# Base Funding Rate

Each NIL contract has a “base funding rate”, which is calculated based on a volatility model for the token pair and the strike price on the contract.
At a high-level, we use the expected volatility of Token A to calculate the average expected ILV change over the next period for the contract’s strike price.
We then arrive at the base funding rate by dividing the average expected ILV change over the next period by the total LP position size represented by the contract.

## Formula

Using the equations below, we can calculate the period base funding rate per NIL contract.

### Historical Volatility

First, calculate the standard deviation of price returns for Token A over a rolling 30 day window. This is a statistical measurement of historical realized volatility widely used in finance.
$σ = \:TokenA_{HV}=\: \:\sqrt{\text{$$\cfrac {\textstyle\sum_{i=1}^n \:(R_i\:–\:\bar{R})^2} {n-1}$$}}$

### Implied Volatility

Then, we incorporate a measure of forward expected price volatility. This is done by measuring the Black-Scholes implied volatility of widely traded ETH option contracts with expiry dates of 30 days into the future. This tells us how the market is pricing ETH's forward looking volatility.
Then, we calculate the spread between ETH's implied volatility and historical volatility.
$ETH_{IVspread} = \: ETH_{IV} \:\: – \:\: ETH_{HV}$
We interpret the ETH IV-HV spread as the market's view on the premium or discount to apply to historical realized volatility, in order to arrive at Token A's market priced implied volatility.
$TokenA_{IV} = \: TokenA_{HV} \: + \: ETH_{IVspread}$
We use the ETH implied volatility spread as a proxy because other tokens do not have meaningfully liquid options markets that we can directly calculate implied volatility from.
Token A's implied volatility tells us how much the market expects the price of Token A to increase or decrease against Token B over the next funding period.

### Expected ILV Change

​Using our ILV equation and the Token A's expected price change from the volatility model, we can calculate the average expected ILV change over the next funding period.
Expected volatility tells us how much we can expect the price of Token A to move, but we do not know whether it will be up or down. ILV incurred is similar (but not exactly the same) from a price increase and a price decrease of the same magnitude, so we average the two values.
$ILVΔ = \: ILV_{PeriodEnd} \:\: – \:\: ILV_{Current}$
$Expected\:ILVΔ_{\:Average} = \: \:\text{$$\cfrac {ILVΔ_{PriceIncrease}\:+\:ILVΔ_{PriceDecrease}} {2}$$}$

### Base Funding Rate

Finally, we calculate the contract's base funding rate for the period by dividing the average expected ILV change by the total LP position size represented by the contract.
$FundingRate_{Base} = \: \:\text{$$\cfrac {Expected\:ILVΔ_{\:Average}} {LP_{Size}}$$}$
This rate can be annualized so LPs can easily make a direct comparison between annualized LP fees + rewards and the annualized ongoing cost of IL protection.
$Annualized Funding Rate_{Base} = \: \:\text{$$\cfrac {Expected\:ILVΔ_{\:Average}*365} {LP_{Size}}$$}$
The base funding rate can be thought of as the market's view of fair pricing of IL protection on the contract, if the price of Token A moved exactly as expected per implied volatility.