Importance sampling applied to Greeks for jump–diffusion models with stochastic volatility

Sergio De Diego, Eva Ferreira and Eulà lia Nualart

Journal of Computational Finance

Abstract: We develop a variance reduction technique, based on importance sampling in con- junction with the stochastic Robbins–Monro algorithm, for option prices of jump– diffusion models with stochastic volatility. This is done by combining the work developed by Arouna for pricing diffusion ;models, and extended by Kawai for Lévy processes without a Brownian ;component. We apply this technique to improve the numerical computation of derivative price sensitivities for general Lévy processes, allowing ;both Brownian ;and jump parts. Numerical ;examples are performed for both the Black–Scholes and Heston models with jumps and for the Barndorff–Nielsen–Shephard model to illustrate the efficiency ;of this numerical technique. The numerical results support that the proposed methodology improves the efficiency of the usual Monte Carlo procedures.

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