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arXiv · 1501.06084

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

Andrei Cozma·Matthieu Mariapragassam·Christoph Reisinger
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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.

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Andrei Cozma, Matthieu Mariapragassam, Christoph Reisinger. 2016-10-21. Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets. https://arxiv.org/abs/1501.06084

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