論波動率模型

內(nèi)容概要

　　本書基于筆者于倫敦帝國理工學(xué)院和三菱UFJ證券國際（倫敦）的聯(lián)合項目中所完成的金融數(shù)學(xué)博士論文.該聯(lián)合項目始于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(chǎn)的建模中的應(yīng)用以及基于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(shù)學(xué)研究方向，特別是在2008年金融危機動蕩的市場中更是受到了學(xué)術(shù)界和金融業(yè)界的熏視，本書最大的貢獻在于提供了當(dāng)前最全面的隨機金融模型架構(gòu)，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(quán)）定價的半解析解。其他幾個章節(jié)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(yè)界中的實際應(yīng)用和衍生品定價的范例。
　　筆者利用跨學(xué)術(shù)和金融業(yè)界的優(yōu)勢，為大家展現(xiàn)了國際金融工程學(xué)術(shù)研究和金融衍生品發(fā)展的最前沿畫卷。

書籍目錄

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

媒體關(guān)注與評論

　  Cong Yi investigates a variety of models for Stochastic Volatility. The book is organised by discussing results first and proofs later. The aim of the book, and the aim of the author, is to produce something useful. The first chapter looks at a changing volatility model where the volatility is constant between stopping times. This is of considerable theoretical interest and can be extended to a class of bounded path wise continuous volatilities.Subsequent Chapters, 2,3,visit Local stochastic Volatility Models and apply these in FX looking at specific classes of financial products. I think these chapters will be of considerable interest to practitioners and, perhaps,also the Monte -Carlo method discussed in Chapter 4. The final chapter looks at a heavyweight Libor market model incorporating Stochastic Volatility and Jumps. Formal expressions for the prices of Caplets and Swaptions are found here but Cong Yi, suggest that the real difficulties lie in the effiaentgreek computation,which may serve as future research topic.　  ——Dr,Chris Barnett Distingusished Research Fellow,Mathematical Finance,Imperial College London　  When Cong Yi was a PhD student of Imperial College, he was sponsored by Mitsubishi UFJ Securities International and worked part time at the department of Risk and Product Development under the guidance ofme.（I am director and Head of Product Development.） His main research at the bank is to investigate models with more advanced features and capabilities to reflect market conditions and movements than the stand ard Black Scholes theory. This work is of great interest in both academic research and practical application. A largepart of his PhD thesis is based on this research, cou pIed with some other fundamental theoretical explorationsin finance. I believe his thesis will attract broad readers.　  ——Dr.Yanmin Li President of Chinese Association of Financial Executives

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