Variance swap

The variance swap is a forward contract in which the underlying is the measured or realized variance of the underlying asset over the life of the swap, and the forward rate (or swap rate) is the variance set on the trade date.

It is important to note that:

• According to market convention the measured or realized variance is calculated by taking daily samples of the underlying asset price (spot rate, stock price or index value, etc.). The absolute daily changes in value are calculated over the life of the swap and the value annualized to provide the familiar % quotation for volatility.
• The swap rate for a variance swap is conventionally quoted in terms of volatility.
• Variance is the mathematical square of the volatility.

The payout of the variance swap is as follows:

Notional per variance point * (realized variance – (traded swap rate * traded swap rate))

The notional input into this calculation (in line with market convention) is the variance notional. This value is itself calculated as follows:

vega notional input by the user in the pricing page ÷ (2 x traded swap rate)

It is important to note the following:

The PV (or present value) result displayed in the Results area is the payout at maturity discounted to today's worth.
For a variance swap the positive payout for a 1% increase in volatility is actually more than the loss for a 1% decrease in volatility.

Note the following about equity variance swaps:

• The calculation of volatility is affected by the number of business days in the swap. By convention, this number is defined as part of the swap contract and should be used for the calculation of volatility even if additional, unexpected holidays occur. This is particularly important for ensuring that the calculation of hedges for the swap is performed accurately.
• The proper calculation of accrued volatility requires that the user specify whether the dividends are reinvested in the asset or not.

Why buy a variance swap?

• A variance swap only involves exposure to volatility, not to the underlying asset itself. It is a delta and gamma neutral strategy.

Both swaps are used by many types of investors. For example:

• A speculative investor may use the swaps to speculate on future volatility, to bet on an increase or decrease in volatility over a period of time or on the future actual direction of the volatility without any gamma exposure. For example, if the investor thinks the volatility will increase, he will buy a variance swap; if he thinks it will decrease, he will sell a variance swap.
• A fund manager can use the swaps as a hedge against volatility. High actual volatility can adversely affect a fund manager’s portfolio forcing them to constantly buy/sell stocks as the underlying market moves.
• A corporation can use the swaps to hedge the volatility exposure of other positions, usually for FX exposure.
  You can of course use other option classes (e.g., vanillas, straddles, binaries) to hedge volatility. However, all these classes involve some sort of delta or gamma exposure. The volatility and variance swaps offer a “pure” vega hedge with no sensitivity to the direction of the underlying asset, i.e., there is no delta or gamma risk involved.