Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension

Understand

In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique.

• Specifically, the options we consider are written on a basket of assets, each of them following a Black-Scholes dynamics.
• In the wake of Ludkovski's approach (2018), we implement here a backward dynamic programming algorithm which considers a finite number of uniformly distributed exercise dates.
• On these dates, the option value is computed as the maximum between the exercise value and the continuation value, which is obtained by means of Gaussian process regression technique and Monte Carlo simulations.