Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

Yijuan Liang and Xiuchuan Xu
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Yijuan Liang: Agricultural Education and Development Research Center, Southwest University, Chongqing 400715, China
Xiuchuan Xu: School of Economics and Management, Southwest University, Chonging 400715, China

Sustainability, 2019, vol. 11, issue 3, 1-21

Abstract: Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.

Keywords: conditional Monte Carlo; variance reduction; multi-asset options; stochastic volatility; martingale control variate (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2019
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