# Hedging

Arrow's Automated Hedging Engine (AHE) tracks the AMM's option obligations.

The Arrow system runs an automated hedging engine to offset changes in the risk profile of the trading pool due to underlying price movements. This works as follows. Along with prices, the AMM calculates a

$\Delta$

(a "delta") or hedge position for each new option added or removed from the system. We use both BSM deltas and skew-adjusted deltas computed using the SVI model implied volatility. For call options, the deltas are$\Delta_{bsm} = N(d_{1}(\sigma_{svi})) \\ \Delta_{skew} = \Delta_{bsm} + \text{vega}_{svi} \partial_{svi}$

The skew-adjusted delta corrects the BSM delta with a term that multiplies the contract's vega (using the SVI IV) by the slope of the SVI curve at the contract's moneyness,

$\partial_{svi}$

The smart contract that houses the trading pool balances then takes that

$\Delta$

and picks up the corresponding balance in the underlying. If the net $\Delta$

is positive, the position is obtained by programmatically swapping stable coin for the underlying (or vice-versa, depending on the sign of the option $\Delta$

) on a DEX such as Pangolin or Trader Joe. If the net

$\Delta$

is negative, the position is obtained by programmatically interacting with an on-chain lending protocol such as BenQi or Banker Joe. In the latter case, if the option $\Delta$

is negative, the short position in the underlying is increased, and if the option $\Delta$

is positive, the short position is decreased.Last modified 3mo ago