A variance swap is an
over-the-counter
Over-the-counter (OTC) drugs are medicines sold directly to a consumer without a requirement for a prescription from a healthcare professional, as opposed to prescription drugs, which may be supplied only to consumers possessing a valid prescr ...
financial derivative
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be u ...
that allows one to
speculate
In finance, speculation is the purchase of an asset (a commodity, goods, or real estate) with the hope that it will become more valuable shortly. (It can also refer to short sales in which the speculator hopes for a decline in value.)
Many s ...
on or
hedge
A hedge or hedgerow is a line of closely spaced shrubs and sometimes trees, planted and trained to form a barrier or to mark the boundary of an area, such as between neighbouring properties. Hedges that are used to separate a road from adjoini ...
risk
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environme ...
s associated with the magnitude of movement, i.e.
volatility, of some
underlying
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be use ...
product, like an
exchange rate
In finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of ...
,
interest rate
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, th ...
, or
stock index
In finance, a stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current stock price levels with past prices to calculate market performance.
Two of the pri ...
.
One leg of the swap will pay an amount based upon the realized
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...
of the price changes of the underlying product. Conventionally, these price changes will be daily
log
Log most often refers to:
* Trunk (botany), the stem and main wooden axis of a tree, called logs when cut
** Logging, cutting down trees for logs
** Firewood, logs used for fuel
** Lumber or timber, converted from wood logs
* Logarithm, in mathe ...
returns
Return may refer to:
In business, economics, and finance
* Return on investment (ROI), the financial gain after an expense.
* Rate of return, the financial term for the profit or loss derived from an investment
* Tax return, a blank document or t ...
, based upon the most commonly used closing price. The other leg of the swap will pay a fixed amount, which is the
strike
Strike may refer to:
People
*Strike (surname)
Physical confrontation or removal
*Strike (attack), attack with an inanimate object or a part of the human body intended to cause harm
*Airstrike, military strike by air forces on either a suspected ...
, 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
In economics, cash is money in the physical form of currency, such as banknotes and coins.
In bookkeeping and financial accounting, cash is current assets comprising currency or currency equivalents that can be accessed immediately or near-imm ...
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
Margin may refer to:
Physical or graphical edges
*Margin (typography), the white space that surrounds the content of a page
*Continental margin, the zone of the ocean floor that separates the thin oceanic crust from thick continental crust
*Leaf ...
.
Structure and features
The features of a variance swap include:
* the variance strike
* the realized variance
* the vega notional: Like other
swap
Swap or SWAP may refer to:
Finance
* Swap (finance), a derivative in which two parties agree to exchange one stream of cash flows against another
* Barter
Science and technology
* Swap (computer programming), exchanging two variables in t ...
s, the payoff is determined based on a
notional amount
The notional amount (or notional principal amount or notional value) on a financial instrument is the nominal or face amount that is used to calculate payments made on that instrument. This amount generally does not change and is thus referred to a ...
that is never exchanged. However, in the case of a variance swap, the notional amount is specified in terms of
vega
Vega is the brightest star in the northern constellation of Lyra. It has the Bayer designation α Lyrae, which is Latinised to Alpha Lyrae and abbreviated Alpha Lyr or α Lyr. This star is relatively close at only from the Sun, an ...
, to convert the payoff into dollar terms.
The payoff of a variance swap is given as follows:
:
where:
*
= variance notional (a.k.a. variance units),
*
= annualised realised variance, and
*
= variance strike.
The annualised realised variance is calculated based on a prespecified set of sampling points over the period. It does not always coincide with the classic statistical definition of variance as the contract terms may not subtract the mean. For example, suppose that there are
observed prices
where