Funding Calculation

Funding Fee:

$$F=-1*R*\frac{T}{8 \ hours} * B*X$$

• F: Amount received/paid

• R: 8-hour rate

• B: Net position (+, -)

• X: On-chain price;

• T: Interval time between funding fees (8 hours)

The funding rate is updated every minute and paid on an 8-hour basis.

Funding Rate (R) Calculation:

$$r = Premium + clamp(IR-Premium, -D, D)$$

$$R=clamp(r, -0.75*M_{i}, 0.75*M_{i})$$

where:

• $Clamp$: Clamp(x, min, max) represents when X<min, then X=min; if x>max, then X=max; If $max\ge a \ge min$,then return X.

• $D$: A dampening factor, D=0.05%

• $IR$: Interest Rate = 0.01%

• $M_{i}$: maintenance margin rate

• $Premium$: Premium Rate

Premium Rate Calculation:

We need to calculate the premium first to get the funding rate R. The premium rate is calculated every minute based on the current distribution of price in the order book:

$Premium(mins)=\frac{(Max(0, \ Impact\ Bid\ Price – Index \ Price) - Max(0, Index\ Price - Impact\ Ask\ Price)) }{Index\ Price}$

At the end of every 8-hour period, we first calculate the premium of each minute(Premium(mins)), and then take the arithmetic mean of the sum of Premium(mins) to get the 8-hour premium(Premium(hours)).

$Premium(hours) = mean(\sum premium(mins))$

where:

• Index Price: Off-chain price, the average of the index prices of major exchanges

• Impact Bid Price: Calculated based on Impact notional value (INV) of the bid-side order book

• Impact Ask Price: Calculated based on the Impact notional value (INV) and the ask-side order book

• Impact Notional Value(INV): A system default effective impact amount. Different trading pairs may have different INV. Current INV is $\frac{3000}{Maintence \ Margin\ Rate}$

Impact Ask Price calculation:

Ask-side order book

Level	Price	Quantity	Notional Quantity	Accumulated Notional Quantity
1	$p_{1}$	$q_{1}$	$p_{1}*q_{1}$	$p_{1}*q_{1}$
2	$p_{2}$	$q_{2}$	$p_{2}*q_{2}$	$p_{1}*q_{1}+p_{2}*q_{2}$
3	$p_{3}$	$q_{3}$	$p_{3}*q_{3}$	$p_{1}*q_{1}+p_{2}*q_{2}+p_{3}*q_{3}$
...	...	...	...	...
n	$p_{n}$	$q_{n}$	$p_{n}*q_{n}$	$\sum p_{n}*q_{n}$

Find the first X level such that $\sum_{i=1}^{X} p_{i}*q_{i}<INV<\sum_{i=1}^{X+1} p_{i}*q_{i}$, e.g. If the first level satisfied the condition, then the Impact Ask Price = $P_{1}$.

Impact Ask Price:

$$\frac{INV}{\sum_{i=1}^{X}q_{i}+\frac{INV-\sum_{i=1}^{X} p_{i}*q_{i}}{P_{x+1}} }$$

Impact Bid Price Calculation:

Similar to the impact ask price calculation.