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Option bounds

Part of: Mathematical economics Approximations and expansions

Published online by Cambridge University Press:  14 July 2016

Victor H. De La Peña ,
Rustam Ibragimov  and
Steve Jordan
Victor H. De La Peña
Affiliation:
Department of Statistics, Columbia University, 2990 Broadway, New York, NY 10027, USA. Email address: vp@stat.columbia.edu
Rustam Ibragimov
Affiliation:
Department of Economics, Yale University, 28 Hillhouse Avenue, New Haven, CT 06511, USA. Email address: rustam.ibragimov@yale.edu
Steve Jordan
Affiliation:
Yale School of Management, Yale University, 135 Prospect Street, New Haven, CT 06520, USA. Email address: steven.jordan@yale.edu
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Abstract

In this paper, we obtain sharp estimates for the expected payoffs and prices of European call options on an asset with an absolutely continuous price in terms of the price density characteristics. These techniques and results complement other approaches to the derivative pricing problem. Exact analytical solutions to option-pricing problems and to Monte-Carlo techniques make strong assumptions on the underlying asset's distribution. In contrast, our results are semi-parametric. This allows the derivation of results without knowing the entire distribution of the underlying asset's returns. Our results can be used to test different modelling assumptions. Finally, we derive bounds in the multiperiod binomial option-pricing model with time-varying moments. Our bounds reduce the multiperiod setup to a two-period setting, which is advantageous from a computational perspective.

Keywords

Option pricingsemi-parametric bounds

MSC classification

Secondary: 91B24: Price theory and market structure 91B30: Risk theory, insurance 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
Type
Part 3. Financial mathematics
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 145 - 156
Copyright
Copyright © Applied Probability Trust 2004 

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