# Trading Fees

## Fixed Fees

A fixed fee structure is implemented for traders based on the total open interest, whether positions are opened or closed:

Taker fixed fee: 0.03% of the notional

Maker fixed fee: 0.07% of the notional

Fixed fees are subject to variation between assets to incentivize the Diem AMM to accept higher-risk assets. Additionally, option fees are capped by 35% of the option price, as follows:

$\large Fixed\ fees = Min(0.35*initial\ premium\ price , fixed\ fee\ * total\ open\ interest)$

### Dynamic Fees

To protect the AMM from over-exposure to market volatility and directional risk, a dynamic fee system is introduced during the buying and selling process to evaluate the risk each position is introducing to liquidity providers, and by offering higher fees accordingly.

The main focus of the dynamic fees is to help rebalance delta and vega manually towards neutral exposure.

### Vega Fee:

Vega measures the option's sensitivity to changes in implied volatility. The following Greek calculates how much the option's price is expected to change for a 1% change in the implied volatility of the asset traded.

When buying an option, the trader is decreasing the AMM's net vega exposure

When selling an option, the trader is increasing the AMM's net vega exposure

By that:

### $\large v_f = \begin{cases} VEGA\_MAKER\_FACTOR & \text{if } |v_1| < |v_0| \\ VEGA\_TAKER\_FACTOR & \text{if } |v_1| \geq |v_0| \end{cases} \$

### $\Large Vega_{fee} = | |v_1|-|v_0||*v_f$

Where $|v_0|$ is the AMM Vega prior to the trade being executed and $|v_1|$ is the AMM Vega after the trade is live

#### Example

Suppose the AMM net Vega $v_0 = 3.2$ and a trader wants to trade an option with a Vega of $v = 0.02$

If the user wants to sell 1 option contract, then they force the AMM to buy 1 contract from the AMM, so the AMM needs to go long 1 contract, and the new AMM net Vega is $v_1 = v_0 + v = 3.22$

$v_1 > v_0$, the AMM will treat the position opened as a taker and the trader needs to pay $0.02*v_f$ where $v_f = VEGA\_TAKER\_FACTOR$

### Delta Fee:

Delta measures the option's price sensitivity to changes in the price of the underlying asset. The following Greek calculates how much the option's price is expected to change for a $1 change in the price of the asset traded.

When buying a Call Option, the trader is decreasing the AMM's net delta exposure as the AMM acts as the seller of the call option

When buying a Put Option, the trader is increasing the AMM's net delta exposure as the AMM acts as the seller of the put option

When selling a call option, the trader is increasing the AMM's net delta exposure as the AMM acts as the buyer of the call option

When selling a put option, the trader is decreasing the AMM's net delta exposure as the AMM acts as the buyer of the put option

By that:

### $\large \Delta f = \begin{cases} \text{DELTA\_MAKER\_FACTOR} & \text{if } |\Delta_1| < |\Delta_0| \\ \text{DELTA\_TAKER\_FACTOR} & \text{if } |\Delta_1| \geq |\Delta_0| \end{cases}$

### $\Large \Delta_{fee} = || \Delta_1|-|\Delta_0||*\Delta_f$

Where $|\Delta_0|$ is the AMM Delta before the trade being executed and $|\Delta_1|$ is the AMM Delta after the trade is live

#### Example

suppose the AMM net Vega $\Delta_0 = 3.1$ and a trader wants to open a put option position with a Delta of $\Delta = - 0.5$, by that the AMM is exposed to $-\Delta$ and needs to increase his Delta exposure by 0.5.

The AMM total Delta exposure will be: $\Delta_1 = \Delta_0 -\Delta = 3.6$

$|\Delta_1| > |\Delta_0|$ , trader is considered as a taker and charged $\Delta_f*0.5$ where $\Delta_f = DELTA\_TAKER\_FEE$

Charging dynamic fees based on maker/taker status will add a layer of stability for the AMM and assure to align incentives between liquidity providers and traders. Normally the vega and delta maker factor is close to zero to incentivize makers to trade into the system and balance the AMM into net zero exposure.

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