Estimating multidimensional density functions for random variables in Wiener space

Abstract

The Malliavin–Thalmaier (Springer Finance, Springer-Verlag, Berlin, 2006) formula was introduced for the simulation of high dimensional probability density functions. However, when this integration by parts formula is applied directly in computer simulations, we show that it is unstable. We propose an approximation to the Malliavin–Thalmaier formula. In this Note, we find the order of the bias and the variance of the approximation error, and we apply the Malliavin–Thalmaier formula for the calculation of Greeks in finance. To cite this article: A. Kohatsu-Higa, K. Yasuda, C. R. Acad. Sci. Paris, Ser. I 346 (2008).