Intuition The one-sentence ideaDelta measures whether trades happened because buyers aggressively lifted the ask or sellers aggressively hit the bid — and Cumulative Delta is just the running total of that tug-of-war over time.
Price alone tells you where the market went. It does not tell you who pushed it there or how hard . Two candles can look identical but one was driven by desperate buyers and the other by trapped sellers.
Delta answers: "Of all the volume that traded, was it initiated by aggressive buyers or aggressive sellers?"
Definition Aggressor / Market OrderEvery trade needs a resting limit order and an incoming market order (the aggressor ). The aggressor is the one who "crosses the spread" and causes the trade to print.
Aggressor buys at the ask → counted as buy volume
Aggressor sells at the bid → counted as sell volume
For a chosen interval (a single trade, a candle, a session):
Delta = ( Volume traded at the ask ) − ( Volume traded at the bid ) \text{Delta} = (\text{Volume traded at the ask}) - (\text{Volume traded at the bid}) Delta = ( Volume traded at the ask ) − ( Volume traded at the bid ) positive delta ⇒ buyers were more aggressive. A negative delta ⇒ sellers were more aggressive.
Take every executed trade in the interval. Each trade has a size v i v_i v i
Classify each trade using the tick / bid-ask rule :
s i = { + 1 trade printed at the ask (buyer aggressor) − 1 trade printed at the bid (seller aggressor) s_i = \begin{cases} +1 & \text{trade printed at the ask (buyer aggressor)}\\ -1 & \text{trade printed at the bid (seller aggressor)} \end{cases} s i = { + 1 − 1 trade printed at the ask (buyer aggressor) trade printed at the bid (seller aggressor)
Delta is the signed sum of all trade sizes:
Δ = ∑ i = 1 N s i v i \boxed{\;\Delta = \sum_{i=1}^{N} s_i \, v_i\;} Δ = i = 1 ∑ N s i v i That's it — delta is nothing more than "buy-initiated volume minus sell-initiated volume". No magic.
Definition Cumulative Delta (CVD)The running sum of delta from a chosen start point (usually session open):
CVD k = ∑ j = 1 k Δ j = CVD k − 1 + Δ k \text{CVD}_k = \sum_{j=1}^{k} \Delta_j = \text{CVD}_{k-1} + \Delta_k CVD k = ∑ j = 1 k Δ j = CVD k − 1 + Δ k net aggression flow building up over time.
Intuition Why cumulative?A single candle's delta is noisy. Summing it smooths the noise and reveals the persistent direction of aggression — like tracking your bank balance instead of individual transactions.
The 20% that gives 80% of the edge is spotting divergence :
Price
CVD
Meaning
Higher high
Higher high
Healthy uptrend, buyers confirm
Higher high
Lower high
Bearish divergence — price up but buyers not following → possible reversal
Lower low
Lower low
Healthy downtrend
Lower low
Higher low
Bullish divergence — sellers exhausted despite new low
Intuition Why divergence mattersIf price makes a new high but CVD does not , the rally is running on limit-order absorption or short-covering, not fresh aggressive buying. The fuel is gone.
Worked example Example 1 — Basic delta of one candleA 1-minute candle prints these trades:
100 contracts at ask, 40 at ask, 30 at bid, 90 at bid.
Step 1: Sum ask volume B = 100 + 40 = 140 B = 100 + 40 = 140 B = 100 + 40 = 140 Why? These are buyer-initiated trades.
Step 2: Sum bid volume S = 30 + 90 = 120 S = 30 + 90 = 120 S = 30 + 90 = 120 Why? Seller-initiated trades.
Step 3: Δ = B − S = 140 − 120 = + 20 \Delta = B - S = 140 - 120 = +20 Δ = B − S = 140 − 120 = + 20 Why? Positive → buyers slightly more aggressive this minute.
Check: Total volume = 140 + 120 = 260 = 140+120 = 260 = 140 + 120 = 260 V + Δ 2 = 260 + 20 2 = 140 = B \frac{V+\Delta}{2} = \frac{260+20}{2}=140 = B 2 V + Δ = 2 260 + 20 = 140 = B
Worked example Example 2 — Building Cumulative DeltaSuccessive candle deltas: + 20 , − 50 , + 10 , + 60 +20, -50, +10, +60 + 20 , − 50 , + 10 , + 60
Step 1: CVD₁ = + 20 = +20 = + 20 Step 2: CVD₂ = 20 + ( − 50 ) = − 30 = 20 + (-50) = -30 = 20 + ( − 50 ) = − 30 Why? Sellers dominated candle 2, dragging the running total negative.
Step 3: CVD₃ = − 30 + 10 = − 20 = -30 + 10 = -20 = − 30 + 10 = − 20 Step 4: CVD₄ = − 20 + 60 = + 40 = -20 + 60 = +40 = − 20 + 60 = + 40 Why? Strong buying candle flipped the net flow positive.
Notice CVD ended at + 40 +40 + 40 20 − 50 + 10 + 60 = 40 20-50+10+60 = 40 20 − 50 + 10 + 60 = 40
Worked example Example 3 — Reconstructing buy volumeA candle has total volume V = 500 V = 500 V = 500 Δ = − 120 \Delta = -120 Δ = − 120 Step 1: B = 500 + ( − 120 ) 2 = 190 B = \frac{500 + (-120)}{2} = 190 B = 2 500 + ( − 120 ) = 190 Step 2: S = 500 − ( − 120 ) 2 = 310 S = \frac{500 - (-120)}{2} = 310 S = 2 500 − ( − 120 ) = 310 Why? More was sold aggressively (310) than bought (190), consistent with negative delta.
