An efficient conditional Monte Carlo method for European option pricing with stochastic volatility and stochastic interest rate

ABSTRACT

This paper studies the variance reduction methods for pricing European options under stochastic volatility and stochastic interest rate model. A general conditional Monte Carlo pricing framework is constructed to reduce the variance and save the time cost of Monte Carlo simulation. Based on Martingale Representation Theorem, two efficient martingale control variates are designed to combine with the conditional Monte Carlo simulation. Numerical results show that this hybrid method has great variance reduction effect and robust performance. The idea is also applicable for pricing other financial derivatives with stochastic volatility and/or stochastic interest rate.

KEYWORDS:

• Conditional Monte Carlo
• martingale control variate
• option pricing
• stochastic volatility
• stochastic interest rate

AMS CLASSIFICATIONS:

• 65C05
• 62P05
• 97M30

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yijuan Liang  http://orcid.org/0000-0002-4011-6601

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China [grant number 11626194] and the China Sponsorship Council [grant number 201806995034].