Pricing Multi-strike Quanto Call Options on Multiple Assets with Stochastic Volatility, Correlation, and Exchange Rates

TL;DR

This paper develops and compares advanced stochastic models for pricing multi-asset quanto options with stochastic volatility, correlation, and exchange rates, demonstrating improved accuracy and efficiency in Monte Carlo simulations.

Contribution

It introduces a comprehensive framework combining GARCH-Jump SV, Weibull SC, and OU SER models, along with variance reduction and correlation hedging techniques for pricing multi-asset quanto options.

Findings

GARCH-Jump SV, Weibull SC, and OU SER model combination performs best.

Milstein discretization scheme balances speed and accuracy.

Incorporating mean reversion improves Monte Carlo pricing results.

Abstract

Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.