Risk-Neutral Parameter Shifts and Derivatives Pricing in Discrete Time

Abstract

We obtain a large class of discrete-time risk-neutral valuation relationships, or “preference-free” derivatives pricing models, by imposing a simple restriction on the state-price density process. The risk-neutral stock-return and forward-rate dynamics are obtained by changing only a location parameter, which can be determined independent of the preference and true location parameters. The Gaussian models ofRubinstein (1976),Brennan (1979), andCâmera (2003), and the gamma model ofHeston (1993)are all special cases. The model provides simple relationships between expected returns and state-price density parameters analogous to the diffusion case.