Modular Pricing of Options

Front Cover
Springer Science & Business Media, 2000 - Business & Economics - 170 pages
0 Reviews
The sound modeling of the smile effect is an important issue in quantitative finance as, for more than a decade, the Fourier transform has established itself as the most efficient tool for deriving closed-form option pricing formulas in various model classes. This book describes the applications of the Fourier transform to the modeling of volatility smile, followed by a comprehensive treatment of option valuation in a unified framework, covering stochastic volatilities and interest rates, Poisson and Levy jumps, including various asset classes such as equity, FX and interest rates, as well as various numberical examples and prototype programming codes. Readers will benefit from this book not only by gaining an overview of the advanced theory and the vast range of literature on these topics, but also by receiving first-hand feedback on the practical applications and implementations of the theory. The book is aimed at financial engineers, risk managers, graduate students and researchers.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
12 Constructing Characteristic Functions
5
13 Economic Interpretation of CFs
10
14 Examination of Existing Option Models
15
15 Equivalence of CFs to PDEs
19
Modular Pricing of Options MPO
25
22 Stochastic Volatilities
28
222 Square Root Process
30
Extensions of MPO to Exotic Options
99
32 Barrier Options
100
322 Two Special Cases
103
323 Numerical Examples
109
33 Lookback Options
115
332 Pricing Formulae with Stochastic Factors
116
34 Asian Options
122
342 The BlackScholes World
123

223 OrnsteinUhlenbeck Process
36
224 Double Square Root Process
49
23 Stochastic Interest Rates
56
232 Square Root Process
58
233 OrnsteinUhlenbeck Process
62
234 Double Square Root Process
65
24 Random Jumps
68
242 Pure Jumps
72
243 Lognormal Jumps
74
244 Pareto Jumps
77
25 Integrating the Modules
80
252 Pricing Kernels for Options and Bonds
87
SI versus SV
88
26 Appendices
93
Derivation of the CFs with Double Square Root Process
96
343 Asian Options in a Stochastic World
128
344 Approximations for Arithmetic Average Asian Options
132
345 A Model for Asian Interest Rate Options
135
35 Correlation Options
138
352 Exchange Options
142
353 Quotient Options
146
354 Product Options
147
36 Other Exotic Options
149
37 Appendices
151
Derivation of the CFs for Correlation Options
154
Conclusions
157
List for Notations and Symbols
161
References
163
Copyright

Common terms and phrases

References to this book

Bibliographic information