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

Zhang Sumei,Zhao Jieqiong

doi:10.1155/2017/3912036

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.

Highlights

A barrier option is a path-dependent option which is exterminated or initiated if the underlying spot price hits the specified barrier level during the life of the option
This paper presents an extension of the double Heston stochastic volatility model by combining Hull-White stochastic interest rates
We propose the double Heston Hull-White (DHHW) model by combining the double Heston stochastic volatility and Hull-White stochastic interest rate

Summary

Introduction

A barrier option is a path-dependent option which is exterminated (knocked out) or initiated (knocked in) if the underlying spot price hits the specified barrier level during the life of the option. Many papers [3,4,5,6,7,8,9] evaluate barrier options under one-factor stochastic volatility models. In recent literatures [14,15,16,17], Hull-White stochastic interest rate which is analytically tractable has been incorporated into one-factor stochastic volatility model for pricing path-dependent options. The model which incorporates multifactor stochastic volatility and stochastic interest rate may be more reasonable for pricing barrier options. The main purpose of this paper is to provide a Monte Carlo method for pricing barrier options under a two-factor stochastic volatility and stochastic interest rate model. The paper develops an efficient Monte Carlo algorithm for pricing barrier options.

The Pricing Model

Simulation Scheme for the DHHW Model

Simulation Algorithm for Pricing Barrier Options

Conclusion

10 Ma5turity