A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims

This paper introduces a theory of equivalent expectation measures, such as the R measure and the RT1 measure, generalizing the martingale pricing theory of Harrison and Kreps (1979) for deriving analytical solutions of expected prices - both the expected current price and the expected future price - of contingent claims. We also present new R-transforms which extend the Q-transforms of Bakshi and Madan (2000) and Duffie et al. (2000), for computing the expected prices of a variety of standard and exotic claims under a broad range of stochastic processes. Finally, as a generalization of Breeden and Litzenberger (1978), we propose a new concept of the expected future state price density which allows the estimation of the expected future prices of complex European contingent claims as well as the physical density of the underlying asset's future price, using the current prices and only the first return moment of standard European OTM call and put options