  In this study, we discuss a machine learning technique to price exotic
options with two underlying assets based on a non-Gaussian Levy process model.
We introduce a new multivariate Levy process model named the generalized normal
tempered stable (gNTS) process, which is defined by time-changed multivariate
Brownian motion. Since the gNTS process does not provide a simple analytic
formula for the probability density function (PDF), we use the conditional
real-valued non-volume preserving (CRealNVP) model, which is a type of
flow-based generative network. Then, we discuss the no-arbitrage pricing on the
gNTS model for pricing the quanto option, whose underlying assets consist of a
foreign index and foreign exchange rate. We present the training of the
CRealNVP model to learn the PDF of the gNTS process using a training set
generated by Monte Carlo simulation. Next, we estimate the parameters of the
gNTS model with the trained CRealNVP model using the empirical data observed in
the market. Finally, we provide a method to find an equivalent martingale
measure on the gNTS model and to price the quanto option using the CRealNVP
model with the risk-neutral parameters of the gNTS model.
