# Micro Price 

By [June](https://paragraph.com/@june-3) · 2022-02-27

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### 定义

*   micro price
    
    *   a limit of expected future mid-prices, conditional on the current mid-price and imbalance
        
    *   以当前的中间价格，价差和订单簿不平衡为条件，对未来预期的中间价格进行限制。
        

### 结论

*   1s mid-price change 和 order book imbalance 成正比
    
*   daily consistent, hourly consistent，但是adjustment 和当阶段的波动性相关
    
*   spread seems not a good driving factor for mid-price change
    
*   Very important to select the right K
    
*   样本内和样本外表现很好，consistency
    
*   2个改变
    
    *   symmetry the micro price adjustment ==> v\[0\] = - v\[-1\]
        
    *   v\[middle\] = 0
        

### 实现

1.  核心逻辑：不同区间的 order book imbalance，对应不同区间的 mid-price adjustment.
    
2.  比如 计算出 ETHUSDT order book imbalance = 0.1 属于 (0.06-0.3)，mid-price adjustment = -0.06025 \[看下面excel链接\], **micro price** = mid-price adjustment
    
3.  只需要把excel 表格带进去，写简单判断区间的语句，就行
    

**计算 order book imbalance**

![Definition  - Orderbook imbalance ](https://storage.googleapis.com/papyrus_images/3c6a8b8e59342010a30d975995a658b28019f78539842b73bef3bd20485dc1d0.png)

Definition - Orderbook imbalance

Q\_b\_t ==> 在时间点t，最优买价上的数量

Q\_a\_t ==> 在时间点t，最优卖价上的数量

**计算 mid price**

![mid-price](https://storage.googleapis.com/papyrus_images/91ed188a2aec610b777d9aca2a9aff58fbbd380c4b5270d5c75ec8244c9db750.png)

mid-price

P\_b\_t ==> 在时间点t，最优买价

P\_a\_t ==> 在时间点t，最优卖价

**计算 micro price**

![micro price,](https://storage.googleapis.com/papyrus_images/6cc263611b868ab2274fe08c3692db8ee92c8bf6c050120f62834f4471ae2c67.png)

micro price,

M ==> mid price

g(I,S) ==> micro price adjustment, 见下图

[https://docs.google.com/spreadsheets/d/18dmRsHIiPc\_bN0OoWAkpptsk7i53Bx9YfoU5q40-ERg/edit?usp=sharing](https://docs.google.com/spreadsheets/d/18dmRsHIiPc_bN0OoWAkpptsk7i53Bx9YfoU5q40-ERg/edit?usp=sharing)

结果
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### Plot ETHUSDT Binance

![ETHUSDT - 2022/02/18 - 2022/02/24, 1s ](https://storage.googleapis.com/papyrus_images/fb6c1b740b00ddd185872764e9c3fc9ef70f7f200512efa5773e391731ca3eb4.png)

ETHUSDT - 2022/02/18 - 2022/02/24, 1s

![mid-price change vs. spread](https://storage.googleapis.com/papyrus_images/da9e34bd234b35d236e289979397568b5233484a9f2902716107107c1044e79f.png)

mid-price change vs. spread

![mid-price change vs. order book imbalance](https://storage.googleapis.com/papyrus_images/396356f7e1fc54015502007540fd82be2f1ddb2c739e00a7920786e527f176c8.png)

mid-price change vs. order book imbalance

![](https://storage.googleapis.com/papyrus_images/bf2535e58e9b296089bd3632018f2888ac4276eebe952d69e2cf521f5f48601b.png)

![](https://storage.googleapis.com/papyrus_images/3e63967be3974b10fec8d053a799566873bd71afda0c788789c3baded206dd28.png)

![](https://storage.googleapis.com/papyrus_images/6a51ba2e0e807b1455c2dd148c75414088e8f1a02ac908221998e07360cc5ee5.png)

![ETH - order book imbalance cut](https://storage.googleapis.com/papyrus_images/f85af816768883f40be24aae1c3a5757ca40847334577595506b14b56dc96f38.png)

ETH - order book imbalance cut

![ETH - micro-price adjustment](https://storage.googleapis.com/papyrus_images/f71b24e6d0914adf6aaf2af7562552dd7533851282d9adeccefcd265087a1746.png)

ETH - micro-price adjustment

### Plot BTCUSDT Binance

![](https://storage.googleapis.com/papyrus_images/60a7b0382cb898d9448b47c2f3daf3000dfeff9a2b4770700c511855010ec64e.png)

![](https://storage.googleapis.com/papyrus_images/4a0d892741fbd115c6be407ed257b68c2da5c82eb9b5bb1d6bb57ed7b2a61570.png)

![](https://storage.googleapis.com/papyrus_images/88f372586b07a0a567a1d2e9bdb6f736cbe24b1a4404563eb0e53f4661eac2ef.png)

![](https://storage.googleapis.com/papyrus_images/af49ef7ca3081d282f80ca4f88a2daf06ef2920cbe1dc6073188f395bd654fdc.png)

![](https://storage.googleapis.com/papyrus_images/f61ff78a2261dbbec02e0a9ec62da3fe712769685d4ea8a01896fb095c0214af.png)

![](https://storage.googleapis.com/papyrus_images/68ba11c15a1fcc3ce1c7f3a4946cd8f553713d37f44e8a4372a7b59ce0fe85c2.png)

![](https://storage.googleapis.com/papyrus_images/191e3ab07ab25f8e7744cdee9e96f3731ad08390c39f7f9615b1f2a3e2fc1368.png)

![up: BTCUSDT- order book imbalance cut;  down: BTCUSDT micro-price adjustment](https://storage.googleapis.com/papyrus_images/e8db0ad94589378c7a0301e5b6d2c1c9e94adbb203326e98c9a2808af7463e5c.png)

up: BTCUSDT- order book imbalance cut; down: BTCUSDT micro-price adjustment

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*Originally published on [June](https://paragraph.com/@june-3/micro-price)*