A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs

In this article we propose a new more general calibration of the Heston Stochastic-Local Volatility (HSLV) model. More precisely, the main contribution is to perform the direct calibration of the whole set of parameters at the same time instead of the usual two steps procedure. Moreover, the propose...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2020-11, Vol.177, p.467-486
Main Authors: Ferreiro-Ferreiro, Ana María, García-Rodríguez, José A., Souto, Luis, Vázquez, Carlos
Format: Article
Language:English
Subjects:
Calibration
Differential Evolution
Global optimization
Heston
Monte Carlo
Multi-GPU
Simulated Annealing
Stochastic-Local Volatility
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Summary:In this article we propose a new more general calibration of the Heston Stochastic-Local Volatility (HSLV) model. More precisely, the main contribution is to perform the direct calibration of the whole set of parameters at the same time instead of the usual two steps procedure. Moreover, the proposed approach allows to use exotic options to calibrate the HSLV model, thus making it more flexible and general. However, as there are no analytical formulas available to price exotic options to calibrate the model, the cost function (the HSLV pricer) involved in the calibration process must be computed using Monte Carlo methods, thus leading to a highly demanding computational problem. Therefore, we also propose efficient parallel GPU implementations of Monte Carlo techniques for the pricers. Furthermore, for solving the resulting global optimization problem, we develop customized parallel multi-CPU implementations of two of the most common stochastic metaheuristic global optimization algorithms: Differential Evolution and Simulated Annealing. A comparison between both algorithms has been made. This second level of parallelization has been carried out by the implementation of the cost function as a single GPU kernel and keeping the OpenMP parallelization for the optimization algorithm, thus leading to a hybrid multi-GPU implementation of the calibrator. All these implementations have been tested with real market data for European and barrier options in the context of foreign exchange markets.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2020.04.001