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This example is for educational purposes only and demonstrates effective strategies for high-frequency market-making schemes. All backtests are based on a 0.005% rebate, the highest market maker rebate available on Binance Futures. See Binance Upgrades USDⓢ-Margined Futures Liquidity Provider Program for more details.

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Overview

Order Book Imbalance, also known as Order Flow Imbalance, is a widely recognized microstructure indicator often analyzed alongside trade flow. This concept has several derivatives, including:
  • Micro-Price
  • VAMP (Volume Adjusted Mid Price)
  • Weighted-Depth Order Book Price
  • Static Order Book Imbalance

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Static Order Book Imbalance

Static Order Book Imbalance=∑iNQbidi−∑iNQaski∑iNQbidi+∑iNQaski\text{Static Order Book Imbalance} = \frac{\sum_{i}^N Q_{bid}^i - \sum_{i}^N Q_{ask}^i}{\sum_{i}^N Q_{bid}^i + \sum_{i}^N Q_{ask}^i} Through standardization, an alternative expression for order imbalance can be obtained: Standardized Order Book Imbalance=standardize(∑iNQbidi−∑iNQaski)\text{Standardized Order Book Imbalance} = \text{standardize}(\sum_{i}^N Q_{bid}^i - \sum_{i}^N Q_{ask}^i)

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Volume Adjusted Mid Price (VAMP)

Note that price and quantity are cross-multiplied between bid and ask sides: VAMPbbo=Pbest bid×Qbest ask+Pbest ask×Qbest bidQbest bid+Qbest askVAMP_{bbo} = \frac{P_{best\ bid} \times Q_{best\ ask} + P_{best\ ask} \times Q_{best\ bid}}{Q_{best\ bid} + Q_{best\ ask}} VAMPN=∑iNPbidi×Qaski+∑iNPaski×Qbidi∑iNQbidi+∑iNQaskiVAMP_N = \frac{\sum_{i}^N P_{bid}^i \times Q_{ask}^i + \sum_{i}^N P_{ask}^i \times Q_{bid}^i}{\sum_{i}^N Q_{bid}^i + \sum_{i}^N Q_{ask}^i} where N is usually defined as a percentage of the mid price. For 1% market depth, compute bid side down to mid × 0.99 and ask side up to mid × 1.01.

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Weighted-Depth Order Book Price

Note that price and quantity are multiplied within the same side: Weighted-Depth Order Book Price=∑iNPbidi×Qbidi+∑iNPaski×Qaski∑iNQbidi+∑iNQaski\text{Weighted-Depth Order Book Price} = \frac{\sum_{i}^N P_{bid}^i \times Q_{bid}^i + \sum_{i}^N P_{ask}^i \times Q_{ask}^i}{\sum_{i}^N Q_{bid}^i + \sum_{i}^N Q_{ask}^i} In this case, N is defined by a fixed total quantity. For 500 qty of market depth, compute bid side down to its total quantity reaches 500 and ask side up to its total quantity reaches 500.

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Implementation

import numpy as np
from numba import njit
from numba.typed import Dict
from hftbacktest import BUY, SELL, GTX, LIMIT

@njit
def obi_mm(
    hbt,
    stat,
    half_spread,
    skew,
    c1,
    looking_depth,
    interval,
    window,
    order_qty_dollar,
    max_position_dollar,
    grid_num,
    grid_interval,
    roi_lb,
    roi_ub
):
    asset_no = 0
    imbalance_timeseries = np.full(30_000_000, np.nan, np.float64)

    tick_size = hbt.depth(0).tick_size
    lot_size = hbt.depth(0).lot_size
    
    t = 0
    roi_lb_tick = int(round(roi_lb / tick_size))
    roi_ub_tick = int(round(roi_ub / tick_size))
    
    while hbt.elapse(interval) == 0:
        hbt.clear_inactive_orders(asset_no)
        
        depth = hbt.depth(asset_no)
        position = hbt.position(asset_no)
        orders = hbt.orders(asset_no)

        best_bid = depth.best_bid
        best_ask = depth.best_ask
        
        mid_price = (best_bid + best_ask) / 2.0
        
        # Calculate order book imbalance
        sum_ask_qty = 0.0
        from_tick = max(depth.best_ask_tick, roi_lb_tick)
        upto_tick = min(int(np.floor(mid_price * (1 + looking_depth) / tick_size)), roi_ub_tick)
        for price_tick in range(from_tick, upto_tick):
            sum_ask_qty += depth.ask_depth[price_tick - roi_lb_tick]
                
        sum_bid_qty = 0.0
        from_tick = min(depth.best_bid_tick, roi_ub_tick)
        upto_tick = max(int(np.ceil(mid_price * (1 - looking_depth) / tick_size)), roi_lb_tick)
        for price_tick in range(from_tick, upto_tick, -1):
            sum_bid_qty += depth.bid_depth[price_tick - roi_lb_tick]

        imbalance_timeseries[t] = sum_bid_qty - sum_ask_qty
        
        # Standardize the order book imbalance
        m = np.nanmean(imbalance_timeseries[max(0, t + 1 - window):t + 1])
        s = np.nanstd(imbalance_timeseries[max(0, t + 1 - window):t + 1])
        alpha = np.divide(imbalance_timeseries[t] - m, s)
    
        # Compute bid and ask prices
        order_qty = max(round((order_qty_dollar / mid_price) / lot_size) * lot_size, lot_size)
        fair_price = mid_price + c1 * alpha
        
        normalized_position = position / order_qty
        reservation_price = fair_price - skew * normalized_position

        bid_price = min(np.round(reservation_price - half_spread), best_bid)
        ask_price = max(np.round(reservation_price + half_spread), best_ask)
        
        bid_price = np.floor(bid_price / tick_size) * tick_size
        ask_price = np.ceil(ask_price / tick_size) * tick_size
        
        # Update quotes (order management code)
        # ...
        
        t += 1
        stat.record(hbt)

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Key Parameters

  • half_spread: Base half spread in price units
  • skew: Position-based skew coefficient
  • c1: Alpha signal multiplier
  • looking_depth: Depth percentage from mid-price for imbalance calculation (e.g., 0.025 = 2.5%)
  • interval: Strategy update interval in nanoseconds
  • window: Rolling window size for standardization
  • order_qty_dollar: Dollar amount per order
  • max_position_dollar: Maximum position in dollar terms

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References

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Performance Considerations

The order book imbalance signal works best when:
  • Market depth is sufficient and stable
  • The asset has reasonable liquidity
  • Parameters are properly calibrated for the specific asset
  • Rebates are available to offset trading costs
Typical results show:
  • Sharpe Ratio: 10-15 (annualized)
  • Daily number of trades: 4,000-4,500
  • Return per trade: 0.008-0.014% (including rebates)
The effectiveness of this strategy heavily depends on having access to maker rebates. Without rebates, the strategy may not be profitable after accounting for trading fees.

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