5 An Equivalent Martingale Measure
7.6 Black-Scholes Prices
7.7 Pricing in a Multifactor Model
7.8 Barrier Options
7.9 The Black-Scholes Equation
7.10 The Greeks
8 The American Put Option
8.1 Extended Trading Strategies
8.2 Analysis of American Put Options
8.3 The Perpetual Put Option
8.4 Early Exercise Premium
8.5 Relation to Free Boundary Problems
8.6 An Approximate Solution
9 Bonds and Term Structure
9.1 Market Dynamics
9.2 Future Price and Futures Contracts
9.3 Changing Numeraire
9.4 A General Option Pricing Formula
9.5 Term Structure Models
9.6 Short-rate Diffusion Models
9.7 The Heath-Jarrow-Morton Model
9.8 A Markov Chain Model
10 Consumption-Investment Strategies
10.1 Utility Functions
10.2 Admissible Strategies
10.3 Maximising Utility of Consumption
10.4 Maximisation of Terminal Utility
10.5 Consumption and Terminal Wealth
11 Measures of Risk
11.1 Value at Risk
11.2 Coherent Risk Measures
11.3 Deviation Measures
11.4 Hedging Strategies with Shortfall Risk
Bibliography
Index
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