Multi-Asset Option Pricing Using Normal Tempered Stable Processes with Stochastic Correlation

Abstract

In this article, the authors develop a new multi-asset option pricing model where underlying dynamics are assumed to follow the normal tempered stable (NTS) process and its correlation structure evolves over time. The model is constructed by extending the constant correlation term in the previous NTS framework to the stochastic correlation making use of the Ornstein-Uhlenbeck process. We then derive its closed-form solution under the risk-neutral measure and apply it to an empirical study of a quanto option. The in-sample tests and calibration practices justify our model specification reflecting the empirical stylized facts on asset returns such as heavy tails, skewness, kurtosis, and stochastic correlation. Building on the empirical results, we can also identify the presence of stochastic correlation in the risk-neutral world.