Estimating the firm value distribution function by entropy optimization and geometric programming

By applying the option pricing theory ideas, this paper models the estimation of firm value distribution function as an entropy optimization problem, subject to correlation constraints. It is shown that the problem can be converted to a dual of a computationally attractive primal geometric programming (GP) problem and easily solved using publicly available software. A numerical example involving stock price data from a Japanese company demonstrates the practical value of the GP approach. Noting the use of Monte Carlo simulation in option pricing and risk analysis and its difficulties in handling distribution functions subject to correlations, the GP based method discussed here may have some computational advantages in wider areas of computational finance in addition to the application discussed here.