A comparative study on barrier option pricing using antithetic and quasi Monte-Carlo simulations

Umeorah, Nneka ORCID: https://orcid.org/0000-0002-0307-5011 and Mashele, Phillip 2018. A comparative study on barrier option pricing using antithetic and quasi Monte-Carlo simulations. Journal of Mathematics and Statistics 14 (1) , pp. 94-106. 10.3844/jmssp.2018.94.106

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Abstract

Monte-Carlo simulations have been utilized greatly in the pricing of derivative securities. Over the years, several variance reduction techniques have been developed to curb the instability, as well as, increase the simulation efficiencies of the Monte-Carlo methods. Our approach in this research work will consider the use of antithetic variate techniques to estimate the fair prices of barrier options. Next, we use the quasi-Monte Carlo method, together with Sobol sequence to estimate the values of the same option. An extended version of the Black-Scholes model will serve as basis for the exact prices of these exotic options. The resulting simulated prices will be compared to the exact prices. The research concludes by showing some results which proves that when random numbers are generated via low discrepancy sequences in contrast to the normal pseudo-random numbers, a more efficient simulation method is ensued. This is further applicable in pricing complex derivatives without closed formsolutions.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Additional Information:	This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Publisher:	Science Publications
ISSN:	1549-3644
Date of First Compliant Deposit:	4 March 2022
Date of Acceptance:	7 May 2018
Last Modified:	15 May 2023 10:25
URI:	https://orca.cardiff.ac.uk/id/eprint/148026

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