Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling

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Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling

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David Heath
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

Additional information is available for the following registered author(s):

Eckhard Platen

Abstract

This paper describes a two-factor model for a diversified market index using the growth optimal portfolio with a stochastic and possibly correlated intrinsic time scale. The index is modeled using a time transformed squared Bessel process of dimension four with a lognormal scaling factor for the time transformation. A consistent pricing and hedging framework is established by using the benchmark approach. here the numeraire is taken to be the growth optimal portfolio. Benchmarked traded prices appear as conditional expectations of future benchmarked prices under the real world probability measure. The proposed minimal market model with lognormal scaling produces the type of implied volatility term structures for European call nd put options typically observed in real markets. In addition, the prices of binary options and their deviations from corresponding Black-Scholes prices are examined.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 101.

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Date of creation: 01 Jun 2003
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Handle: RePEc:uts:rpaper:101

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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-06-02 (All new papers)
NEP-FIN-2004-06-02 (Finance)

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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. [Downloadable!]
Other versions:
- David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor and Francis Journals, vol. 6(3), pages 197-206, June. [Downloadable!] (restricted)
Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 1-22, March. [Downloadable!] (restricted)
Other versions:
- Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]

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