  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.
