Maximum Entropy Distributions Inferred from Option Portfolios on an Asset

Details Maximum Entropy Distributions Inferred from Option Portfolios on an Asset Maximum Entropy Distributions Inferred from Option Portfolios on an Asset

2009-03-26

arxiv.org/abs/0903.4542v3

Economy

Quantitative Finance

Pricing of Securities

23 pages, 5 figures, to appear in Finance and Stochastics

Scientific paper

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. 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.

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