How variance perpetuals work

This page explains the product in plain terms. For the exact rules, see Funding and the fixed charge and the contract reference.

Variance in one paragraph

Variance measures how much a price moves. It does not measure the direction. The contract takes the log return between two oracle prices and squares it. A move of -4% and a move of +4% give almost the same squared return. No move gives zero.

$$r=\ln \frac{P_{\text{new}}}{P_{\text{previous}}},\text{squared return}=r^2$$

The order price in the book is annualized variance. A quote of 1.573 is equal to an annual volatility of about 125%, because $\sqrt{1.573}\approx 1.254$. A quote of 0.36 is equal to an annual volatility of 60%. The volatility value is a display conversion only. The contract uses variance.

The two sides

Side	Receives	Pays
Long	The realized-variance leg: a payment for each squared return	The fixed charge: a payment for each second of time
Short	The fixed charge	The realized-variance leg

The contract nets the two legs at each accepted oracle observation. This net payment is the funding.

A long position is like insurance against price moves. In a calm market, the long pays more than it receives. In a jump, the long receives more than it pays.

One observation with numbers

One contract has a multiplier of 100 USDC per unit of annualized variance. The funding horizon is 7 days. The year has 365 days.

Take one long contract in the MON market. The charge is 1.573. The observation interval is 60 seconds.

Calm interval. The price does not move. The long pays the fixed charge:

$$\text{fixed charge}=100\times 1.573\times \frac{60}{604800}=0.0156\text{USDC}$$

For one day without a price move, that charge is about 22.47 USDC for each contract.

Jump interval. The price falls by a log return of -0.04, which is a drop of about 3.92%. The long receives the realized-variance leg:

$$\begin{array}{rl}\text{realized leg}& =100\times \frac{365}{7}\times {0.04}^2=8.3429\text{USDC}\\ \text{net payment}& =8.3429-0.0156=8.3273\text{USDC to the long}\end{array}$$

A rebound of +0.03 pays the long again. The direction does not change the sign of the squared return.

Break-even. The long gains in an interval when the realized leg is larger than the fixed charge. With the mark $K$, the interval $\mathrm{\Delta }t$, and the year $Y$ in seconds, that is:

$$|r|>\sqrt{K\frac{\mathrm{\Delta }t}{Y}}=\sqrt{1.573\times \frac{60}{31536000}}\approx 0.0017$$

In this example, the long gains when the price moves by more than about 0.17% in 60 seconds.

The return cap

The contract pays a squared return of at most 0.0025 for each observation. This is a log return of 0.05, which is a move of about +5.13% or -4.88%. A larger move receives the capped payment.

What "fixed" means

The charge is fixed for the interval that the contract settles. It is not fixed for the life of the position. After each observation, the current book mark becomes the charge of the next interval.

The charge is a variance value. A charge of 1.573 is not an interest rate of 1.573%. The charge is also not a trading fee.

Three sources of profit and loss

Source	When it changes	Formula
Funding	At each accepted observation	contracts * (realized leg - fixed charge) for a long
Mark profit and loss	When the book mark changes	contracts * 100 * (mark - entry price)
Trading fee	At each fill	0.05% of contracts * 100 * execution price, for each side

When makers expect more variance, they raise their quotes. The mark rises, and a long position gains from the mark also.

A new position waits for one observation

The contract keeps two position values for each account:

• The book position changes at once when an order fills.
• The funding position changes at the next accepted observation, after the contract pays the prior interval.

Thus a trader cannot see a price move, buy, and receive the payment for that move. A new position gets its first funding at the second observation after the fill. A closed position keeps its funding position, and the margin for it, until the next accepted observation.

See Delayed funding activation.

Where the price comes from

Two different prices are in each market:

Price	Source	Use
Oracle price of MON or ETH	The test oracle, at each observation	The squared return of the realized-variance leg
Variance mark	The order book	The fixed charge, the margin, and the mark profit and loss

The mark is the midpoint of the average bid price and the average ask price for 2 contracts on each side. Each side must have two or more different owners, and the spread must be 20% of the midpoint or less. If the book cannot give a valid mark, the mark freezes. See Order book and mark.

What an LP gets from it

A liquidity provider in an AMM loses a small amount each time the price moves, in the two directions. This loss grows with the squared return. A long variance position receives a payment that also grows with the squared return. The Hedging demo shows the two values for the same observations.

The hedge does not remove the direction risk of the tokens that the LP holds. See LP hedge model.