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. RUBINSTEIN (1976) DERIVES THE BLACK-SCHOLES FORMULA in a discrete-time model by imposing a restriction on the joint distribution of the asset price and the representative agent's marginal utility. Similar to the complete-markets diffusion result, the option price is independent of the expected stock return and the agent's preference parameters. As Heston (1993) points out, the noteworthy property is the elimination of three parameters, a stock-price-distribution parameter and two preference parameters (governing subjective time discounting and risk aversion), through the use of stock and bond prices. This so-called riskneutral valuation relationship (RNVR) has been extended to alternative joint distributions of stock price and marginal utility by Brennan (1979), Câmera (2003, and others. RNVRs are important because they provide conditions in a discrete-time equilibrium setting under which (1) derivative prices are obtained using only parameters that can, in practice, be estimated with precision, and (2) derivative prices provide no information about the preference or expected return parameters that is not already ref lected in the stock price. RNVRs resemble the pricing method in the complete-markets diffusion setting, but are obtained through a distributional assumption on marginal utility instead of assumptions of continuous trading and complete markets.Since RNVRs impose assumptions on the joint distribution of prices and the state-price density (or stochastic discount factor), they are more restrictive than the method of risk-neutral pricing, which basically requires only frictionless markets and the absence of arbitrage. Risk-neutral probabilities * Mark Schroder is at the Eli Broad Graduate School of Management, Michigan State University.I am grateful to Naveen Khanna, Hong Liu, an anonymous referee, and the editor, Richard Green, for comments and suggestions. This paper subsumes the earlier working paper "Preference-free Pricing of Contingent Claims in Discrete Time Models," 1999.
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