Deep Importance Sampling

TL;DR

This paper introduces a neural network-based importance sampling method for variance reduction in Monte Carlo simulations of path-dependent financial payoffs, demonstrating significant variance reduction and robustness.

Contribution

It proposes a novel path-dependent importance sampling algorithm using neural networks to adaptively reduce variance in Monte Carlo estimations for complex financial derivatives.

Findings

Variance reduction factors between 2 and 9 achieved.

Method is robust and suitable for offline training updates.

Effective for various complex payoff structures.

Abstract

We present a generic path-dependent importance sampling algorithm where the Girsanov induced change of probability on the path space is represented by a sequence of neural networks taking the past of the trajectory as an input. At each learning step, the neural networks' parameters are trained so as to reduce the variance of the Monte Carlo estimator induced by this change of measure. This allows for a generic path dependent change of measure which can be used to reduce the variance of any path-dependent financial payoff. We show in our numerical experiments that for payoffs consisting of either a call, an asymmetric combination of calls and puts, a symmetric combination of calls and puts, a multi coupon autocall or a single coupon autocall, we are able to reduce the variance of the Monte Carlo estimators by factors between 2 and 9. The numerical experiments also show that the method is very robust to changes in the parameter values, which means that in practice, the training can be done offline and only updated on a weekly basis.