Analytic Pricing of Contingent Claims Under the Real-World Measure

Shane Miller and Eckhard Platen ()

No 216, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: benchmark approach; real-world pricing; growth optimal portfolio; minimal market model; zero-coupon bonds; exchange prices; interest rate caps and floors (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2008-02-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Published as: Miller, S. and Platen, E., 2008, "Analytic Pricing of Contingent Claims Under the Real-World Measure", International Journal of Theoretical and Applied Finance, 11(8), 841-867.

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp216.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp216.pdf [301 Moved Permanently]--> https://www.uts.edu.au/globalassets/sites/default/files/qfr-archive-02/QFR-rp216.pdf)

Related works:
Journal Article: ANALYTIC PRICING OF CONTINGENT CLAIMS UNDER THE REAL-WORLD MEASURE (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:216

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().