Abstract
The Malliavin-Thalmaier formula was introduced in [4] for use in Monte-Carlo simulation. But when this formula is applied directly for computer simulation, we show that it is unstable. We propose an approximation of the Malliavin-Thalmaier formula. First we prove the central limit theorem to obtain the values of the parameters in Monte-Carlo simulations which achieves a prescribed error level. To prove it, we need the order of the bias and variance of the approximation error. Next we give an idea of the optimal approximation parameter and constants, which is often used in the kernel density estimation method. Finally we apply the Malliavin-Thalmaier formula and the approximated version to some models in finance and compare their results.
