論波動率模型

3.Foreign tation tation

內容簡介

《論波動率模型》基於筆者於倫敦帝國理工學院和三菱UFJ證券國際（倫敦）的聯合項目中所完成的金融數

學博士論文.該聯合項目始於2005年年底，旨在探討隨機波動率在股票、外匯、利率等金融資產的建模中的套用以及基於此模型之上對金融衍生品的定價。隨機（非常量）的波動率模型是近些年來熱門的金融數學研究方向，特別是在2008年金融危機動盪的市場中更是受到了學術界和金融業界的熏視，《論波動率模型》最大的貢獻在於提供了當前最全面的隨機金融模型架構，包括隨機波動率、局部波動率、隨機利率以及跳躍過程對外匯走勢的建模，以及對金融衍生品（歐式期權）定價的半解析解。其他幾個章節涉及了對另外的波動率模型的提出和討論，以及隨機波動率模型在金融業界中的實際套用和衍生品定價的範例。
筆者利用跨學術和金融業界的優勢，為大家展現了國際金融工程學術研究和金融衍生品發展的最前沿畫卷。

目錄

List of Figures
List of Tables
Abstract
Acknowledgements
l.General Introduction, Changing Volatility Models and European Options Pricing
1.1 Generallntroduction
1. 2 Introduction to Changing Volatility Models
1. 3 Model Completeness and European Option Pricing
1.4 Single Period Volatility Changing Problems
1. 4. 1 Fixed Volatility Changing Time with BamerB
1. 4. 2 Random Volatility Changing Time with a Hitting BarrierB
1.5 Multi-Period Volatility Changing Problems
1.6 Extension to Incomplete Market
1. 6. 1 A Simple Random Volatility Changing Model
Extension to Stochastic Volatility Model
1. 6. 2 Future Research
1.7 Appendix: Proof
1. 7. 1 Proof of Proposition 1. 1
1. 7. 2 Proof of Proposition 1. 2
1. 7. 3 Proof of Proposition 1. 3
1. 7.4 Proof of Proposition 1. 4
1. 7. 5 Proof of Proposition 1. 5
1. 7. 6 Proof of Proposition 1. 6
1. 7. 7 Theorem 2. 2 of [132] : Uniqueness of the
F.quivalent martingale Measure
2.Introduction to Stochastic Volatility and Local Stochastic Volati
lity Models
2. 1 Stochastic Volatility Models-A General Set-Up
2. 1. 1 Model Set-Up
2. 1. 2 Change of Measure and Model Incompleteness
2. 2 Making the Stochastic Volatility Economy Complete
2. 3 European Option Price
2. 4 Local Stochastic Volatility Models: An Introduction
2. 5 Adjustment to the Calculation of GREEKS in a Non
Constant Implied Volatility Model
3.Foreign Exchange Options with Local Stochastic Volatility and Stochastic Interest Rates
3. 1 Introduction
3.2 The FX-IR Hybrid Model
3.3 Asymptotic Expansion
3. 3. 1 A Brief Introduction
3. 3. 2 European Option Pricing and Implied Volatility
3.4 Model Implementation and Numerical Results
3. 5 FX Option Pricing via Fourier Transform under Stochastic Interest Rates, Stochastic Volatility and the Jump Process
3. 5. 1 The Multi-Factor Model
3. 5. 2 Change of Measure and Option Pricing
3. 5. 3 Model Implementation
3. 5. 4 Calibration Results for the USD/JPY Market
3. 6 Perfect Hedging with Stochastic Interest Rates and Local Stochastic Volatility
3. 6. 1 Hedging with Options
……
4. Non-Biased Monte Carlo Simulation for a Heston-Type Stochastic Volatility Model
5. The LIBOR Market Model with Stochastic Volatility and Jump
Processes
Bibliography