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|
|Date of revision:|
|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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- Eckhard Platen, 2003.
"An Alternative Interest Rate Term Structure Model,"
Research Paper Series
97, Quantitative Finance Research Centre, University of Technology, Sydney.
- Eckhard Platen, 2005. "An Alternative Interest Rate Term Structure Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 717-735.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Shane Miller & Eckhard Platen, 2004.
"A Two-Factor Model for Low Interest Rate Regimes,"
Asia-Pacific Financial Markets,
Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 107-133, March.
- Hardy Hulley & Shane Miller & Eckhard Platen, 2005. "Benchmarking and Fair Pricing Applied to Two Market Models," Research Paper Series 155, Quantitative Finance Research Centre, University of Technology, Sydney.
- David Heath & Eckhard Platen, 2006.
"Local volatility function models under a benchmark approach,"
Taylor & Francis Journals, vol. 6(3), pages 197-206.
- David Heath & Eckhard Platen, 2004. "Local Volatility Function Models under a Benchmark Approach," Research Paper Series 124, Quantitative Finance Research Centre, University of Technology, Sydney.
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