Preposterior analysis for option pricing

The second partial derivative of a European-style vanilla option with respect to the current price of the underlying asset—the option gamma—defines a probability density function for the current underlying price. By use of entropy maximization it is possible to obtain an option gamma, from which the associated option pricing formula can be recovered by integration. A number of pricing formulae are obtained in this manner, corresponding to different specifications of the constraints. When the available market information consists solely of a set of traded option prices, the entropic formulation leads to a model-independent calibration procedure. The result thus obtained also allows one to recover the relevant Greeks.