Gambling and Pricing of Derivatives

16 Pages Posted: 7 Sep 1998

See all articles by Erik Aurell

Erik Aurell

Swedish Institute of Computer Science (SICS) - Intelligent Systems Laboratory

Roberto Baviera

Polytechnic University of Milan - Department of Mathematics

Ola Hammarlid

Stockholm University - Department of Mathematics

Maurizio Serva

University of L'Aquila - Department of Physics

Angelo Vulpiani

Universita' di Roma & Instituto Nazionale di Fisic

Date Written: May 26, 1998

Abstract

We introduce a criterion how to price derivatives in incomplete markets, which is based on the theory of optimal strategies in repeated multiplicative games. Arguments are presented why such growth-optimal strategies should be relevant to the problem of pricing derivatives. Under the assumptions of no trading costs, and no restrictions on lending, we find an appropriate equivalent martingale measure that prices the underlying and the derivative securities. We compare our approach with other alternative pricing procedures in the literature. We also discuss the lognormal approximation to the compounded martingale measure over many time-steps, and its limits of applicability.

JEL Classification: G13, G14

Suggested Citation

Aurell, Erik M. and Baviera, Roberto and Hammarlid, Ola and Serva, Maurizio and Vulpiani, Angelo, Gambling and Pricing of Derivatives (May 26, 1998). Available at SSRN: https://ssrn.com/abstract=99837 or http://dx.doi.org/10.2139/ssrn.99837

Erik M. Aurell (Contact Author)

Swedish Institute of Computer Science (SICS) - Intelligent Systems Laboratory ( email )

Box 1263
Kista SE-16429
Sweden
+46-8-633 15 11 (Phone)

Roberto Baviera

Polytechnic University of Milan - Department of Mathematics ( email )

P.zza L. da Vinci, 32
Milan, 20133
Italy

Ola Hammarlid

Stockholm University - Department of Mathematics ( email )

Stockholm, S-106 91
Sweden

Maurizio Serva

University of L'Aquila - Department of Physics ( email )

Coppito di L'Aquila, 67010
Italy
+39 862 43 3153 (Phone)

Angelo Vulpiani

Universita' di Roma & Instituto Nazionale di Fisic ( email )

P.le A. Moro 2
Rome, I-00185
Italy

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