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We investigate the implications of recovering real-world conditional expectation of return functions using options on the S&P 500 index and Treasury bond futures. First, we construct estimates of the probability of disasters, defined as higher than 6%, 5%, or 4% equity market declines over option expiration cycles. This measure of disaster probability forecasts realized disasters. Second, we employ options on the futures of the 10- and 30-year Treasury bonds to construct estimates for the expected return of bond futures. These measures display forecasting ability for subsequent futures returns beyond the level, slope, and curvature variables extracted from the yield curve. [ABSTRACT FROM AUTHOR]

We show that a model featuring an average commodity factor, a carry factor, and a momentum factor is capable of describing the cross-sectional variation of commodity returns. More parsimonious one- and two-factor models that feature only the average and/or carry factors are rejected. To provide an economic interpretation, we show that innovations in global equity volatility can price portfolios formed on carry, while innovations in a commodity-based measure of speculative activity can price portfolios formed on momentum. Finally, we characterize the relation between the factors and the investment opportunity set. History: Accepted by Neng Wang, finance. Supplemental Material: Data and the Internet appendix are available at https://doi.org/10 1287/ mnsc.2017.2840. Keywords: commodity asset pricing models * carry * momentum * innovations in equity volatility * speculative activity, 1. Introduction The interaction of storage and convenience yield, and the hedging motives of producers, consumers, and speculators, has led to the development of theories about the behavior of commodity [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jfineco.2005.09.005 Byline: Gurdip Bakshi (a), Nengjiu Ju (b), Hui Ou-Yang (c) Abstract: The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-ordering of continuous-time stochastic volatility models, the absence or presence of nonlinearities in the drift function, and the desirability of pursuing more flexible diffusion function specifications. Author Affiliation: (a) Department of Finance, Smith School of Business, University of Maryland, College Park, MD 20742, USA (b) School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong (c) Fuqua School of Business, Duke University, Durham, NC 27708, USA Article History: Received 18 August 2004; Revised 17 August 2005; Accepted 23 September 2005 Article Note: (footnote) [star] We are grateful for the feedback of the referee whose detailed comments have substantially improved this paper. We acknowledge useful comments by Yacine AiA[umlaut]t-Sahalia, Doron Avramov, Charles Cao, Peter Carr, Ren-Raw Chen, Bob Dittmar, Steve Heston, Gautam Kaul, Mark Loewenstein, Dilip Madan, Bertrand Melenberg, Jun Pan, Matt Pritsker, Bill Schwert, Tyler Shumway, Guojun Wu, and Liuren Wu. Seminar participants at Michigan Business School, Rutgers University, 2004 European Finance Association meetings (Maastricht), and 2005 China International Conference in Finance provided several constructive suggestions. Computer codes used to implement the continuous-time models are available from the authors.

The research indicates that index option prices incorporate a negative volatility risk premium, thus providing a possible explanation of why Black-Scholes implied volatilities of index options on average exceed realized [...]