Discretising the Heston model: an analysis of the weak convergence rate

摘要

In this article, we analyse the weak convergence rate of a discretisation scheme for the Heston model. Under mild assumptions on the smoothness of the payoff, and on the Feller index of the volatility process, respectively, we establish a weak convergence rate of order one. Moreover, under almost minimal assumptions, we obtain weak convergence without a rate. These results are accompanied by several numerical examples. Our error analysis relies on a classical technique from Talay&Tubaro (1990), a recent regularity estimate for the Heston PDE (Feehan & Pop, 2013) and Malliavin calculus.