Antonelli, Fabio - Scarlatti, Sergio

publication Finance and Stochastics ISSN 0949-2984 electronic: 1432-1122 publisher Springer Healthcare Communications year - volume - issue - page 2009 - 13 - 2 - 269 Pages 269 access full text

abstract

In this paper we present a new approach for solving the pricing equations (PDEs) of European call options for very general stochastic volatility models, including the Stein and Stein, the Hull and White, and the Heston models as particular cases. The main idea is to express the price in terms of a power series of the correlation parameter between the processes driving the dynamics of the price and of the volatility. The expansion is done around correlation zero and each term is identified via a probabilistic expression. It is shown that the power series converges with positive radius under some regularity conditions. Besides, we propose (as in Alós in Finance Stoch. 10:353–365, 2006) a further approximation to make the terms of the series easily computable and we estimate the error we commit. Finally we apply our methodology to some well-known financial models.

keyword(s)

Options, Stochastic volatility, SDEs, PDEs, Duhamel’s principle,