DepthSlope

How fast resting liquidity accumulates away from the mid. The mean per-side OLS slope of cumulative size against distance from the mid — a deep book reads a large slope, a thin one a small slope.

Quick reference

Item	Value
Family	Microstructure
Input type	OrderBook — sorted bid/ask depth snapshot
Output type	f64
Output range	≥ 0 for a well-formed book
Default parameters	none
Warmup period	1
Interpretation	Resting-book depth / liquidity resilience

Formula

slope_side = OLS slope of (|priceᵢ − mid|, Σ_{j≤i} sizeⱼ)
depthSlope = (slope_bid + slope_ask) / 2

For each side the cumulative resting size (walking outward from the touch) is regressed on the level's distance from the mid; the output is the mean of the two side slopes. Stateless and O(levels) per update. See crates/wickra-core/src/indicators/depth_slope.rs.

Parameters

None. Construct with DepthSlope::new().

Inputs / Outputs

Indicator<Input = OrderBook, Output = f64>. The bindings take a depth snapshot as four arrays — update(bid_px, bid_sz, ask_px, ask_sz) — with bids best-first (descending price) and asks best-first (ascending price). Python / Node batch accept a list of such snapshots and return a 1-D array. WASM is streaming-only.

Warmup

warmup_period() == 1; emits on the first snapshot.

Edge cases

• Fewer than two levels per side. No slope can be fit; returns 0 (including an empty book).
• Non-negative by construction. Because the response is cumulative size it never decreases with distance, so the slope is a magnitude, not a direction.
• Front- vs back-loaded books. Two books of equal total depth differ in slope: the one that thickens away from the touch reads larger than the one whose size sits at the touch.

Examples

Rust

use wickra::{DepthSlope, Indicator, Level, OrderBook};

let book = OrderBook::new(
    vec![Level::new(99.0, 1.0).unwrap(), Level::new(98.0, 2.0).unwrap()],
    vec![Level::new(101.0, 1.0).unwrap(), Level::new(102.0, 2.0).unwrap()],
).unwrap();
assert!(DepthSlope::new().update(book).unwrap() > 0.0);

Python

import wickra as ta

ds = ta.DepthSlope()
# distances 1,2 -> cumulative 1,3 -> OLS slope 2 per side
print(ds.update([99.0, 98.0], [1.0, 2.0], [101.0, 102.0], [1.0, 2.0]))  # 2.0

Node

const { DepthSlope } = require('wickra');
const ds = new DepthSlope();
console.log(ds.update([99, 98], [1, 2], [101, 102], [1, 2])); // 2

Interpretation

DepthSlope summarises the shape of the resting book in a single number — how quickly cumulative liquidity builds as you move away from the touch.

• Large slope. A deep, cushioned book: size accumulates fast just behind the touch, so a marketable order walks only a little before it is filled.
• Small slope. A shallow, gappy book: liquidity is sparse away from the touch, so the same order walks far and moves the price. The fragile regime.
• Resting vs. executed. Unlike KylesLambda, which infers impact from executed flow, DepthSlope reads prospective impact straight off the posted quotes — a forward-looking, pre-trade view.

Common pitfalls

• Feed-depth dependence. The slope depends on how many levels your venue publishes; a 5-level feed and a 50-level feed are not comparable. Only compare snapshots of equal published depth.
• Posted, not committed. It measures the resting book, which can be spoofed or pulled in an instant. Confirm with a flow-based measure such as TradeImbalance before trusting it.
• Two levels minimum. With fewer than two levels on a side no slope can be fit and the side contributes 0; a thin snapshot can read deceptively flat.

References

• Randi Næs and Johannes A. Skjeltorp, Order Book Characteristics and the Volume–Volatility Relation, Journal of Financial Markets, 2006.
• Kenneth A. Kavajecz, A Specialist's Quoted Depth and the Limit Order Book, Journal of Finance, 1999 — depth as a liquidity dimension.
• Jean-Philippe Bouchaud, Julius Bonart, Jonathan Donier, Martin Gould, Trades, Quotes and Prices, 2018 — the shape of the limit-order book.

See also

• OrderBookImbalanceFull — net depth pressure, the imbalance of the book rather than its slope.
• Microprice — fair value from top-of-book sizes.
• KylesLambda — realised impact from executed flow.
• Indicators-Overview — the full taxonomy.