Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling
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.
|Date of creation:||01 Jun 2003|
|Publication status:||Published as: Heath, D. and Platen, E., 2003, "Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling", Quantitative Finance, 3(6), 442-450.|
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- Eckhard Platen, 2001.
"A Minimal Financial Market Model,"
Research Paper Series
48, Quantitative Finance Research Centre, University of Technology, Sydney.
- Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
- Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
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