**Asset** refers to one of the selected components of the Volatility Index

**Business Day** for an asset refers to a day where all constituent Assets are trading and has a settlement Close Price

**ATM** or At the Money is a situation where an optionβs strike price is identical to the current market price of the underlying security

**Near the Money** refers to an options contract whose strike price is close to the current market price of the corresponding underlying security

**OTM** or Out of the Money is used to describe an option contract that only contains extrinsic value and have no intrinsic value. An OTM Call option has a strike price that is higher than the market price of the underlying Asset. An OTM Put option has a strike price that is lower than the market price of the underlying Asset

Vol Indices also known as the V series Indices at AiLA are designed to represent the level of implied volatility in a particular commodity sector or across commodity sectors. These indices are composed of the implied volatility recorded at market close for the at the money option with a strike that is nearest to the settlement price of the underlying asset.

The implied volatility is calculated using a black 76 model by using the settlement premium of the at the money option for the relevant asset. In a basket we weight each of these assets by the Vega of the asset traded over the year. This means that we look at total volume traded for each asset and then calculate the total Vega for the asset and divide it by the Vega of that sector.

- When considering which assets to include in our volatility index, we consider the following factors:
- Location β Primarily U.S. based except for Brent crude due to its high trading volume
- Option liquidity
- Consistency of trading of ATM/Near the Money option strikes

- The volatility indices cover assets from three major sectors β Energy, Agriculture and Metals

a. For each asset, the closest option contract with at least thirty calendar days to expiry is used

b. "Serial" contracts (contracts which expire into the next available future month), weekly expiry and other forms of early expiry contract are not considered due to poor liquidity

c. Contract selection is updated daily based on 2a)

- The index considers ATM implied volatility of each asset
- The ATM level is determined by the end of day settlement price of the nearest underlying futures contract with at least thirty calendar days to expiry
- Available option strikes are spaced at discrete intervals for each asset β E.g, Corn strikes move in five cent intervals, WTI Crude in fifty cent intervals
- The nearest OTM Call and Put strikes relative to the ATM level are used for the implied volatility calculation, or in the case that the ATM level falls exactly on an available strike, then calls and puts of that strike are used

- The Black 76 pricing formula for options on futures is used for calculating the implied volatility, IV
_{i,t,y}for asset i on Trading Day t of year y - Trading Day is defined as a day where all n constituent assets of the Volatility Index are trading
- The risk-free rate used for discounting in the calculation is taken from the US Treasury yield curve on the Trading Day
- The Implied Volatility is calculated by taking the settlement price of the option and back-solving using Black 76
- The Vega (option price sensitivity to 1% move in Implied Volatility) is calculated using Black 76 and the Implied Volatility. This is used in Weighting further elaborated in 5)
- The ATM Implied Volatility and Vega are taken as the linear interpolation of the ATM price level between the call and put strikes, or the average of values for the call and put if the strikes are equal to the ATM price level

- On each Trading Day, the Total Vega of each asset is calculated where:

Where ππ_{π,π‘,π¦}= Total Vega of asset π on trading day π‘ of year π¦

where π΄πππ_{π,π‘,π¦}= At the Money Vega of asset π on trading day π‘ of year π¦

where πΉπππ_{π,π‘,π¦}= Volume traded of underlying futures of asset π on trading day π‘ of year π¦

- The Annual Weighting is calculated each Trading Day for each asset using values for the previous calendar year:

Where π_{π,π¦}is the Weight for asset π on year π¦

where There are π trading days in year (π¦β1)

where There are π constituent assets in the Index

- The Annual Weighting is applied to each assetβs Implied Volatility each trading day to generate the Implied Volatility Index level. The Index Value is calculated on each trading day t of year y:

For any queries regarding the Methodology or Data Inputs, please contact [email protected]