The variance swap has gained increasing popularity among institutional investors seeking synthetic exposure to equity market volatility. While demonstrated as a useful hedge to numerous trading strategies, the potential loss associated with the long variance swap in a low volatility environment was deemed too high by many who would otherwise employ them as a hedge to their credit or equity portfolios. Investors' desire to use the volatility markets to hedge risk while only committing a defined dollar amount to the hedging strategy ultimately spawned a new product: options on realized variance.
Options On Realized Variance
The payout of an option on realized variance is ultimately determined in a manner similar to that of a variance swap, i.e. the payment is based on the future realized variance of the underlying relative to an agreed-upon strike level. For example, with a call on realized variance, the option buyer would pay a premium amount for the right to receive the excess of realized variance relative to the strike but would not owe additional money should future realized variance fall below the strike price. In graph 1, we compare the payout of the long variance swap and the call option on realized variance.
Note the 'breakeven' realized volatility level, where the payout of the variance swap is equal to the payout of the option on realized variance, is not exactly equal to the strike minus the initial call premium (normally quoted in volatility points). That is because an investor long variance will always receive a convex payout. The profit earned from "being right" is positively asymmetric to the loss suffered from "being wrong" by the same amount in volatility terms.
Other Applications
Although the majority of transactions to date have seen investors buying calls on realized variance, others have used them differently. Call spreads on realized variance have been implemented to reduce the amount of upfront premium paid to obtain exposure to subsequently realized variance. Investors who have experienced several years of relatively quiet markets and believe that future realized volatility will be less than predicted have also purchased puts on realized variance to obtain short exposure to market volatility without exposure to the potential loss that a short variance swap position allows. This amounts to a short vol, long so-called vol of vol profile. In graph 2, we plot the profit/loss of two possible short volatility strategies since January 1, 1990, using a short six-month variance swap versus employing a long six-month put on realized variance:
As illustrated in graph 2, the profit/loss of the different strategies track one another, but the tail risk associated with a period of increased realized volatility (such as in late 2002) is greatly diminished by the use of the put on realized variance. In fact, for a six-month variance swap at USD200,000 per volatility point, sold at 17% on May 1, 2002, an investor would have lost USD4.3 million, as compared with the USD600,000 premium for a put on realized variance, struck at 17% for three volatility points at USD200,000 per volatility point. This product appeals to those investors who have interest in selling volatility but who want to commit only a specific amount to the strategy.
Options On Variance Swaps
Another permutation currently contemplated may appeal to those investors whose exposure is more concentrated in implied rather than realized volatility. An option on realized variance permits an investor to gain exposure to realized volatility (gamma). An option on a variance swap, on the other hand, permits an investor to instead gain exposure to implied volatility (vega). An option on a variance swap is a contract where a party pays an upfront premium for the right to buy or sell a variance swap in the future for a pre-determined amount at a pre-determined strike. For example, an investor who purchases a six-month call on a one-year variance swap struck at 16 for USD100,000 per volatility point, has the right, but not the obligation, to buy a one-year variance swap struck at 16 for up to USD100,000 per volatility point. This right expires in six months. Only if and when the client decides to exercise the option and execute a variance swap will he obtain gamma exposure.
This potential new product has advantages to the alternatives that currently allow an investor to profit from a change in implied volatility. Last year, the CBOE launched the VIX futures contract as a vehicle to express a view on the level of the VIX at some point in the future. A more prevalent method employed by investors seeking vega exposure is the forward starting variance swap--a combination of two variance swaps. If an investor wanted to gain exposure to the level of one-year variance over the next six months, but did not want exposure to realized volatility during that six-month period, he would buy an 18-month variance swap and sell a six-month variance swap. By combining the two trades in the proper ratio, the investor neutralizes the exposure to realized volatility but maintains exposure to implied volatility. In this transaction, the investor will become long a one-year variance swap after 6 months have passed.
Each of these alternatives has drawbacks, however. VIX futures only isolate a particular month and suffer from liquidity issues. Variance swaps are liquid, but a forward starting variance swap may not meet the needs of investors who want to pay a defined amount of premium to hedge their vega exposure. Options on variance swaps facilitate taking a view on implied volatility while only committing a precise dollar amount to the position.
The Vol Of Vol
By combining puts and calls to form a straddle on realized variance, an investor can create pure vol of vol exposure. An option on realized variance can be thought of much the same way as a standard equity option--the pricing model will take as inputs the spot price, strike price, carry, time to expiration and volatility. With an option on realized variance, however, the spot price is itself a volatility level (i.e. the at-the-money level of variance) and the equivalent to the volatility input in a standard option-pricing model becomes a vol of vol input. Therefore, an investor buying or selling a straddle on realized variance may structure a trade that is reasonably directionally neutral--roughly delta zero where the underlying of the option is realized volatility--but allows an investor to take a view on the vol of vol.
Consider an example where an investor sells a straddle on realized variance struck at 16 vol and collects 3.50 volatility points (i.e. with an initial vega of USD100,000/vol point, the investor would receive USD350,000). To determine the realized volatility levels at breakeven (VolBE), the value of the option at expiration should equal the upfront premium received.
Because of the convexity of a variance swap payout, when converting from variance back to volatility levels, the breakeven on the put is farther away from the strike than the breakeven on the call:
The investor in this example anticipates realized volatility would fall between 12 and 19.18, with maximum profit at a realized volatility level at the strike of the straddle, or 16. While the straddle would not likely be dynamically delta-hedged, the investor could choose to buy or sell variance swaps periodically to facilitate a short vol of vol view as opposed to taking a view, on whether subsequent realized volatility will fall within the aforementioned range.
Conclusion
Advances in synthetic volatility products such as variance swaps, options on realized variance, and options on variance swaps offer investors access to a wider set of hedging alternatives. While the option products were originally designed to offer a less expensive method to hedge portfolios negatively correlated to equity market volatility, they have been tailored in innovative ways to meet specific investment objectives and expectations.
This week's Learning Curve was written by Ali Samadi, v.p. and equity derivative strategist at Banc of America Securitiesin New York.
