SPX Calibration of Option Approximations under Rough Heston Model

The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also known as rough Heston model has been derived as th...

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Autores principales:	Siow Woon Jeng, Adem Kiliçman
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	rough Heston model option pricing Padé approximants approximation formulas SPX calibration Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4e175e19895b4d31acd2b0240ec5ef2a
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id	oai:doaj.org-article:4e175e19895b4d31acd2b0240ec5ef2a
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spelling	oai:doaj.org-article:4e175e19895b4d31acd2b0240ec5ef2a2021-11-11T18:14:36ZSPX Calibration of Option Approximations under Rough Heston Model10.3390/math92126752227-7390https://doaj.org/article/4e175e19895b4d31acd2b0240ec5ef2a2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2675https://doaj.org/toc/2227-7390The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also known as rough Heston model has been derived as the macroscopic level of microscopic Hawkes process where it acts as a high-frequency price process. Unlike the pricing of options under the classical Heston model, it is significantly harder to price options under rough Heston model due to the large computational cost needed. Previously, some studies have proposed a few approximation methods to speed up the option computation. In this study, we calibrate five different approximation methods for pricing options under rough Heston model to SPX options, namely a third-order Padé approximant, three variants of fourth-order Padé approximant, and an approximation formula made from decomposing the option price. The main purpose of this study is to fill in the gap on lack of numerical study on real market options. The numerical experiment includes calibration of the mentioned methods to SPX options before and after the Lehman Brothers collapse.Siow Woon JengAdem KiliçmanMDPI AGarticlerough Heston modeloption pricingPadé approximantsapproximation formulasSPX calibrationMathematicsQA1-939ENMathematics, Vol 9, Iss 2675, p 2675 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	rough Heston model option pricing Padé approximants approximation formulas SPX calibration Mathematics QA1-939
spellingShingle	rough Heston model option pricing Padé approximants approximation formulas SPX calibration Mathematics QA1-939 Siow Woon Jeng Adem Kiliçman SPX Calibration of Option Approximations under Rough Heston Model
description	The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also known as rough Heston model has been derived as the macroscopic level of microscopic Hawkes process where it acts as a high-frequency price process. Unlike the pricing of options under the classical Heston model, it is significantly harder to price options under rough Heston model due to the large computational cost needed. Previously, some studies have proposed a few approximation methods to speed up the option computation. In this study, we calibrate five different approximation methods for pricing options under rough Heston model to SPX options, namely a third-order Padé approximant, three variants of fourth-order Padé approximant, and an approximation formula made from decomposing the option price. The main purpose of this study is to fill in the gap on lack of numerical study on real market options. The numerical experiment includes calibration of the mentioned methods to SPX options before and after the Lehman Brothers collapse.
format	article
author	Siow Woon Jeng Adem Kiliçman
author_facet	Siow Woon Jeng Adem Kiliçman
author_sort	Siow Woon Jeng
title	SPX Calibration of Option Approximations under Rough Heston Model
title_short	SPX Calibration of Option Approximations under Rough Heston Model
title_full	SPX Calibration of Option Approximations under Rough Heston Model
title_fullStr	SPX Calibration of Option Approximations under Rough Heston Model
title_full_unstemmed	SPX Calibration of Option Approximations under Rough Heston Model
title_sort	spx calibration of option approximations under rough heston model
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4e175e19895b4d31acd2b0240ec5ef2a
work_keys_str_mv	AT siowwoonjeng spxcalibrationofoptionapproximationsunderroughhestonmodel AT ademkilicman spxcalibrationofoptionapproximationsunderroughhestonmodel
_version_	1718431882147790848

SPX Calibration of Option Approximations under Rough Heston Model

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