A General Framework for Asset Pricing

Abstract

Gerber and Shiu (1994) and Henne and Reichling (2006) have independently derived similar stochastic discount factor asset pricing principles in justifying their arguments regarding asset pricing. In this paper, we show that if we slightly modify the two principles, they reach the same asset pricing principle. To be speci fic, in deriving their pricing principles, both Gerber and Shiu (1994) and Henne and Reichling (2006) deal with the case of a single risk-free asset and a single risky asset for which Gerber and Shiu (1994) further assume a financial derivative. Here, we simply extend their logic to portfolios of the entire capital market, in line with the portfolio theory by Markowitz (1952, 1956, 1959), Sharpe (1964), Lintner (1965), and Mossin (1966), to make the two principles converge to each other. And based on the converged version of the pricing principles, we show that the capital asset pricing model by Sharpe (1964), Lintner (1965), and Mossin (1966), the capital asset pricing model with time-dependent beta by Henne and Reichling (2006), the arbitrage pricing theory by Ross (1976), the Gerber-Shiu model by Gerber and Shiu (1994) (a generalization of the Black-Scholes model by Black and Scholes (1973) and Merton (1973b)), and the Esscher insurance premium pricing principle by Buhlmann (1980) can all be derived under a unified pricing principle.