Robust product Markovian quantization

Rudd, R; McWalter, TA; Kienitz, J; Platen, E

Robust product Markovian quantization

Rudd, R McWalter, TA Kienitz, J Platen, E

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Publisher:: Infopro Digital Services
Publication Type:: Journal Article
Citation:: Journal of Computational Finance, 2022, 25, (4), pp. 55-78
Issue Date:: 2022-01-01

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Field	Value	Language
dc.contributor.author	Rudd, R
dc.contributor.author	McWalter, TA
dc.contributor.author	Kienitz, J
dc.contributor.author	Platen, E https://orcid.org/0000-0003-4595-3123
dc.date.accessioned	2022-12-13T04:30:13Z
dc.date.available	2022-12-13T04:30:13Z
dc.date.issued	2022-01-01
dc.identifier.citation	Journal of Computational Finance, 2022, 25, (4), pp. 55-78
dc.identifier.issn	1460-1559
dc.identifier.issn	1755-2850
dc.identifier.uri	http://hdl.handle.net/10453/164359
dc.description.abstract	Recursive marginal quantization (RMQ) allows the construction of optimal discrete grids for approximating solutions to stochastic differential equations in d dimensions. Product Markovian quantization (PMQ) reduces this problem to d onedimensional quantization problems by recursively constructing product quantizers, as opposed to a truly optimal quantizer. However, the standard Newton–Raphson method used in the PMQ algorithm suffers from numerical instabilities, inhibiting widespread adoption, especially for use in calibration. By directly specifying the random variable to be quantized at each time step, we show that PMQ, and RMQ in one dimension, can be expressed as standard vector quantization. This reformulation allows the application of the accelerated Lloyd algorithm in an adaptive and robust procedure. Further, in the case of stochastic volatility models, we extend the PMQ algorithm by using higher-order updates for the volatility or variance process. We illustrate the technique for European options using the Heston model, and more exotic products using the stochastic alpha–beta–rho (SABR) model.
dc.language	English
dc.publisher	Infopro Digital Services
dc.relation.ispartof	Journal of Computational Finance
dc.relation.isbasedon	10.21314/JCF.2021.015
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 1502 Banking, Finance and Investment
dc.title	Robust product Markovian quantization
dc.type	Journal Article
utslib.citation.volume	25
utslib.for	0102 Applied Mathematics
utslib.for	0103 Numerical and Computational Mathematics
utslib.for	1502 Banking, Finance and Investment
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access	*
pubs.consider-herdc	false
dc.date.updated	2022-12-13T04:30:11Z
pubs.issue	4
pubs.publication-status	Published
pubs.volume	25
utslib.citation.issue	4

Abstract:

Recursive marginal quantization (RMQ) allows the construction of optimal discrete grids for approximating solutions to stochastic differential equations in d dimensions. Product Markovian quantization (PMQ) reduces this problem to d onedimensional quantization problems by recursively constructing product quantizers, as opposed to a truly optimal quantizer. However, the standard Newton–Raphson method used in the PMQ algorithm suffers from numerical instabilities, inhibiting widespread adoption, especially for use in calibration. By directly specifying the random variable to be quantized at each time step, we show that PMQ, and RMQ in one dimension, can be expressed as standard vector quantization. This reformulation allows the application of the accelerated Lloyd algorithm in an adaptive and robust procedure. Further, in the case of stochastic volatility models, we extend the PMQ algorithm by using higher-order updates for the volatility or variance process. We illustrate the technique for European options using the Heston model, and more exotic products using the stochastic alpha–beta–rho (SABR) model.

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http://hdl.handle.net/10453/164359