Dynamic Bid-Ask Spreads

On SDX, the AMM charges a bid-ask spread fee that serves as the primary mechanism for liquidity providers to earn a fair return, while minimizing risks through rebalancing of greeks. As the mark price of an option is composed of the intrinsic value $V_I$ and time value $V_T$, two bid-ask spread multipliers are applied independently on each value and combined to get an option price, , that will be paid for the specific trade.

$$P = I * V_I + F * V_T$$

For intrinsic value, a fee of $I * V_I$ is added or subtracted for ask and bid orders respectively. $I$ is a pool level parameter that can range from 0% to 10%. This represents a fixed fee on intrinsic value that the AMM is charging to make the order for a trade.

For time value, it is multiplied by $F$, a factor that is the combination of the individual greek pricing factors, $F_{G}$, and subjected to max and min bounds and volatility shock effects, and serves to incentivize trades that rebalance greeks.

$$F = \alpha_\delta*F_\delta + \alpha_\gamma*F_\gamma + \alpha_\nu*F_\nu + \alpha_\theta * F_\theta \\ where \\ \sum_{G\in \{\,\alpha,\gamma,\nu,\theta\}} \alpha_G = 1 \; \\ and \\ F_{min}\le F \le F_{max}\\$$

Each greek pricing factor, $F_G$, is calculated using a cubic function with the normalized post-trade greek $G_{norm}$ as an input, subject to max and min bounds. Parameters $a, b, c, d, k, n$ are shared for both bid and ask orders for the same greek, while $bid\_adj$ differs between bid and ask to form the spread.

$$F_G=f(G_{norm}, O, M, D) = \\aG_{norm}^3 + bG_{norm}^2 + cG_{norm} + d + bid\_adj + kM^{n}D\\ where\\ G_{norm} = Post\ Trade\ Normalized\ Greek\\ O\in\{{call, put}\}\\M = |Strike-Spot|/Spot\\n \in\{{1, 2, 3, 4}\}\ \\ D (direction) = -1\ if\ bid\ or\ 1\ if \ ask\\ and\\ F_{min\_ask}\le F_{G\_ask} \le F_{max\_ask}\\ F_{min\_bid}\le F_{G\_bid} \le F_{max\_bid}\\$$

$$G_{norm} = \frac{\sum_{} G_i + G_{underlying}*underlying\_held}{NAV_{underlying}}\\ where \\ i\in{Open\; Positions} \\ G_{underlying} = G\; per \;unit\; underlying,\; s.t. \\ G_{underlying,\{\gamma,\nu,\theta\}} = 0 \\ G_{underlying,\delta} = 1$$

$$NAV_{underlying} = \\ \frac{stable\_collateral\_held}{underlying\_spot\_price} + underlying\_collateral\_held + \\ positions\_value\_in_\_underlying+option\_collateral\_in_\_underlying$$

For instance, suppose a vault seeks to maintain a target normalized delta of 0.5 and the sale of put options causes the normalized delta to increase from 0.4 to 0.7. At 0.7 normalized delta, an ask-price factor produced by the cubic function could be 1.5 - which implies that the asking price would be 1.5x that of mark price, should the fee be solely weighted by the delta price factor.

Since $f(G_{norm}, O, M, D)$ is defined by a set of configurable parameters, $a,b,c,d,k, n$ for each option type and trade direction, this allows formulation of price factor curves like below:

The dynamic bid-ask spread fee is configured, via parameter $k$ multiplied by moneyness term, $M^n$, to widen on strikes that are further out of the money, to account for the higher risks of making for a less liquid market. At the money strikes would simply have a dynamic spread of $\pm k$, as $M = 1$.