Analytic Pricing of Contingent Claims Under the Real-World Measure

Shane Miller and Eckhard Platen ()
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Shane Miller: Citigroup Global Markets Australia Pty Ltd

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)
Date: 2008-02-01
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Journal Article: ANALYTIC PRICING OF CONTINGENT CLAIMS UNDER THE REAL-WORLD MEASURE (2008)
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Persistent link: http://EconPapers.repec.org/RePEc:uts:rpaper:216

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