Automatic control variates for option pricing using neural networks

Abstract Many pricing problems boil down to the computation of a high-dimensional integral, which is usually estimated using Monte Carlo. In fact, accuracy Carlo estimator with M simulations given by σ M {\frac{\sigma}{\sqrt{M}}} . Meaning that its convergence immune dimension problem. However, this can be relatively slow depending on variance σ function integrated. To resolve such problem, one would perform some reduction techniques as importance sampling, stratification, or control variates. paper, we will study two approaches for improving Neural Networks. The first approach relies fact many financial are low effective dimensions. We expose method reduce in order keep only necessary variables. integration then done fast numerical Gaussian quadrature. second consists building an automatic variate neural networks. learn integrated (which incorporates diffusion model plus payoff function) build network highly correlated it. As use exactly, it variate.