Journal Article Changes of Numeraire for Pricing Futures, Forwards, and Options Get access Mark Schroder Mark Schroder Michigan State University Address correspondence to Mark Schroder, The Eli Broad Graduate School of Management, Department of Finance, Michigan State University, 323 Eppley Center, East Lansing, MI 48824-1121, or email: [email protected]. Search for other works by this author on: Oxford Academic Google Scholar The Review of Financial Studies, Volume 12, Issue 5, October 1999, Pages 1143–1163, https://doi.org/10.1093/rfs/12.5.1143 Published: 01 June 2015

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.

We study the role of private information in the equity lending market in a rational expectations model with endogenous loan fees. When all investors are privately informed, an increase in information precision reduces the fee by increasing trade aggressiveness and decreasing demand dispersion. However, when some investors are uninformed, the information asymmetry tends to increase the fee, and, thus, the overall effect of an increase in precision is ambiguous. We show that the fee can be incrementally informative given the stock price and that fee opaqueness tends to increase the fee but has an ambiguous effect on the stock price.

Evidence shows that the stochastic discount factor (SDF) is not always a downward-sloping function of S&P 500 returns when estimated using options data. In contrast, our results suggest that SDFs as functions of individual stock returns are generally downward sloping. A simple jump-diffusion model can reconcile these empirical findings. The same model also implies a steeper implied-volatility curve for the index than for the typical stock, a well-known empirical fact from the options literature. Both the SDF and volatility-curve results can be explained by a common source of jump risk among stocks, together with diversification of Brownian risk in the index. We also devise novel empirical tests of SDF monotonicity based on average returns of option trading strategies, thus avoiding the estimation of the return density functions.

We show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation, and corresponding models without habit formation. The isomorphism can be used to mechanically transform known solutions not involving habit formation to corresponding solutions with habit formation. For example, the Constantinides (1990) and Ingersoll (1992) solutions are mechanically obtained from the familiar Merton solutions for the additive utility case, without recourse to a Bellman equation or first-order conditions. More generally, recent solutions to portfolio selection problems with recursive utility and a stochastic investment opportunity set are readily transformed to novel solutions of corresponding problems with utility that combines recursivity with habit formation. The methodology also applies in the context of Hindy–Huang–Kreps (1992) preferences, where our isomorphism shows that the solution obtained by Hindy and Huang (1993) can be mechanically transformed to Dybvig’s (1995) solution to the optimal consumption-investment problem with consumption ratcheting.