Risk-Neutral Pricing of Quanto Options with Generative Machine Learning Techniques

In this article, we develop an option pricing model for exotic options using generative machine learning techniques. We focus on pricing exotic options with dual underlying assets, utilizing a non-Gaussian Lévy process called the generalized normal tempered stable (gNTS) process. This multivariate process, a variation of time-changed multivariate Brownian motion, lacks a straightforward analytic formula for its probability density function. To overcome this, we employ the conditional real-valued non-volume preserving (CRealNVP) model, a type of flow-based generative network, to approximate the probability density function. We then explore no-arbitrage pricing within the gNTS framework for a quanto option. The CRealNVP model is trained to learn the probability density function of the gNTS distribution through a training set derived from Monte Carlo simulations. Subsequently, we use this trained model to estimate the parameters of the gNTS model based on empirical market data. Finally, we propose a methodology to establish an equivalent martingale measure for the gNTS model, enabling us to price the quanto option using the risk-neutral parameters obtained via the CRealNVP model. This comprehensive approach integrates advanced machine learning techniques with financial modeling to enhance the pricing accuracy of complex financial derivatives.