Pricing options under stochastic volatility: a power series approach (Q964675)

The authors present a new approach for solving the pricing equations (partial differential equations, PDEs) of European call options for very general stochastic models, including the Stein and Stein, the Hull and White, and the Heston models. The backward Kolmogorov PDEs, satisfied by the price function, are solved by a series expansion around zero in powers of the correlation coefficient. It turns out that direct processing of PDE permits to generate a whole family of PDEs with appropriate terminal conditions, whose solutions identify the coefficients of the series. Employing Duhamel's principle, the solutions are created recursively, and their probabilistic representation is given exploiting the Feynman-Kac formula. Under some regularity conditions, the convergence of the series with positive radius is proved. The estimation of error is also presented, if one replaces the series by a finite sum.