Efficient Variance Reduction for American Call Options Using Symmetry Arguments

Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the esti...

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Autores principales:	François-Michel Boire, R. Mark Reesor, Lars Stentoft
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	antithetic sampling control variates importance sampling Monte Carlo simulation put-call symmetry Risk in industry. Risk management HD61 Finance HG1-9999
Acceso en línea:	https://doaj.org/article/ffed81f9d5c44812bc1d4be51d003b80
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spelling	oai:doaj.org-article:ffed81f9d5c44812bc1d4be51d003b802021-11-25T18:08:20ZEfficient Variance Reduction for American Call Options Using Symmetry Arguments10.3390/jrfm141105041911-80741911-8066https://doaj.org/article/ffed81f9d5c44812bc1d4be51d003b802021-10-01T00:00:00Zhttps://www.mdpi.com/1911-8074/14/11/504https://doaj.org/toc/1911-8066https://doaj.org/toc/1911-8074Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the estimated call price by applying variance reduction techniques to corresponding symmetric put options. First, by comparing performance for pairs of call and (symmetric) put options for which the solution coincides, our results show that efficiency gains from variance reduction methods are different for calls and symmetric puts. Second, control variates should always be used and is the most efficient method. Furthermore, since control variates is more effective for puts than calls, and since symmetric pricing already offers some variance reduction, we demonstrate that drastic reductions in the standard deviation of the estimated call price is obtained by combining all three variance reduction techniques in a symmetric pricing approach. This reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets. Finally, we show that our findings are not particular to using in-sample pricing but also hold when using an out-of-sample pricing approach.François-Michel BoireR. Mark ReesorLars StentoftMDPI AGarticleantithetic samplingcontrol variatesimportance samplingMonte Carlo simulationput-call symmetryRisk in industry. Risk managementHD61FinanceHG1-9999ENJournal of Risk and Financial Management, Vol 14, Iss 504, p 504 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	antithetic sampling control variates importance sampling Monte Carlo simulation put-call symmetry Risk in industry. Risk management HD61 Finance HG1-9999
spellingShingle	antithetic sampling control variates importance sampling Monte Carlo simulation put-call symmetry Risk in industry. Risk management HD61 Finance HG1-9999 François-Michel Boire R. Mark Reesor Lars Stentoft Efficient Variance Reduction for American Call Options Using Symmetry Arguments
description	Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the estimated call price by applying variance reduction techniques to corresponding symmetric put options. First, by comparing performance for pairs of call and (symmetric) put options for which the solution coincides, our results show that efficiency gains from variance reduction methods are different for calls and symmetric puts. Second, control variates should always be used and is the most efficient method. Furthermore, since control variates is more effective for puts than calls, and since symmetric pricing already offers some variance reduction, we demonstrate that drastic reductions in the standard deviation of the estimated call price is obtained by combining all three variance reduction techniques in a symmetric pricing approach. This reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets. Finally, we show that our findings are not particular to using in-sample pricing but also hold when using an out-of-sample pricing approach.
format	article
author	François-Michel Boire R. Mark Reesor Lars Stentoft
author_facet	François-Michel Boire R. Mark Reesor Lars Stentoft
author_sort	François-Michel Boire
title	Efficient Variance Reduction for American Call Options Using Symmetry Arguments
title_short	Efficient Variance Reduction for American Call Options Using Symmetry Arguments
title_full	Efficient Variance Reduction for American Call Options Using Symmetry Arguments
title_fullStr	Efficient Variance Reduction for American Call Options Using Symmetry Arguments
title_full_unstemmed	Efficient Variance Reduction for American Call Options Using Symmetry Arguments
title_sort	efficient variance reduction for american call options using symmetry arguments
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ffed81f9d5c44812bc1d4be51d003b80
work_keys_str_mv	AT francoismichelboire efficientvariancereductionforamericancalloptionsusingsymmetryarguments AT rmarkreesor efficientvariancereductionforamericancalloptionsusingsymmetryarguments AT larsstentoft efficientvariancereductionforamericancalloptionsusingsymmetryarguments
_version_	1718411599430025216

Efficient Variance Reduction for American Call Options Using Symmetry Arguments

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