Volatility Risk Premium

The volatility risk premium is the difference between the volatility implied by option prices and the volatility that the underlying asset actually goes on to show. Over long periods and across many markets, implied volatility has on average been higher than subsequent realized volatility. Options have, in that sense, been priced above the level that later movement justified, and sellers of options have earned the difference.

The premium is a form of risk premium: a reward paid to investors for bearing a risk that others wish to shed. It is most thoroughly documented for options on equity indices, but it has also been found in options on individual shares, bonds, currencies and commodities. It is the economic basis of strategies described as selling volatility.

In its simplest form the premium is:

• $\sigma_{\text{implied}}$ is the implied volatility of options at the start of a period.
• $\sigma_{\text{realized}}$ is the volatility of the underlying measured over that same period, once it has passed.

Academic work usually states it in terms of variance, the square of volatility, because the payoff of a variance swap is exactly the difference between the two variances.

Suppose one-month index options trade at an implied volatility of 18 percent, and over the following month the index realizes 14 percent. The premium for that month is 4 volatility points. In variance terms it is $0.18^2 - 0.14^2 = 0.0324 - 0.0196 = 0.0128$. The figure for any single month can be negative: when markets turn turbulent, realized volatility exceeds what was implied and option sellers lose. The premium is a statement about the average.

For the S&P 500, implied volatility as measured by the VIX index has exceeded subsequent realized volatility in a large majority of months since the index was introduced. Research by Peter Carr and Liuren Wu, published in 2009, measured variance risk premiums on major share indices and individual shares and found them to be large and negative from the buyer's point of view, meaning that buyers of variance lost on average. Other studies have found that the size of the premium varies over time and that a high premium has tended to precede higher returns on shares.

• Demand for insurance. Many investors hold shares and buy puts for hedging. They are willing to pay more than the expected payout, as with any insurance, and this demand lifts option prices.
• Volatility rises in bad times. Volatility jumps when share prices fall, so a position that gains from higher volatility pays off when investors' other assets are losing. Such protection is valuable, and its sellers require compensation.
• Crash risk. Sellers face the possibility of sudden, very large losses that cannot be hedged away. The premium compensates them for returns with strongly negative skewness.
• Limited capital. The dealers and funds that sell options have finite capacity to bear losses, particularly in crises, when the premium tends to be widest.

On these explanations the premium is fair payment for risk and not a pricing error. The same demand for downside protection produces the volatility skew in index options.

Several positions collect the premium. Selling a short straddle or a strangle and applying delta hedging isolates it most directly. Writing a covered call or selling cash-secured puts combines it with exposure to the share market, and exchanges publish benchmark indices that track such strategies. An iron condor collects it with a capped loss. Institutional investors also use variance swaps and volatility futures. Rule-based versions of these approaches are discussed under systematic options trading.

The return pattern of selling volatility is steady small gains punctuated by rare large losses. Realized volatility far exceeded implied levels in October 2008 and in March 2020, and option sellers suffered losses equal to years of accumulated premium. On 5 February 2018, a sharp rise in volatility caused exchange-traded products that were short volatility futures to lose most of their value in a day.

Because losses arrive together with falls in share prices, the strategy offers little diversification when it is most needed, and the use of leverage can turn a severe loss into a total one. A long record of gains is not evidence of low risk. Summary measures that rely on the standard deviation of returns understate the danger, so the maximum drawdown and stress tests are more informative.

The premium is a cost to those who hold options for protection. A portfolio that continually buys index puts will, on average, lose the premium each year in exchange for gains in crashes. Whether that trade is worthwhile depends on the investor's ability to withstand large losses. Some funds specialize in holding such protection, accepting a steady cost for a large payoff in rare events. Volatility arbitrage traders sit between the two sides, buying or selling depending on whether the premium on offer looks too small or too large.

• Cboe Global Markets