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

Author: 

Cozma, A
Mariapragassam, M
Reisinger, C

Publication Date: 

24 January 2018

Journal: 

SIAM Journal on Financial Mathematics

Last Updated: 

2021-07-21T02:08:44.97+01:00

Issue: 

1

Volume: 

9

DOI: 

10.1137/17M1114569

page: 

127-170

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.

Symplectic id: 

743788

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article