Static and dynamic SABR stochastic volatility models: calibration and option pricing using GPUs

TL;DR

This paper demonstrates how GPU technology accelerates the calibration and option pricing of static and dynamic SABR stochastic volatility models, significantly reducing computational time and enabling Monte Carlo methods.

Contribution

It introduces GPU-accelerated algorithms for calibrating SABR models using Simulated Annealing and Monte Carlo simulations, including a novel expression for dynamic model parameters.

Findings

GPU speedup of around 200 times for asymptotic formula calibration

Monte Carlo calibration feasible with GPU, impractical on CPU

Numerical results confirm model accuracy and expected behavior

Abstract

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.