Quanto Option Pricing with Lévy Models

We develop a multivariate Lévy model and apply the bivariate model for the pricing of quanto options that captures three characteristics observed in real-world markets 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 Lévy process, exponential tilting subordinator. We refer to this model as a multivariate exponential tilting process. We then compare using a time series of daily log-returns and market prices of European-style quanto options the relative performance of the exponential tilting process to that of the Black–Scholes and the normal tempered stable process. We find that, due to more flexibility on capturing the information of tails and skewness, the proposed modeling process is superior to the other two processes for fitting market distribution and pricing quanto options.