A **variance swap** is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index.

One leg of the swap will pay an amount based upon the realized variance of the price changes of the underlying product. Conventionally, these price changes will be daily log returns, based upon the most commonly used closing price. The other leg of the swap will pay a fixed amount, which is the strike, quoted at the deal’s inception. Thus the net payoff to the counterparties will be the difference between these two and will be settled in cash at the expiration of the deal, though some cash payments will likely be made along the way by one or the other counterparty to maintain agreed upon margin.

Structure and features

The features of a variance swap include:

- the
**variance strike** - the
**realized variance** - the
**vega notional**: Like other swaps, the payoff is determined based on a notional amount that is never exchanged. However, in the case of a variance swap, the notional amount is specified in terms of vega, to convert the payoff into dollar terms.

Pricing and valuation

The variance swap may be hedged and hence priced using a portfolio of European call and put options with weights inversely proportional to the square of strike.^{[2][3]}

Any volatility smile model which prices vanilla options can therefore be used to price the variance swap. For example, using the Heston model, a closed-form solution can be derived for the fair variance swap rate. Care must be taken with the behaviour of the smile model in the wings as this can have a disproportionate effect on the price.

Uses

Many traders find variance swaps interesting or useful for their purity. An alternative way of speculating on volatility is with an option, but if one only has interest in volatility risk, this strategy will require constant delta hedging, so that direction risk of the underlying security is approximately removed. What is more, a replicating portfolio of a variance swap would require an entire strip of options, which would be very costly to execute. Finally, one might often find the need to be regularly rolling this entire strip of options so that it remains centered on the current price of the underlying security.

The advantage of variance swaps is that they provide pure exposure to the volatility of the underlying price, as opposed to call and put options which may carry directional risk (delta). The profit and loss from a variance swap depends directly on the difference between realized and implied volatility.^{[5]}

Another aspect that some speculators may find interesting is that the quoted strike is determined by the implied volatility smile in the options market, whereas the ultimate payout will be based upon actual realized variance. Historically, implied variance has been above realized variance,^{[6]} a phenomenon known as the Variance risk premium, creating an opportunity for volatility arbitrage, in this case known as the rolling short variance trade. For the same reason, these swaps can be used to hedge Options on Realized Variance.

Related instruments

Closely related strategies include straddle, volatility swap, correlation swap, gamma swap, conditional variance swap, corridor variance swap, forward-start variance swap, option on realized variance and correlation trading.

References

- ^ Jump up to:
^{a}^{b}*“Variance and Volatility Swaps”. FinancialCAD Corporation. Retrieved 2009-09-29.* **^***Demeterfi, Derman, Kamal, Zou (1999). “More Than You Ever Wanted To Know About Volatility Swaps”**(PDF)**. Goldman Sachs Quantitative Strategies Research Notes.***^***Bossu, Strasser, Guichard (2005). “Just What You Need To Know About Variance Swaps”**(PDF)**. JPMorgan Equity Derivatives report.***^***Carr, Madan (1998). “Towards a Theory of Volatility Trading”**(PDF)**. In “Volatility: New Estimation Techniques for Pricing Derivatives,” R. Jarrow (ed.) RISK Publications, London.***^***Curnutt, Dean (February 2000). “The Art of the Variance Swap”. Derivatives Strategy. Retrieved 2008-09-29.***^***Carr, Wu (2007). “Variance Risk Premia”. AFA 2005 Philadelphia Meetings. SSRN 1024284.*Missing or empty |url= (help)