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

David Heath and Eckhard Platen ()

No 101, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: index derivatives; minimal market model; lognormal scaling; growth optimal portfolio; fair pricing; binary options (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2003-06-01
New Economics Papers: this item is included in nep-fin
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Citations: View citations in EconPapers (11)

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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Journal Article: Pricing of index options under a minimal market model with log-normal scaling (2003)
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