It implies that at the height of the 2008–9 crisis, the one-month equity premium was at least 55.0% (annualized), and that the one-year equity premium was at least 21.5%. Although it averages about 5% over the sample period, it varies dramatically, and at fairly high frequency. This lower bound has striking properties. Identity that relates the equity premium to risk-neutral variance and show, under a weak assumption (the negative correlation condition), that SVIX provides a lower bound for the forward-looking equity premium. Section 4 connects the SVIX index to the equity premium. In any conditionally lognormal model VIX would be lower than SVIX, so this is model-free evidence that we do not live in a conditionally lognormal world. VIX is higher than SVIX throughout the sample, and the gap between the two-an index of nonlognormality-spikes at times of market stress.
#It follows 2 rt series#
In Section 3, I construct the time series of SVIX from January 1996 to January 2012 using S&P 500 index option price data from OptionMetrics. Just as VIX is based on the strike of a variance swap, one can consider an index, SVIX, that is based on the strike of a simple variance swap. There is no corresponding result for variance swaps. Perhaps most important, I show that my hedging and pricing results also hold, to very high accuracy, if monitoring and hedging occurs at discrete points in time, rather than continuously this is, of course, the case that applies in practice.
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Simple variance swaps are also robust to several potential concerns regarding practical implementation. Second, they measure the risk-neutral variance of simple returns. First, they are simple to price and hedge: in particular, they can be hedged in the presence of jumps. Simple variance swaps are simple in two senses. In Section 2, I define and analyze the simple variance swap contract. The presence of jumps also invalidates the conventional interpretation of the VIX index, so I provide a more general interpretation. This problem applies with particular force to individual stocks, which are more susceptible to jumps than indices are. The fundamental problem is that there is no known way to replicate the payoff of a variance swap if the underlying asset’s price can jump. To explain why, I review the standard theory of variance swap pricing and hedging in Section 1. The single-name variance swap market was particularly severely affected: it collapsed, and has not recovered.
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Unfortunately, the variance swap market experienced turmoil as the stock market dropped sharply during the credit crisis of 2008–9. They also play an informational role by providing evidence about perceptions of future volatility. These derivatives permit investors and dealers to hedge and to speculate in volatility itself. An emblem of this market, the VIX index, is often described in the financial press as “the fear index” its construction is based on theoretical results on the pricing of variance swaps. In recent years, a large market in volatility derivatives has developed. I thank Torben Andersen, Andy Atkeson, Jack Busta, John Campbell, Peter Carr, Mike Chernov, John Cochrane, George Constantinides, Bernard Dumas, Darrell Duffie, Bob Hall, Stefan Hunt, Chris Jones, Stefan Nagel, Anthony Neuberger, Monika Piazzesi, Steve Ross, Myron Scholes, Costis Skiadas, Andreas Stathopoulos, Viktor Todorov seminar participants at USC, the SITE 2011 conference, the Kellogg Finance Conference, the NBER Summer Institute, INSEAD, LSE, and EPFL/University of Lausanne and the Editor, Associate Editor, and two anonymous referees for their comments. Keywords: variance swap, VIX, equity premium, jumps, entropy.
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The SVIX index points to an equity premium that-in contrast to the prevailing view in the literature-is extraordinarily volatile and that spiked dramatically at the height of the recent crisis. SVIX is consistently lower than VIX in the time series, which rules out the possibility that the market return and stochastic discount factor are conditionally lognormal. This paper introduces the simple variance swap, a more robust relative of the variance swap that can be priced and hedged even if the underlying asset’s price can jump, and constructs SVIX, an index based on simple variance swaps that measures market volatility. Simple Variance Swaps Ian Martin∗ January, 2013Ībstract The events of 2008–9 disrupted volatility derivatives markets and caused the single-name variance swap market to dry up completely it has never recovered.