Efficient simulation of the price and the sensitivities of basket options under time-changed Brownian motions

ABSTRACT

We propose a new variance reduction method for the price and the sensitivities of basket options under time-changed Brownian motion models. The new algorithm combines the pathwise derivative method with control variates, conditional Monte Carlo, and randomized quasi–Monte Carlo. Control variates are constructed by using the conditioning variables of lower bounds of basket options for the purpose of variance reduction. Conditional Monte Carlo further reduces the variance by integrating out the selected conditioning variable. The smoothing effect of conditional Monte Carlo enhances the pathwise derivative and the randomized quasi–Monte Carlo methods. Computational experiments show that the new algorithm yields significant variance reductions.

KEYWORDS:

• Basket options
• Greeks
• time-changed Brownian motion
• Monte Carlo
• variance reduction
• randomized quasi–Monte Carlo

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 91G60

Acknowledgements

I thank Prof. Wolfgang Hörmann and Prof. David Goldsman for their helpful suggestions and for proofreading the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by Boğaziçi Research Fund Project 6923 and The Scientific and Technological Research Council of Turkey (TÜBİTAK) 2219 International Postdoctoral Research Scholarship Program.