Variance swap
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In finance, a variance swap is a financial derivative whose payoff is equal to the difference between the square of annualized realized volatility (that is, the annualized realized variance) of returns on the underlying price and a fixed quantity, sometimes known as the variance strike, over a given period. It is effectively a forward contract on the realized variance.
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[edit] 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.
The payoff of a variance swap is given as follows:
- <math>N_{var}(\sigma_{realized}^{2}-\sigma_{strike}^{2})</math>
where:
- <math>N_{var}</math> = variance notional (a.k.a. variance units),
- <math>\sigma_{realized}^{2}</math> = annualized realized variance, and
- <math>\sigma_{strike}^{2}</math> = variance strike.[1]
The annualized realized variance is calculated based on a prespecified set of sampling points over the period. It does not coincide with the classic statistical definition of variance, but follows the usual market convention of not subtracting the mean.
It is market practice to determine the number of contract units as follows:
- <math>N_{var}=\frac{N_{vol}}{2\sigma_{strike}}</math>
where <math>N_{vol}</math> is the corresponding vega notional for a volatility swap.[1] This makes the payoff of a variance swap comparable to that of a volatility swap, another less popular instrument used to trade volatility.
The payout of a variance swap is often capped.
[edit] 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.
Using the Heston model, a closed-form solution can be derived for the fair variance swap rate.
[edit] Uses
Variance swaps can be used to trade volatility directly. Although options strategies can be used to trade volatility, strategies that are not delta neutral may be vulnerable to movements in the underlying price. Even if investors use a delta neutral options strategy, their profit and loss profile exhibits a complicated dependence on the underlying price and time.
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.[2]
[edit] 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 realised variance and correlation trading.
[edit] References
- ^ a b Variance and Volatility Swaps. FinancialCAD Corporation. Retrieved on 2009-09-29.
- ^ Curnutt, Dean (2000-02). The Art of the Variance Swap. Derivatives Strategy. Retrieved on 2009-09-29.
- Bossu, Strasser, Guichard (2005), Just What You Need To Know About Variance Swaps, JPMorgan Equity Derivatives report. PDF
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