Foreign exchange options on Heston-CIR model under L\'{e}vy process framework

TL;DR

This paper develops a new Heston-CIR Le9vy process model for foreign exchange options, providing improved pricing formulas and numerical methods validated with real market data.

Contribution

It introduces a novel four-factor Heston-CIR Le9vy model with proven solution properties and applies LSM for American option pricing under stochastic volatility and interest rates.

Findings

New pricing formula fits market data better

Proven existence and uniqueness of the model solution

Numerical results demonstrate model effectiveness

Abstract

In this paper, we consider the Heston-CIR model with L\'{e}vy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and uniqueness of the solution to this model. Second, we examine the strong convergence of the L\'{e}vy process with stochastic domestic short interest rates, foreign short interest rates and stochastic volatility. Then, we apply Least Squares Monte Carlo (LSM) method for pricing American options under our model with stochastic volatility and stochastic interest rate. Finally, by considering real-world market data, we illustrate numerical results for the four-factor Heston-CIR L\'{e}vy model.