- Thimme, J., Völkert, C. (2012): Ambiguity in the Cross-Section of Expected Returns: An Empirical Assessment, Working Paper. (available at SSRN) (Abstract)
This paper estimates and tests the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji (2005, 2009) based on stock market data. We introduce a novel methodology to estimate the conditional expectation which characterizes the impact of a decision maker's ambiguity attitude on asset prices. Our point estimates of the ambiguity parameter are between 25 and 40, whereas our risk aversion estimates are considerably lower. The substantial difference indicates that market participants are ambiguity averse. Furthermore, we evaluate if ambiguity aversion helps explaining the cross-section of expected returns. Compared with Epstein and Zin (1989) preferences, we find that incorporating ambiguity into the decision model improves the fit to the data while keeping relative risk aversion at more reasonable levels.
- Völkert, C. (2012): The Distribution of Uncertainty: Evidence from the VIX Options Market, Working Paper. (available at SSRN) (Abstract)
This paper investigates the informational content implied in the risk-neutral distribution of the VIX, a leading barometer of economic uncertainty. We extract the risk-neutral distribution from VIX option prices over the sample period from 2006 to 2011 using a non-parametric approach. We analyze the time-series behavior of the option-implied moments and assess whether the information implied in the risk-neutral distribution has predictive power. The risk-neutral distribution considerably changed shape during the financial crisis. Furthermore, risk-neutral moments contain useful information with respect to the likelihood of upward jumps in volatility. Consistent with investors disliking high levels of economic uncertainty, we find that the overall shape of the estimated volatility pricing kernel is increasing. For certain periods, there is a puzzling U-shape. The behavior of the volatility pricing kernel over time reveals that the financial crisis has affected investors' attitudes towards risk.
- Thimme, J., Völkert, C. (2011): High Order Smooth Ambiguity Preferences and Asset Prices, Working Paper. (available at SSRN) (Abstract)
This paper extends the recursive smooth ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005, 2009) by relaxing the uniformity imposed on higher order acts. This generalization permits a separation of intertemporal substitution, risk aversion, and ambiguity aversion towards different sources of uncertainty. Our decision model is suited in situations where subjects may treat several kinds of uncertainty in different manners. We apply our preference specification to a consumption-based asset pricing model with long-run risks and assess the impact of ambiguity on asset prices and predictability patterns. We find that modeling attitudes towards uncertainty through high order smooth ambiguity preferences has important implications for asset prices. Our model significantly improves upon the special cases of Epstein and Zin (1989) utility and standard smooth ambiguity preferences.
- Branger, N., Völkert, C. (2011): The Fine Structure of Variance: Consistent Pricing of VIX Derivatives, Working Paper. (available at SSRN) (Abstract)
This paper provides a tractable framework for consistently modeling and pricing the two most actively traded options on the Chicago Board Options Exchange (CBOE), namely SPX and VIX options. We derive the dynamics of the CBOE volatility index and give semi-closed form solutions for derivatives on it in a general affine jump-diffusion setup. We compare the implications of several special cases of the general model with the major empirical properties of VIX derivatives and the time-series behavior of the VIX. We show that commonly employed affine jump-diffusion models cannot reproduce the basic patterns observed in the data. The fine structure of the variance process is essential to reconcile the empirical regularities with the theoretical models. We find that both variance jumps and a stochastic volatility of variance seem to be important factors in this respect.
- Branger, N., Völkert, C. (2010): What is the Equilibrium Price of Variance Risk? A Long-Run Risks Model with Two Volatility Factors, Working Paper. (available at SSRN) (Abstract)
This paper explores how economic uncertainty evolves over time and how it is priced in the market. We solve for the variance premium, the prices of equity index options, and the prices of volatility related derivatives in a long-run risks model. We find that both short-run and long-run uncertainty factors are necessary to explain the empirical characteristics of variance risk while remaining consistent with consumption and asset pricing data. The variance premium is mainly driven by the risk of a sudden increase in the overall level of uncertainty. Out-of-the-money equity index put options and out-of-the-money call options on variance provide insurance against market crashes. Consistent with the data, these contracts are priced at a premium.
