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Evaluating moving average options is a tough computational challenge for theenergy and commodity market as the payoff of the option depends on the pricesof a certain underlying observed on a moving window so, when a long window isconsidered, the pricing problem becomes high dimensional. We present anefficient method for pricing Bermudan style moving average options, based onGaussian Process Regression and Gauss-Hermite quadrature, thus named GPR-GHQ.Specifically, the proposed algorithm proceeds backward in time and, at eachtime-step, the continuation value is computed only in a few points by usingGauss-Hermite quadrature, and then it is learned through Gaussian ProcessRegression. We test the proposed approach in the Black-Scholes model, where theGPR-GHQ method is made even more efficient by exploiting the positivehomogeneity of the continuation value, which allows one to reduce the problemsize. Positive homogeneity is also exploited to develop a binomial Markovchain, which is able to deal efficiently with medium-long windows. Secondly, wetest GPR-GHQ in the Clewlow-Strickland model, the reference framework formodeling prices of energy commodities. Finally, we consider a challengingproblem which involves double non-Markovian feature, that is the rough-Bergomimodel. In this case, the pricing problem is even harder since the whole historyof the volatility process impacts the future distribution of the process. Themanuscript includes a numerical investigation, which displays that GPR-GHQ isvery accurate and it is able to handle options with a very long window, thusovercoming the problem of high dimensionality.

Moving average options: Machine Learning and Gauss-Hermite quadrature for a double non-Markovian problem