Every option price is a small bet on where the index will finish, and a full chain holds hundreds of them at once: calls and puts at every strike, each priced by the market. Read one at a time they are a list of prices. Read together, they contain something more useful, a picture of how likely the market thinks every finishing level is. That picture is the implied distribution, and it turns the chain into a single curve you can put your finger on: the chance of finishing above a level, the chance of finishing below it, and how much more the market fears one side than the other. This guide explains what the implied distribution is, how it is read off option prices, how to read its shape, and what it cannot tell you.
The idea in one sentence
The price of a call at a strike is the market’s price for finishing above that strike, weighted by how far above. Compare the prices of calls at neighbouring strikes and the difference tells you how much probability the market assigns to finishing between them. Do that across the whole strike ladder and the probabilities line up into a curve: the implied distribution of the index at expiry. The technique is old and has a name, the Breeden-Litzenberger result, and the curve it produces is what a finance textbook calls the risk-neutral distribution. The name matters later, because risk-neutral is not the same as real-world.
How the curve is actually built
The raw arithmetic, taking second differences of call prices across strikes, does not survive contact with a real option chain. Quotes at the far strikes are wide and jumpy, and one stale price produces a spike in the curve that means nothing. So the Volatility page does it in three steps. It takes the strikes with real trading and fits a smooth curve through their implied volatilities against their distance from spot, a quadratic in log-moneyness, so the smile is captured without the noise. It then re-prices calls at every strike off that smooth curve. And it takes the second differences of those smoothed prices across the strike grid, which gives the probability of finishing at each strike, rescaled so the whole curve sums to one.
The result is a curve over strikes, with the expected daily move shown alongside it, refreshed from the chain as the session runs. It needs a chain with real premium in it, so on the first minutes of a fresh expiry it can be thin until the quotes fill.
Reading the shape
Three features carry the reading. The first is the peak: the strike the market treats as the most likely finishing point. It usually sits close to spot, and its distance from spot is the market’s lean. The second is the width. A wide, flat curve says the market is pricing a large range of outcomes, a narrow, tall one says it expects the index to finish close to where it is, and the width matches the expected move: most of the probability sits inside spot plus or minus the at-the-money straddle.
The third is the asymmetry, and it is the feature the expected move cannot show. An index implied distribution almost always has a fatter left tail than right: the market assigns more probability to a large fall than to a large rise of the same size. That is the skew made visible, the price of downside protection turned into odds. When the left tail fattens further, protection is being bid; when it thins, the crowd has stopped paying for it.
From the curve you can read a probability for any level: add up the probability to the right of a strike and you have the market’s odds of finishing above it. That is the most concrete thing the implied distribution offers, and it is worth being precise about what kind of odds they are.
What the implied distribution is not
It is not a forecast of where the index will go. The curve is derived from prices, and prices contain a risk premium: buyers pay extra for downside protection, which inflates the left tail beyond the real-world chance of a crash. The risk-neutral probability of a five percent fall is systematically higher than the frequency of five percent falls, and that gap is the writers’ compensation, the same premium the India VIX guide describes as implied against realised. Read the curve as what the market is charging for, not as what will happen.
It is also only as good as the quotes it is built from. A thin chain, a far expiry, or the first minutes after a roll produce a curve that is more model than market. And it describes expiry, not tomorrow: a curve for a contract three weeks out says nothing about the path in between.
The distribution, the expected move and max pain
Three numbers on the same page describe the same chain from different angles, and it helps to keep them apart. The expected move is the width of the curve, read from the straddle: one number for the range. The implied distribution is the whole curve, including its asymmetry and tails. Max pain is a different animal entirely: the strike where option buyers in aggregate lose the most, computed from open interest rather than prices, which is why the max pain guide treats it as a positioning fact rather than a probability. When the peak of the distribution and max pain sit at different strikes, the market’s odds and the writers’ interest disagree, and on expiry sessions that disagreement is worth watching.
A worked reading
The peak sits one strike below spot, the curve is narrow, and the left tail is fat while the right tail is thin. The market expects the index to finish close to here, leans slightly lower, and is paying heavily for protection against a large fall while barely pricing a large rise. If the same afternoon the term structure inverts and the 25-delta skew widens, the left tail is fattening in real time: protection being bid into stress. If instead the curve widens on both sides with no change in asymmetry, the market is pricing more movement without picking a side, which is what an event before expiry looks like.
Where to read the implied distribution
The Volatility page in OIData carries the market-implied distribution for NIFTY, BANK NIFTY and SENSEX at the current expiry, refreshed from the chain, with the expected daily move beside it and the India VIX, IV rank, term structure, 25-delta skew and IV surface cards above it. The Straddles and Strangles page carries the expected move the distribution’s width corresponds to, and the option chain carries the prices it is built from.
Implied distribution FAQ
What is the implied distribution? The probability the options market assigns to every finishing level at expiry, derived from option prices across the strike ladder. It is a curve over strikes, not a single number.
How is it calculated? By the Breeden-Litzenberger result: the second difference of call prices across strikes gives the probability of finishing between them. In practice the implied volatilities are smoothed first so wide quotes at far strikes do not produce spikes.
Is it a prediction? No. It is a risk-neutral distribution, which contains the premium buyers pay for protection. Its left tail is fatter than the real-world chance of a crash by exactly that premium.
How does it differ from the expected move? The expected move is the width of the curve, one number from the straddle. The distribution is the whole curve, including the asymmetry between the tails.
Takeaways
- The implied distribution turns a whole option chain into the market’s odds for every finishing level at expiry.
- Read its peak for the lean, its width for the expected move, and its tails for what the market fears more.
- It is built from smoothed implied volatilities, and it is risk-neutral: what the market charges for, not what will happen.
- Keep it apart from max pain, which comes from open interest rather than prices.