Exotic Option Pricing and Advanced Levy Models

A Levy process is a stochastic process that generalizes a Brownian motion with jumps or other features. Conceivably, they might be used in financial engineering to more accurately model the evolution of underlier values and address issues with volatility skew. Merton proposed their use in financial engineering in 1973, but research has gone well beyond the simple jump-diffusion process he used.

 

This book is an edited collection of articles on Levy processes in financial engineering. They survey the considerable literature and delve into a variety of topics. Be aware that most of this material is not yet ready for prime time. Little of it is actually used on trading floors. Accordingly, the book primarily targets researchers at the intersection of advanced probability theory and financial engineering.

The book is very mathematical, and it uses concepts from probability theory that most practicing financial engineers will have little familiarity with. The extensive lists of references mention more mathematics journals than they do finance journals.

Contents

1. Levy processes in finance distinguished by their coarse and fine path properties

2. Simulation methods with Levy processes

3. Risks in returns : a pure jump perspective

4. Model risk for exotic and moment derivatives

5. Symmetries and pricing of exotic options in Levy models

6. Static hedging of Asian options under stochastic volatility models using fast Fourier transform

7. Impact of market crises on real options

8. Moment derivatives and Levy-type market completion

9. Pricing perpetual American options driven by spectrally one-sided Levy processes

10. On Asian options of American type

11. Why be backward? : forward equations for American options

12. Numerical valuation of American options under the CGMY process

13. Convertible bonds : financial derivatives of game type

14. The spread option optimal stopping game

I think probability theorists who are interested in applying their expertise to financial engineers will find the book most useful, but people approaching the topic from a financial engineering background will, with some work, also find the material accessible.

Overall, the articles are excellent. They are substantive, rigorous and well written. For theorists who want to immerse themselves in the cutting-edge research on financial engineering with Levy processes, the book is superb. [11/18105]

 

For related books, see sections:

Financial Engineering - Intermediate Theory

Financial Engineering - Advanced Theory

Financial Engineering - Modeling Volatility

Mathematics - Stochastic Calculus

Finance - Financial Econometrics

Mathematics - Time Series Analysis

 

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