Patent ID: 8417613

Claim:
A method for calculating a value of an American stock option implemented by a processor of a computer, comprising: (a) creating a discrete approximation for a self-convolving probability distribution with a deterministic number of points, the points representing potential returns for a stock underlying the option; (b) creating a discrete approximation of a delta function for one entry of value 1 at a current time t=zero; (c) creating by the processor a discrete probability distribution of returns for the stock underlying the option, for a number T of times from the current time t=zero through an expiry for the option; (d) calculating a discrete probability distribution for the return of a stock, and hence for the discrete probability distribution for the value for the option at expiry; and (e) iteratively determining by the processor a value of the option at a time t=i, for i from T−1 to zero in reverse time order, wherein each iteration comprises: performing a discrete convolution of the discrete probability distribution for the time t=i with the discrete probability distribution for the time t=i+1, wherein the value of the option at time t=zero comprises the current value of the option.