Monte Carlo acceleration method for pricing variance derivatives under stochastic volatility models with jump diffusion

Abstract

Monte Carlo acceleration method for pricing variance derivatives under stochastic volatility models with jump diffusion is researched in the paper. Control variate and importance sampling techniques are used to reduce the variance of the simulated price of the derivative. Based on the closed-form solution of a simplified model with piecewise deterministic volatility and jump diffusion, control variate technique is proposed to reduce the simulation errors. Then importance sampling method is also introduced to solve the rare event of the jump part in the model. Through the analysis of the first and second moments of the underlying processes and simplified processes, the method to construct the efficient control variate is proposed. Importance sampling method enhances the effects of the control variate technique. The numerical experiments illustrate the high efficiency of the acceleration method, in accordance with the theoretical analysis. The methods in the paper can also be extended to the pricing of other path-dependent derivatives.

Keywords:

• Monte Carlo
• variance derivatives
• stochastic volatility
• control variate

2010 AMS Subject Classifications:

• 35C05
• 65C05
• 60J65

Acknowledgements

The authors are very grateful for the anonymous referee's suggestions and helpful comments.

This work was supported by the National Natural Science Foundations of China (No.11226252 and No.11171256), the Special Fund for Shanghai Colleges Outstanding Young Teachers Scientific Research Project (No.ZZCD12007), Shanghai Pujiang Program (No.11PJC059), E-Institute of Shanghai Municipal Education Commission (No.03004) and Research Projects of Young Teachers in SUFE (No.2011220656).