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Machine learning methods, such as Gaussian process regression (GPR), havebeen widely used in recent years for pricing American options. GPR isconsidered as a potential method for estimating the continuation value of anoption in the regression-based Monte Carlo method. However, it has somedrawbacks, such as the unreliability in high-dimensional cases and the highcomputational cost when the number of simulated paths is large. In this paper,we apply the deep kernel learning and variational inference to GPR in order toovercome these drawbacks, and test its performance under geometric Brownianmotion and Merton's jump diffusion models. The experiments show that theproposed method outperforms the Least Square Monte Carlo method inhigh-dimensional cases, especially with jump diffusion models.

A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-dimensional American Options