Option pricing bounds in an a α stable security market
- 1 January 1997
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 13 (4) , 817-839
- https://doi.org/10.1080/15326349708807453
Abstract
This article considers the problem of pricing options in a market where the underlying process is assumed to be driven by a Lúvy α-stable motion, which includes, as a special case, the Gaussian “geometric Wiener process” . With finite trading opportunities, to obtain pricing models requires very specific preference restrictions. Rather than place such assumptions on investor behavior, we give up exact pricing, and bound option prices under stochastic dominance type restrictions. The bounds are investigated for differing degrees of leptokurtosis in the distribution of stock returns. In addition, their behavior is explored as the trading frequency increases. The resulting pricing relationships allow us to obtain insight which may explain the volatility smile effectKeywords
This publication has 30 references indexed in Scilit:
- The valuation of options for alternative stochastic processesPublished by Elsevier ,2002
- Option Pricing When Jump Risk Is Systematic1Mathematical Finance, 1992
- The Stable-Law Model of Stock ReturnsJournal of Business & Economic Statistics, 1988
- An Intertemporal General Equilibrium Model of Asset PricesEconometrica, 1985
- Fact and Fantasy in the Use of OptionsCFA Magazine, 1975
- A Comparison of the Stable and Student Distributions as Statistical Models for Stock PricesThe Journal of Business, 1974
- The Pricing of Options and Corporate LiabilitiesJournal of Political Economy, 1973
- Parameter Estimates for Symmetric Stable DistributionsJournal of the American Statistical Association, 1971
- The Behavior of Stock-Market PricesThe Journal of Business, 1965
- The accuracy of the Gaussian approximation to the sum of independent variatesTransactions of the American Mathematical Society, 1941