A computer-implemented method is provided for valuing and hedging payoffs
that are determined by an underlying non-marketed variable that moves
randomly. The value assigned is that which is obtained by projecting the
instantaneous return of the future payoff onto the span of marketed
assets. An explicit method is provided for determining this value by
determining a suitable market representative. In a continuous-time
embodiment, the methodology is based on an extended Black-Scholes
equation that accounts for the correlation between the underlying
non-tradable asset and marketed assets. Once this extended equation is
solved, the value of the payoff, the optimal hedging strategy, and the
residual risk of the optimal hedge can be determined. In alternate
embodiments, the same value is determined as the discounted expected
value of the payoff, using risk-neutral probabilities for the
non-marketed variable. These risk-neutral probabilities are again
determined by the relation of the underlying variable to the payoff of a
most-correlated marketed asset. The risk-neutral version of the method
applies in both continuous-time and discrete-time frameworks, providing
asset valuation, optimal hedging, and evaluation of the minimum residual
risk after hedging.