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|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.qfrc.uts.edu.au/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
- Eckhard Platen, 2001.
"A Minimal Financial Market Model,"
Research Paper Series
48, Quantitative Finance Research Centre, University of Technology, Sydney.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
- Schönbucher, Philpp J., . "A Market Model for Stochastic Implied Volatility," Discussion Paper Serie B 453, University of Bonn, Germany, revised May 1999.
- 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
98-024, New York University, Leonard N. Stern School of Business-.
- Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 211-239, June.
- Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
- 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.
- Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:101. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford)
If references are entirely missing, you can add them using this form.