Patent ID: 8417615

Claim:
A computer-implemented method, comprising: by a computing device: receiving historical price data, the historical price data indicating one or more historical prices for a financial instrument; receiving maturity data, the maturity data indicating one or more expiration dates, each of the one or more expiration dates being an expiration date for one or more options on the financial instrument; selecting an expiration date from the one or more expiration dates; receiving forward price or discount factor data, the forward price or discount factor data indicating a forward price or a discount factor applicable to the financial instrument at each of the one or more expiration dates; computing a set of two extremal martingale probability distributions based at least in part on the historical price data, the forward price or discount factor data, and the selected expiration date, wherein the two extremal martingale probability distributions comprise a minimum extremal martingale probability distribution and a maximum extremal martingale probability distribution, wherein each of the two extremal martingale probability distributions indicates probabilities of possible prices for the financial instrument at the selected expiration date, and wherein each of the two extremal martingale probability distributions is determined by a fractional linear transformation of a distribution parameter function; and storing the set of two extremal martingale probability distributions.