Quanto Option Pricing with Lévy Models

Abstract

We develop a multivariate Levy model for the pricing of quanto options that captures three characteristics observed in real-world market for stock prices and currencies: jumps, heavy tails and skewness. The model is developed by using a bottom-up approach from a subordinator. We do so by replacing the time of a Brownian motion with a non-decreasing Levy process, rapidly decreasing subordinator. We refer to this model as a multivariate rapidly decreasing Levy process. We consider two benchmarks: Black-Scholes and normal tempered stable process, the later constructed using a classical tempered stable subordinator. We then compare using a time series of daily log-returns and market prices of European-style quanto options the relative performance of the rapidly decreasing Levy process to that of Black-Scholes and the normal tempered stable process. We find that the proposed modeling process is superior to the other two processes for pricing quanto options.