Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence

Abstract

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 probability density function (PDF) of the gNTS process is not given by a simple analytic formula, we use the conditional real-valued non-volume preserving (CRealNVP) model, which is a sort of flow-based generative networks. After that, 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 also 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.