For the calibration of the parameters in static and dynamic SABR stochastic volatility models, we propose the application of the GPU technology to the Simulated Annealing global optimization algorithm and to the Monte Carlo simulation. This calibration has been performed for EURO STOXX 50 index and EUR/USD exchange rate with an asymptotic formula for volatility or Monte Carlo simulation. Moreover, in the dynamic model we propose an original more general expression for the functional parameters, specially well suited for the EUR/USD exchange rate case. Numerical results illustrate the expected behavior of both SABR models and the accuracy of the calibration. In terms of computational time, when the asymptotic formula for volatility is used the speedup with respect to CPU computation is around 200 with one GPU. Furthermore, GPU technology allows the use of Monte Carlo simulation for calibration purposes, the computational time with CPU being prohibitive.

© 2013 Elsevier. This manuscript version is made available under the CCBY- NC-ND 4.0 license https://creativecommons.org/licenses/by-ncnd/ 4.0/. This version of the article has been accepted for publication in Mathematics and Computers in Simulation (ISSN 1872-7166). The Version of Record is available online at 10.1016/j.matcom.2013.05.007. Derechos Atribución-NoComercial-SinDerivadas 3.0 España