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Mathematical Problems in Engineering
Volume 2017, Article ID 3912036, 8 pages
https://doi.org/10.1155/2017/3912036
Research Article

Efficient Simulation for Pricing Barrier Options with Two-Factor Stochastic Volatility and Stochastic Interest Rate

School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China

Correspondence should be addressed to Zhang Sumei; moc.anis@iemusggnahz

Received 11 August 2017; Accepted 8 October 2017; Published 14 November 2017

Academic Editor: Fazal M. Mahomed

Copyright © 2017 Zhang Sumei and Zhao Jieqiong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents an extension of the double Heston stochastic volatility model by combining Hull-White stochastic interest rates. By the change of numeraire and quadratic exponential scheme, this paper develops a new simulation scheme for the extended model. By combining control variates and antithetic variates, this paper provides an efficient Monte Carlo simulation algorithm for pricing barrier options. Based on the differential evolution algorithm the extended model is calibrated to S&P 500 index options to obtain the model parameter values. Numerical results show that the proposed simulation scheme outperforms the Euler scheme, the proposed simulation algorithm is efficient for pricing barrier options, and the extended model is flexible to fit the implied volatility surface.