An extension of the Black-Scholes model of security valuation

Abstract

This paper provides a formula for the market value of a security whose dividends and liquidation value depend on securities with diffusion dividend and price processes. The solution is in terms of the Feynman-Kac formula, solving the partial differential equation determining the derivative sucurity's unique arbitrage-free value. The interest rate process may be stochastic. Markets need not be dynamically complete.