Dr. Clemens Völkert
Lehrstuhl für Derivate und Financial Engineering
- 2002-2008: Studium der Betriebswirtschaftslehre, Universität zu Köln
- 2004-2008: Studium der Regionalwissenschaften Ostasien, Universität zu Köln
- 2005: Tongji University, Shanghai, V.R. China
- 2006: University of Calgary, Calgary, Kanada
- 2010: University of New South Wales, Sydney, Australien
- seit Oktober 2008: Wissenschaftlicher Mitarbeiter am Lehrstuhl für Derivate und Financial Engineering
- November 2012: Promotion zum Dr. rer. pol., Titel der Dissertation: Essays on Asset Pricing and Volatility Derivatives
- Asset Pricing
- Branger, N., Kraftschik, A., Völkert, C. (2015): 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 options on the S&P 500 and on the VIX. We derive the dynamics of the VIX in a general affine jump-diffusion setup and provide semi-closed form solutions for derivatives written on this index. A comparison of several model specifications shows that it is of special importance to account for volatility clustering when it comes to pricing VIX options. Thus, a model should allow for stochastic volatility of variance (SVV) or variance jumps with a stochastic jump intensity. We find that the SVV model outperforms models with variance jumps both in- and out-of-sample. Only this model is able to simultaneously explain both the level and dynamics of the risk-neutral moments' variance, while still generating sufficient skewness and kurtosis.
- Branger, N., Kraftschik, A., Völkert, C. (2013): The Variance Process Implied in VIX Options: Affine vs. Non-Affine Models, Working Paper.
- 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.
- 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.
- Thimme, J., Völkert, C. (2015): High Order Smooth Ambiguity Preferences and Asset Prices, Review of Financial Economics, Vol. 27, November 2015, 1-15. (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 attitude, and attitudes 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 generates a highly volatile price-dividend ratio and predictability patterns in line with the data.
- Thimme, J., Völkert, C. (2015): Ambiguity in the Cross-Section of Expected Returns: An Empirical Assessment, Journal of Business and Economic Statistics, Vol. 33, Issue 3, July 2015, 418-429. (Abstract)
This article estimates and tests the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji 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 60, 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 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. Supplementary materials for this article are available online.