Modular Pricing of Options
An Application of Fourier
Analysis
Zhu,
J., Eberhard-Karls-Universität Tübingen, Germany
This book provides a
comprehensive, up-to-date treatment of the application of Fourier analyses to pricing
standard and exotic options, and discusses three different factors: stochastic volatility,
stochastic interest rate and random jump. The modeling of volatility and interest rate
falls into four different alternatives: constant, mean-reverting Ornstein-Uhlenbeck
process, mean-reverting square root process and mean-reverting double square root process,
while random jumps are specified as pure jumps, lognormal jumps and Pareto jumps. This
framework called Modular Pricing of Options includes most of the existing options pricing
formulas as special cases.
Keywords: Fourier analysis,
Option pricing, Stochastic volatility, Random jumps, Stochastic interest rate
170 pages