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Finance and Stochastics
Published in: Finance and Stochastics 2/2012

01-04-2012

Maximum entropy distributions inferred from option portfolios on an asset

Authors: Cassio Neri, Lorenz Schneider

Published in: Finance and Stochastics | Issue 2/2012

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Abstract

We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly (J. Financ. Quant. Anal. 31:143–159, 1996). We give a simple and robust algorithm for our method and compare our results to theirs. We present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options. Finally, we apply our approach to options on the S&P 500 index.
previous article Strict local martingale deflators and valuing American call-type options
next article A pure martingale dual for multiple stopping

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Footnotes
1
In Csiszár’s paper, the minus sign in front of the definition of entropy is dropped and its minimisation (rather than maximisation) is studied.
 
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Metadata
Title
Maximum entropy distributions inferred from option portfolios on an asset
Authors
Cassio Neri
Lorenz Schneider
Publication date
01-04-2012
Publisher
Springer-Verlag
Published in
Finance and Stochastics / Issue 2/2012
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI
https://doi.org/10.1007/s00780-011-0167-7

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