A Maximum Entropy Approach to the Measurement of Event Risk
Geometric Brownian motion (GBM) has played a key role in finance since the introduction of continuous-time pricing models by Black and Scholes (1973) and Merton (1973). If prices follow GBM in continuous time, logarithmic returns are normally distributed and this provides a theoretical justification for the use of the normal distribution as a model for log-returns. In addition, the mathematical tractability of the normal distribution is a considerable advantage from the practictioners’ point of view.
On the other hand, several empirical studies ...