Parallelized Local Volatility Estimation Using GP-GPU Hardware Acceleration

Abstract

We introduce an inverse problem for the local volatility model in option pricing. We solve the problem using the Levenberg-Marquardt algorithm and use the notion of the Frechet derivative when calculating the Jacobian matrix. We analyze the existence of the Frechet derivative and its numerical computation. To reduce the computational time of the inverse problem, a GP-GPU environment is considered for parallel computation. Numerical results confirm the validity and efficiency of the proposed method.