Check: B + S = 500 B+S = 500 B + S = 500 B − S = − 120 B-S = -120 B − S = − 120
Common mistake "Positive delta means price must go up."Why it feels right: More buying should push price up, right?
The fix: Delta measures aggression , not outcome. If aggressive buyers keep buying but a big limit seller absorbs all of it, price stays flat or even falls despite positive delta. This absorption is itself a powerful signal — the resting seller is winning.
Common mistake "Delta and volume are the same thing."Why it feels right: Both are computed from trades.
The fix: Volume is B + S B+S B + S B − S B-S B − S zero delta if buying and selling aggression were balanced.
Common mistake "Cumulative Delta resets are just cosmetic."Why it feels right: It's the same running sum.
The fix: The start point matters enormously . Session-anchored CVD tells a different story than a rolling-window CVD. Always know your anchor before reading divergence.
Common mistake "The bid/ask classification is exact."Why it feels right: Exchanges timestamp trades precisely.
The fix: In practice, trades between bid and ask, or fast quote changes, force algorithms (tick rule, Lee-Ready) to estimate the aggressor. Delta is a very good approximation , not gospel.
Recall What is the formula for delta and what does its sign mean?Δ = B − S \Delta = B - S Δ = B − S
Recall GivenV = 800 V=800 V = 800 Δ = + 200 \Delta=+200 Δ = + 200 B B B B = V + Δ 2 = 800 + 200 2 = 500 B = \frac{V+\Delta}{2} = \frac{800+200}{2} = 500 B = 2 V + Δ = 2 800 + 200 = 500
Recall Price makes a new high but CVD makes a lower high. What is this and what does it warn?Bearish divergence — the new price high isn't backed by fresh aggressive buying; possible reversal / exhaustion.
Recall Feynman: explain delta to a 12-year-old.Imagine a tug-of-war rope. Every second, we count how many kids pull hard on the buy side minus how many pull hard on the sell side. If more buy-kids yank, the number is positive. Cumulative delta is just adding up that number every second so you can see which team is slowly winning over the whole game — even if the rope's flag (the price) hasn't moved much yet.
"Ask = Attack up, Bid = Batter down."
Delta = A sk − B id. Cumulative = keep a B ank B alance of the battle (running total).
Delta is defined as which subtraction? Volume at ask minus volume at bid (
B − S B-S B − S ).
A positive delta means what? Aggressive buyers (market buys lifting the ask) dominated the interval.
Cumulative Delta is computed how? Running sum of each interval's delta:
C V D k = C V D k − 1 + Δ k CVD_k = CVD_{k-1}+\Delta_k C V D k = C V D k − 1 + Δ k .
Total volume in terms of B and S? Given V and Δ, formula for buy volume B? B = ( V + Δ ) / 2 B = (V+\Delta)/2 B = ( V + Δ ) /2 .
Given V and Δ, formula for sell volume S? S = ( V − Δ ) / 2 S = (V-\Delta)/2 S = ( V − Δ ) /2 .
Price new high + CVD lower high = ? Bearish divergence (buying aggression not confirming the high).
Price new low + CVD higher low = ? Bullish divergence (selling exhaustion despite new low).
Why can positive delta occur while price falls? A large resting limit seller absorbs the aggressive buying (absorption).
Difference between volume and delta? Volume = B+S (unsigned magnitude); Delta = B−S (signed net aggression).
What is the 'aggressor' in a trade? The market order that crosses the spread and causes the trade to print.
Can a high-volume candle have zero delta? Yes — if aggressive buying and selling are perfectly balanced.
Divergence signals reversal
Intuition Hinglish mein samjhoDekho, price chart tumhe sirf yeh batata hai ki bhaav kahan gaya. Lekin delta tumhe batata hai ki us move ke peeche kaun zyada aggressive tha — buyers ya sellers. Jab koi trader market order daal ke ask pe kharidta hai (spread cross karke), woh buy-side aggression hai. Jab koi bid pe market sell karta hai, woh sell-side aggression. Delta ka formula simple hai: ask ka volume minus bid ka volume (Δ = B − S \Delta = B - S Δ = B − S
Cumulative Delta (CVD) bas har candle ke delta ka running total hai — jaise bank balance. Ek candle ka delta noisy hota hai, par jab tum sab jod dete ho toh saaf dikhta hai ki net mein kaun jeet raha hai. Yeh line chart ki tarah plot hota hai.
Sabse important cheez (yeh 80/20 wala point hai): divergence dhoondhna. Agar price naya high bana raha hai par CVD naya high nahi bana raha — iska matlab rally mein fresh aggressive buying nahi hai, shayad reversal aa sakta hai (bearish divergence). Ulta, price naya low par CVD higher low = sellers thak gaye (bullish divergence).
Ek trap yaad rakhna: positive delta ka matlab yeh nahi hai ki price upar jaayega. Agar koi bada limit seller saara aggressive buying absorb kar raha hai, toh price ruk sakta hai ya gir sakta hai — aur yeh absorption khud ek powerful signal hai. Delta aggression naapta hai, guaranteed result nahi.
