> For the complete documentation index, see [llms.txt](https://docs.kryptox.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.kryptox.finance/risk-and-liquidations/pricing-and-funding.md).

# Pricing & Funding

## **概述**

本协议采用由**指数价格（Index Price）**、标记价格（Mark Price）**和**资金费率（Funding Rate）构成的定价体系，用于实现：

* 外部市场价格锚定
* 抗操纵的风险控制
* 永续合约价格向现货价格收敛

***

## **1. 指数价格（Index Price）**

指数价格基于多个交易所现货价格的加权平均计算：

```
Index Price = Σ (w_i × P_i)
```

其中：

* P\_i：第 i 个交易所现货价格
* w\_i：对应权重，满足 Σ w\_i = 1

为增强鲁棒性：

* 当价格偏离中位数超过 5% 时进行裁剪：

```
P_i' = min(max(P_i, 0.95*Medium), 1.05*Medium)
```

* 异常或失效数据对应权重置为 0

最终：

```
Index Price = Σ (w_i × P_i')
```

指数价格每秒更新一次。

***

## **3. 标记价格（Mark Price）**

标记价格用于清算与盈亏计算。

***

### **3.1 计算公式**

```
Mark Price = P × C + Index Price × (1 - C)
```

**其中**

* P = Index Price + MA(Basis)
  * MA(Basis) = MovingAverage(Basis, 2.5 min)
  * Basis = (Bid₁ + Ask₁) / 2 - Index Price
* C = clamp(Basis / MA(Basis), 0.3, 0.7)

### **3.2 机制特性**

* 当市场偏离较小时：Mark Price 更接近盘口价格
* 当偏离较大时：Mark Price 向 Index Price 收敛
* MA 平滑降低短时噪音影响

***

## **4. 资金费率（Funding Rate）**

资金费率由 利率（Interest, I）**与**溢价指数（Premium Index, P）构成，用于驱动永续合约价格向指数价格收敛。

***

### **4.1 资金费率公式**

```
F = Clamp(MA [{(ask1 + bid1) / 2 - Index} / Index + I], b, a)
```

其中：

* F：资金费率
* ask1 / bid1：来自订单簿的最优买卖价格
* 移动平均(MA)计算方式：以当前时间点为基准，向前回溯对应结算周期长度内的溢价指数数据，并对窗口内的所有有效数据进行计算，溢价指数数据按每分钟采样。
  * 假设某合约的资金费用结算周期为8 小时，当时间为14:59 时，资金费率计算所使用的MA 数据范围为07:00 至14:59 期间每分钟采集的溢价指数数据，共480 个数据点（n = 480）。
* I：利率，当前USDT的日利率为0.06%。每8小时结算的周期利率 I = 0.06% / (24 / 8)

上下限约束

* a = (IMR\_min - MMR\_min) × 0.75
* b = -(IMR\_min - MMR\_min) × 0.75

***

### **4.2 资金费支付**

```
Funding Payment = Position Size × Funding Rate
```

* Funding Rate > 0：多头支付空头
* Funding Rate < 0：空头支付多头


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