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 of Rubinstein (1976) , Brennan (1979) , and Câmera (2003) , and the gamma model of Heston (1993) are all special cases. The model provides simple relationships between expected returns and state‐price density parameters analogous to the diffusion case.

This paper expresses the constant elasticity of variance option pricing formula in terms of the noncentral chi‐square distribution. This allows the application of well‐known approximation formulas and the derivation of a whole class of closed‐form solutions. In addition, a simple and efficient algorithm for computing this distribution is presented.

This paper expresses the constant elasticity of variance option pricing formula in terms of the noncentral chi-square distribution. This allows the application of well-known approximation formulas and the derivation of a whole class of closed-form solutions. In addition, a simple and efficient algorithm for computing this distribution is presented.