  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.
