Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets

Abstract

We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the log-Euler scheme for the exchange rate. We establish the exponential integrability of full truncation Euler approximations for the Cox-Ingersoll-Ross process and find a lower bound on the explosion time of these exponential moments. Under a full correlation structure and a realistic set of assumptions on the so-called leverage function, we prove the strong convergence of the exchange rate approximations and deduce the convergence of Monte Carlo estimators for a number of vanilla and path-dependent options. Then, we perform a series of numerical experiments for an autocallable barrier dual currency note.

38 pages

References in corpus (1)

• Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries

Cited by in corpus (3)

• A mixed Monte Carlo and PDE variance reduction method for foreign exchange options under the Heston-CIR model
• Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process
• Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models