Distribution-free option pricing

Nobody doubts the power of the Black and Scholes option pricing method, yet there are situations in which the hypothesis of a lognormal model is too restrictive. A natural way to deal with this problem consists of weakening the hypothesis, by fixing only successive moments and possibly the mode of t...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2007-03, Vol.40 (2), p.179-199
Main Authors: Schepper, Ann De, Heijnen, Bart
Format: Article
Language:English
Subjects:
Assets
Black–Scholes
Distribution
Hypotheses
IE50
IM10
Information economics
Limited information
Marginal pricing
Model testing
Option pricing
Studies
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Summary:Nobody doubts the power of the Black and Scholes option pricing method, yet there are situations in which the hypothesis of a lognormal model is too restrictive. A natural way to deal with this problem consists of weakening the hypothesis, by fixing only successive moments and possibly the mode of the price process of a risky asset, and not the complete distribution. As a consequence of this generalization, the option price is no longer a unique value, but rather a range of possible values. In the present paper, we show how to find upper and lower bounds for this range, a range which turns out to be quite narrow in a lot of cases.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2006.04.002