Fri, Apr 17, 2009 | Jared Woodard
Two academic papers recently discussed over at the CXO Blog provide some good analysis of the volatility risk premium in equity index options. The volatility risk premium is just the difference between the realized volatility of the underlying and the volatility implied by options prices. What numerous academic studies have found is that index options are consistently priced at a higher volatility than is realized over the relevant time period.
“The Volatility Premium” (Eraker 2008) locates one source of this premium in the occurrence of large jumps in realized volatility – the idea is that investors are willing to pay a premium for options (especially puts) above current levels of volatility in order to guard against the possibility of some major shock:
The estimates of the jump parameters in the model are suggestive of extremely rare, but large volatility jumps. The jump intensity in the model is proportional to the level of the volatility process, l1 Vt . The estimate of l1 = 118.6 implies that jumps occur on average every 10th year. When they do occur, the average jump size is more than twice that of the long run average volatility. Under the risk neutral measure, jumps occur much more frequently with an estimated arrival intensity of 183Vt corresponding to a jump every sixth year, or about 50% more frequently than under the ob jective measure. Jump sizes are also about 50% greater under the risk neutral distribution. These risk adjustments potentially lead to sizable premiums for jump risks in options markets.
As CXO notes, the negative mean returns observed for put buyers are consistent across all starting volatility levels for both delta-hedged and unhedged positions. However, while delta-hedged call buyers also see negative returns, unhedged call buyers do not, suggesting that calls do not feature this risk premium to the same extent as puts. My favorite sentence in the article: “This suggests that the reason why buying call options is pro?table is simply that they provide a positive exposure to stock price or market risk.”
Another explanation for the volatility premium in index options is that they provide insurance against adverse changes in correlation among individual equities. What (Driessen, Maenhout, and Vilkov 2006) refer to as the correlation risk premium is the additional premium paid to protect the diversification benefits of individual equity options. Intuitively, an investor with a book of equity options will be displeased if correlations increase dramatically and those individual names begin to merely mimic market volatility, so he will hedge against that correlation risk via index options. However, there’s no arb to be had here since transaction costs appear to consume the premium; that’s generally the problem with dispersion-type strategies.
Collecting this volatility risk premium is actually one of the goals of our iron condor newsletter. Iron condors are often explained in terms of expressing a neutral view about the price movement of an asset, but they can also be thought of as a means of profiting from the difference between implied and realized volatility over some period of time. One of the primary problems with option selling strategies one might pursue based on the papers above is that small, consistent profits can easily be wiped out by those large periodic jumps in realized volatility, as pictured above. The most obvious way to begin addressing that problem is to opt for risk-defined option spreads like condors and butterflies in lieu of straddles and other naked positions. Another intuitive measure is to become a less aggressive net seller as time increases since the last major volatility jump or period of high correlation.