We study the dynamic relation between aggregate stock market risks and risk premia via an exploration of the time series of equity-index option surfaces. The analysis is based on estimating a general parametric asset pricing model for the risk-neutral equity market dynamics using a panel of options on the S&P 500 index, while remaining fully nonparametric about the actual evolution of market risks. We find that the risk-neutral jump intensity, which controls the pricing of left tail risk, cannot be spanned by the market volatility (and its components), so an additional factor is required to account for its dynamics. This tail factor has no incremental predictive power for future equity return volatility or jumps beyond what is captured by the current and past level of volatility. In contrast, the novel factor is critical in predicting the future market excess returns over horizons up to one year, and it explains a large fraction of the future variance risk premium. We contrast our findings with those implied by structural asset pricing models that seek to rationalize the predictive power of option data. Relative to those studies, our findings suggest a wider wedge between the dynamics of equity market risks and the corresponding risk premia with the latter typically displaying a far more persistent reaction following market crises.

We develop a new parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness-maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained nonparametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model fit for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time. A large-scale Monte Carlo study indicates that the inference procedures work well for empirically realistic model specifications and sample sizes. In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying risk premia of extreme events, i.e., jumps, as well as a more flexible relation between the risk premia and the level of risk. We show that both extensions provide a significantly improved characterization, both statistically and economically, of observed option prices.

This is the accepted version of the paper.This version of the publication may differ from the final published version. Bates, our referee, for helpful comments and suggestions. We are also grateful to Torben Andersen, Giovanni Barone-Adesi, Francesco Permanent repository linkCorielli, Christian Gourieroux, Peter Gruber, Patrick Gagliardini, Loriano Mancini, Nour Meddahi, Alain Monfort, Fulvio Pegoraro, Roberto Renó, Viktor Todorov, and Fabio Trojani for their constructive discussions and remarks. We also thank the participants at the SoFiE conference held in Chicago. All errors are our own responsibility. The authors acknowledge the Swiss National Science Foundation Pro*Doc program, the NCCR FinRisk, and the Swiss Finance Institute for partial financial support. AbstractWe develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.

We provide a general valuation approach for capital budgeting decisions involving the modularization in the design of a system. Within the framework developed by Baldwin and Clark (Baldwin, C. Y., K. B. Clark. 2000. Design Rules: The Power of Modularity. MIT Press, Cambridge, MA), we implement a valuation approach using a numerical procedure based on the least-squares Monte Carlo method proposed by Longstaff and Schwartz (Longstaff, F. A., E. S. Schwartz. 2001. Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. 14(1) 113-147). The approach is accurate, general, and flexible.real options, modularity, least-squares Monte Carlo

We study short-maturity ("weekly") S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer-dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always "signaled" by the level of market volatility and elude standard asset pricing models. for helpful comments. Yupeng Wang provided skillful research assistance. Finally, we are very grateful to John Angelos and Mike Warsh from the CBOE for detailed explanations regarding the institutional organization of trading in weekly options, and to Luca Benzoni and Ivana Ruffini from the Federal Reserve Bank of Chicago for facilitating this information exchange.