In this paper we propose an efficient method to compute the price of American basket options, based on Machine Learning and Monte Carlo simulations  . Specifically, the options we consider are written on a basket of assets, each of them following a Black-Scholes dynamics. The method we propose is a backward dynamic programming algorithm which considers a finite number of uniformly distributed exercise dates. On these dates, the value of the option is computed as the maximum between the exercise value and the continuation value, which is approximated via Gaussian Process Regression. Specifically, we consider a finite number of points, each of them representing the values reached by the underlying at a certain time. First of all, we compute the continuation value only for these points by means of Monte Carlo simulations and then we employ Gaussian Process Regression to approximate the whole continuation value function . Numerical tests show that the  algorithm is fast and reliable  and it can handle also American options on very large baskets of assets, overcoming the problem of the curse of dimensionality.
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 . Such a method performs well for low dimension baskets but it is not accurate for very high dimension baskets. In order to improve the dimension range, we employ the European option price as a control variate, which allows us to treat very large baskets and moreover to reduce the variance of price estimators . Numerical tests show that the proposed algorithm is fast and reliable , and it can handle also American options on very large baskets of assets, overcoming the problem of the curse of dimensionality.
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In the wake of Ludkovski's approach (2018), we implement here
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value of the option
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approximated via Gaussian Process Regression. Specifically, we consider a finite number of points, each of them representing the values reached by the underlying at a certain time. First of all, we compute the continuation value only for these points by means of
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and then we employ Gaussian Process Regression to approximate the whole continuation value function
. Such a method performs well for low dimension baskets but it is not accurate for very high dimension baskets. In order to improve the dimension range, we employ the European option price as a control variate, which allows us to treat very large baskets and moreover to reduce the variance of price estimators
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