Pricing Power Options under the Heston Dynamics using the FFT

Numerous studies have presented evidence that certain financial assets may exhibit stochastic volatility or jumps, which cannot be captured within the Black-Scholes environment. This work investigates the valuation of power options when the variance follows the Heston model of stochastic volatility. A closed form representation of the characteristic function of the process is derived from the partial differential equation (PDE) of the replicating portfolio. The characteristic function is essential for the computation of the European power option prices via the Fast Fourier Transform (FFT) technique. Numerical results are presented.