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

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