Investor and Central Bank Uncertainty and Fear Measures Embedded in Index Options∗

We provide a structural Bayesian equilibrium learning model that captures the interaction of the uncertainty about fundamentals of investors and the central bank. In our model central bank policy is able to affect fundamental state transitions and investors can learn about future fundamental states from observing policy variables. We show that investors’ fear measures — implied volatility (ATMIV) and put-call implied volatility ratios (P/C) — lead industrial capacity utilization, which the central bank reacts to so the fear measures can be used to predict interest rates. The model endogenously generates several of the time series properties of option prices including the counter (pro) cyclicality of ATMIV (P/C), the V-shape (inverse V-shape) relation between ATMIV (P/C) and monetary policy variables, the positive relation between the level and absolute changes in ATMIV, the negative beta of volatility as a priced systematic risk factor, and an economically significant amount of time variation in the volatility premium. We thank seminar participants at UNC Chapel Hill, Duke, and Penn. State for their valuable comments. Address (David): Address: 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada. Phone: (403) 220-6987. Fax: (403) 210-3327. E. Mail: [email protected]. Address (Veronesi): Booth School of Business, University of Chicago, 5807 South Woodlawn Avenue, Chicago, IL, 60637. Phone: (773) 702-6348. E-mail: [email protected]. David thanks the SSHRC for a research grant. Since the classic work of Breeden and Litzenberger (1978) it has been clear that option prices contain valuable information on investors’ forward looking state price density function. It has been less clear, however, if this information is any way linked to macro economic fundamentals that should affect agents’ state prices. While it is intuitive that corporate stock and options prices react to corporate news, there is also substantive evidence that they react to monetary policy shocks. For example, Bernanke and Kuttner (2005) report that monetary policy surprises affect the stock market, while Rigobon and Sack (2003) show that the monetary policy responds to stock returns with a greater reaction during times of higher volatility, and more recently Bekaert, Hoerova, and Duca (2010) find a significant reaction of options prices to lead and lag measures of monetary policy. This compelling empirical evidence though spurs a fundamental question: What is the relation between option prices, corporate fundamentals, and the action of the Central Bank? In this paper we provide a simple dynamic equilibrium model that links options prices to fundamentals and monetary policy, and provide additional empirical evidence of the complex relation between these variables. Before moving on, it is useful to first present some empirical relations between options and monetary policy. In particular, our analysis focuses on two popularly quoted market wide ‘fear’ indexes constructed from options prices. The first, the implied volatility of at-the-money (ATMIV) options, which was originally created by Whaley (1993) and trades on the Chicago Board Options Exchange under the ticker VIX, is described by the exchange as: One of the most interesting features of VIX, and the reason it has been called the “investor fear guage,” is that, historically, VIX hits its highest levels during times of financial turmoil and investor fear. [CBOE Bulletin on VIX, 2003]. The second is the ratio of implied volatilities of out-of-the-money put to call options (P/C), which is a direct market assessment of downside relative to upside risk. This measure has also been studied extensively since the work of Bates (1991) to imply, in particular, investors’ fears about a market crash. Quarterly time series plots of these variables for options with three months to maturity are shown in Figure 1. Comparing to the top panel gives the surprising stylized fact that the two fear measures ATMIV and the P/C are negatively related, with the ATMIV (P/C) being generally counter (pro) cyclical. While it is intuitive that a fear index such as ATMIV is high during downturns, it is less obvious why the downside-risk fear index P/C is high during booms and low during recessions.