Actuarial Transform Pricing

Abstract

This article studies four transform pricing methods in the context of general equilbrium (GE) framework. The four methods, viz. the Esscher transform, indifference pricing, the Wang transform, and the standard deviation loading, are popular among actuarial literature and practice. The transform pricing methods offer a convenient solution to contingent claim pricing problem with the underlying risk exposure cannot be fully hedged. We show analytically that these four methods are similar and close to the GE approach if the utility has an exponential function, and the underlying distribution is Normal. When the payoff distribution is non-gaussian, prices produced by the four methods vary widely. Moreover, some transform methods may lead to prices that are not coherent, violating one or more of the following properties, additivity, homogeneity, scale invariance and monotonicity. We discuss the implications of our findings on incomplete market pricing.

Keywords: Esscher transform, indifference pricing, Wang transform, standard deviation loading

JEL Classification: D52, G13, C22