Assessment of Accuracy of Finite Difference Methods in Evaluation of Options within Heston Model

The recent analytical closed-form result ('http://ssrn.com/abstract=2549033' http://ssrn.com/abstract=2549033) discovered by Market Memory Trading L.L.C. (“MMT”) for the probability density function of the European style options with stochastic volatility, considered within the Heston model, has allowed for the first time an opportunity to assess the approximate nature of various numerical methods used for evaluation of these options. Our goal is to investigate the accuracy of the popular Crank-Nicolson Method (CNM), a two-dimensional variant of the finite difference method, applied to the vanilla options with stochastic volatility. Exact results for option prices for wide ranges of parameters of the underlying return and its variance were supplied by MMT. For brevity, studies reported are restricted to call options