Pricing of index options under a minimal market model with log-normal 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 timescale. The index is modelled using a time transformed squared Bessel process with a log-normal 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 log-normal scaling produces the type of implied volatility term structures for European call and 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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Volume (Year): 3 (2003)
Issue (Month): 6 ()
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References listed on IDEAS
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- Sanjiv R. Das & Rangarajan K. Sundaram, 1998.
"Of Smiles and Smirks: A Term-Structure Perspective,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
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"A Minimal Financial Market Model,"
Research Paper Series
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- Franks, Julian R & Schwartz, Eduardo S, 1991. "The Stochastic Behaviour of Market Variance Implied in the Prices of Index Options," Economic Journal, Royal Economic Society, vol. 101(409), pages 1460-75, November.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, March.
- Schönbucher, Philpp J., . "A Market Model for Stochastic Implied Volatility," Discussion Paper Serie B 453, University of Bonn, Germany, revised May 1999.
- Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
- Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
- Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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