Analytic pricing of contingent claims under the real-world measure

Miller, SM; Platen, E

Analytic pricing of contingent claims under the real-world measure

Miller, SM Platen, E

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Publication Type:: Journal Article
Citation:: International Journal of Theoretical and Applied Finance, 2008, 11 (8), pp. 841 - 867
Issue Date:: 2008-12-01

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Field	Value	Language
dc.contributor.author	Miller, SM	en_US
dc.contributor.author	Platen, E https://orcid.org/0000-0003-4595-3123	en_US
dc.date.issued	2008-12-01	en_US
dc.identifier.citation	International Journal of Theoretical and Applied Finance, 2008, 11 (8), pp. 841 - 867	en_US
dc.identifier.issn	0219-0249	en_US
dc.identifier.uri	http://hdl.handle.net/10453/10069
dc.description.abstract	This article derives a series of analytic formulae for various contingent claims under the real-world probability measure using the stylised minimal market model (SMMM). This model provides realistic dynamics for the growth optimal portfolio (GOP) as a well-diversified equity index. It captures both leptokurtic returns with correct tail properties and the leverage effect. Under the SMMM, the discounted GOP takes the form of a time-transformed squared Bessel process of dimension four. From this property, one finds that the SMMM possesses a special and interesting relationship to non-central chi-square random variables with zero degrees of freedom. The analytic formulae derived under the SMMM include options on the GOP, options on exchange prices and options on zero-coupon bonds. For options on zero-coupon bonds, analytic prices facilitate efficient calculation of interest rate caps and floors. © 2008 World Scientific Publishing Company.	en_US
dc.relation.ispartof	International Journal of Theoretical and Applied Finance	en_US
dc.relation.isbasedon	10.1142/S0219024908005056	en_US
dc.subject.classification	Finance	en_US
dc.title	Analytic pricing of contingent claims under the real-world measure	en_US
dc.type	Journal Article
utslib.citation.volume	8	en_US
utslib.citation.volume	11	en_US
utslib.for	150201 Finance	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	15 Commerce, Management, Tourism and Services	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.issue	8	en_US
pubs.publication-status	Published	en_US
pubs.volume	11	en_US

Abstract:

This article derives a series of analytic formulae for various contingent claims under the real-world probability measure using the stylised minimal market model (SMMM). This model provides realistic dynamics for the growth optimal portfolio (GOP) as a well-diversified equity index. It captures both leptokurtic returns with correct tail properties and the leverage effect. Under the SMMM, the discounted GOP takes the form of a time-transformed squared Bessel process of dimension four. From this property, one finds that the SMMM possesses a special and interesting relationship to non-central chi-square random variables with zero degrees of freedom. The analytic formulae derived under the SMMM include options on the GOP, options on exchange prices and options on zero-coupon bonds. For options on zero-coupon bonds, analytic prices facilitate efficient calculation of interest rate caps and floors. © 2008 World Scientific Publishing Company.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/10069