A New Method of Employing the Principle of Maximum Entropy to Retrieve the Risk Neutral Density

Abstract

This paper suggests a new method of implementing the principle of maximum entropy to retrieve the risk neutral density of future stock, or any other asset, returns from European call and put prices. Instead of options prices used by previous studies the method maximizes the entropy measure subject to values of the risk neutral moments. These moments can be retrieved from market option prices in a first step, at each point of time. Compared to other existing methods of retrieving the risk neutral density based on the principle of maximum entropy, the benefits of the method that the paper suggests is the use of all the available information provided by the market more sufficiently. To evaluate the performance of the suggested method, the paper compares the new method proposed to other risk neutral density estimation techniques based on a number of simulation and empirical exercises.