# Funding Rate
### **Overview**
The **funding rate** is a mechanism used in perpetual contracts to keep their prices aligned with the spot market. Unlike traditional futures contracts, which converge to the spot price at expiration, **perpetual contracts have no expiration or delivery**. Instead, they use the **funding rate** to maintain price anchoring.
### **Funding Fee Settlement Rules**
* Funding is settled every 8 hours:
* 00:00 GMT+8
* 08:00 GMT+8
* 16:00 GMT+8
* Only traders **holding a position at the time of settlement** are subject to funding fees.
* **Funding direction**:
* If the funding rate F > 0:\
Longs **pay** funding fees, and Shorts **receive**
* If the funding rate F < 0:\
Shorts **pay** funding fees, Longs **receive**
> The platform does **not charge** any funding fees. All fees are **peer-to-peer**.
#### **Funding Fee Calculation**
$$
\text{Funding Fee} = \text{Position Value} \times \text{Funding Rate}
$$
$$
\text{Position Value} = \text{Position Size} \times \text{Contract Size} \times \text{Mark Price}
$$
### **Funding Rate Components**
#### 1. **Composite Rate**
For a contract pair (e.g., BTC/USDT):
* Underlying asset: BTC
* Quote asset: USDT
$$
\text{Composite Rate} = \frac{r\_q - r\_u}{N}
$$
Where:
* rq: Quote currency interest rate
* ru: Underlying currency interest rate
* N: Number of funding settlements per day
**Example**:
$$
r\_q = 0.06%, \quad r\_u = 0.03%, \quad N = 3
$$
$$
\text{Composite Rate} = \frac{0.06% - 0.03%}{3} = 0.01%
$$
#### 2. **Funding Rate Basis Rate**
This reflects the decay of the funding impact over the settlement cycle:
$$
\text{Basis Rate} = F \times \left( \frac{t}{T} \right)
$$
Where:
* F: Funding rate of the current period
* t: Time remaining until next settlement (in minutes)
* T: Total duration of the funding cycle (480 minutes)
**Example**:
$$
F = 0.01%, \quad t = 450, \quad T = 480
$$
$$
\text{Basis Rate} = 0.01% \times \left( \frac{450}{480} \right) = 0.009375%
$$
#### 3. **Reasonable Price**
$$
\text{Reasonable Price} = P\_{\text{index}} \times (1 + \text{Basis Rate})
$$
**Example**:
$$
P\_{\text{index}} = 10,000, \quad \text{Basis Rate} = 0.005%
$$
$$
\text{Reasonable Price} = 10,000 \times (1 + 0.00005) = 10,000.5
$$
### **Depth-Weighted Prices**
Let:
* Pb: Depth-weighted bid price (buy orders)
* Pa: Depth-weighted ask price (sell orders)
* Pr: Reasonable price
### **Premium Index Calculation**
$$
\text{Premium Index} = \frac{\max(0, P\_b - P\_r) - \max(0, P\_r - P\_a)}{P\_{\text{index}}} + \text{Basis Rate}
$$
#### **Cases**:
1. If Pa ≥ Pr ≥ Pb, then:
Premium Index=Basis Rate\text{Premium Index} = \text{Basis Rate}Premium Index=Basis Rate
$$
\text{Premium Index} = \text{Basis Rate}
$$
2. If Pb > Pr, then:
$$
\text{Premium Index} = \frac{P\_b - P\_r}{P\_{\text{index}}} + \text{Basis Rate}
$$
3. If Pr > Pa, then:
$$
\text{Premium Index} = \frac{P\_a - P\_r}{P\_{\text{index}}} + \text{Basis Rate}
$$
### **Average Premium Index**
The **average premium index** at time ttt is the **arithmetic mean** of all premium index values from t - 60 minutes to t.
### **Final Funding Rate Formula**
The final **funding rate** is constrained within predefined bounds:
$$
F = \text{clamp} \left( \text{AvgPremium} + \text{clamp}(C - \text{AvgPremium}, D\_{\text{max}}, D\_{\text{min}}), F\_{\text{max}}, F\_{\text{min}} \right)
$$
Where:
* F: Final funding rate
* C: Composite rate
* Dmax, Dmin: Premium deviation bounds
* Fmax, Fmin: Funding rate bounds
#### **Clamp Function**:
$$
\text{clamp}(x, \text{max}, \text{min}) = \begin{cases} \text{max}, & \text{if } x > \text{max} \ \text{min}, & \text{if } x < \text{min} \ x, & \text{otherwise} \end{cases}
$$
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