Analytic Pricing of Contingent Claims Under the Real-World Measure
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.
|Date of creation:||01 Feb 2008|
|Publication status:||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.|
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