The intuition
From Albert “Pete” Kyle’s 1985 model of informed trading. Lambda (λ) is the slope that links signed order flow to price change: push X of net buying into the book, price moves λ·X. It is really a liquidity gauge — high λ means the book is fragile and small orders shove price around; low λ means it is deep and absorbs flow without budging.
Send the same order into a deep book versus a thin one — high λ (thin) lurches price; low λ (deep) absorbs it.
ΔP ≈ λ · Q ΔP is the price change, Q is net signed order flow (buys minus sells). λ — Kyle’s lambda — is the impact coefficient, estimated by regressing price changes on signed flow. Bigger λ = thinner, more fragile market.
lambda >= highest(lambda, 60) && absImb >= 40 Live as the lambda variable — bps of mid-move per $1M of net signed flow, regressed inside each candle from the depth stream (Cont-Kukanov-Stoikov). Because its scale varies by symbol, pair it with lookback — lambda >= highest(lambda, 60) flags a fresh fragility extreme — and confirm with book imbalance: a strong absImb on a high-λ book is a cheap, easy-to-fake move. Flip it to read the trustworthy case: the same imbalance on a low-λ (deep) book is far more reliable.
- 1 A pair shows a thin book — little notional resting near the touch.
- 2 A modest market sweep moves price sharply → high λ.
- 3 Flagged as fragile: moves there are cheap to cause and easy to fake — size your reads accordingly.
Lambda is a liquidity/fragility measure, not a direction. It is regime-dependent (it widens in stress) and most useful as context — e.g. trusting an imbalance signal more on a low-λ, deep book than on a thin one.
Further reading
- Kyle — “Continuous Auctions and Insider Trading” (Econometrica, 1985)
- Cartea, Jaimungal & Penalva — Algorithmic and High-Frequency Trading
Related
FAQ
Is Kyle’s lambda a liquidity measure or a signal?
It is a liquidity/fragility measure — price impact per unit of flow. It is best used as context that tells you how much to trust a directional read, not as a standalone signal.
What does a high lambda mean?
A thin, fragile book: small orders move price a lot. A low lambda means deep, resilient liquidity that absorbs flow with little price movement.
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