NIFTY, BANKNIFTY, SENSEX Bell Curve
Live {Sym} implied probability curve extracted from option prices (Breeden–Litzenberger): probability mass per strike, the mode strike, and the odds of staying within ±50, ±100 and ±200 points. Free, no login.
What the implied bell curve is
Every option price encodes a probability. Under the Breeden–Litzenberger result (1978), the second derivative of the call price with respect to strike equals the discounted risk-neutral probability density at that strike. On a listed chain the derivative becomes a second difference across neighbouring strikes: density(K) ∝ C(K−Δ) − 2·C(K) + C(K+Δ). Stack that number for every strike and you get the distribution option traders are collectively paying for — not a forecast by OptionAlgo, but the consensus embedded in live premiums.
How this page builds it from the live chain
The page pulls the live call chain for the current expiry, computes the second difference at each interior strike, clips negative values (they come from stale or crossed quotes, not negative probability) and normalises the curve to 100%. The table then lists the probability mass at each strike with a bar so the shape is visible at a glance. The hero card summarises it: the mode strike (the peak), how many strikes contribute, and the probability that settles within ±50, ±100 and ±200 points of the current spot — those bands are simply the mass summed over the strikes inside each range.
Reading the shape: mode, skew and fat tails
Compare the mode with spot. A mode sitting *below* spot with a heavier left tail is the classic index signature — put demand for crash protection lifts downside probability. A wide, flat bell means the market expects movement (cross-check the [expected move](/expected-move) and [ATM IV](/iv)); a tall, narrow bell means it expects a pin, which is the environment [butterflies](/butterfly-scanner) are built for. Lopsided mass on one side is a directional skew — worth reading alongside the [put-call ratio](/pcr) and [OI analysis](/oi-analysis) before assuming the crowd is right.
Using the band odds in strategy selection
The ±band probabilities are a direct input to structure selection. If P(±100) is high, the market is pricing a range: range-bound structures (iron condors, butterflies) are priced for it, and so is their risk. If it is low, straddle and strangle buyers are being paid for the expected movement. The real edge is disagreement — when your own view of the range differs from the implied one. Practically, many traders place short strikes just outside the band where the implied probability of a touch drops sharply, and use the mode strike as the natural centre for pin trades.
Limitations you should know
This is a risk-neutral distribution: it contains the risk premium that option sellers charge, so it is not the real-world probability — tails are systematically fatter than what usually happens. Discrete strikes and bid-ask noise make the far tails jumpy; give more weight to the shape near spot. The curve covers only the current expiry and refreshes every 60 seconds on this public page. It is educational data intelligence — OptionAlgo is not SEBI registered and nothing here is investment advice.
Frequently Asked Questions
Is this the probability will actually end at a strike?
It is the risk-neutral probability implied by option prices, which includes a risk premium. Treat it as what the market is pricing, not a physical forecast.
Why don't the table rows add up to exactly 100%?
Rounding, plus strikes outside the listed range are not shown. The curve itself is normalised to 100% before display.
What is the mode strike?
The strike with the highest implied probability mass — the peak of the bell. It often sits near heavy open-interest strikes and the max-pain level.
Why does the curve look lumpy or spiky?
Second differences amplify quote noise. A stale or wide-spread strike creates a spike at its neighbours. Read the overall shape, not individual bars.
How can I use it for an iron condor?
Place the short strikes just outside the ±band that carries the probability you are comfortable with (for example the ±100 or ±200 band), then verify the premium justifies that priced probability.
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