  In this work, we present a novel machine learning approach for pricing
high-dimensional American options based on the modified Gaussian process
regression (GPR). We incorporate deep kernel learning and sparse variational
Gaussian processes to address the challenges traditionally associated with GPR.
These challenges include its diminished reliability in high-dimensional
scenarios and the excessive computational costs associated with processing
extensive numbers of simulated paths Our findings indicate that the proposed
method surpasses the performance of the least squares Monte Carlo method in
high-dimensional scenarios, particularly when the underlying assets are modeled
by Merton's jump diffusion model. Moreover, our approach does not exhibit a
significant increase in computational time as the number of dimensions grows.
Consequently, this method emerges as a potential tool for alleviating the
challenges posed by the curse of dimensionality.
