Volatility Skew & Term Structure

The original Black-Scholes framework assumed a single volatility for the underlying. On that assumption every strike expiring on the same day should print the same implied volatility, and the IV column would be a flat line. Real chains have never looked like that, and after the crashes of the late 1980s they stopped even pretending to. Once implied volatility is understood as a price rather than a forecast — the point made in the implied volatility module — the variation stops being puzzling. Different strikes are different products with different demand, and different demand produces different prices.

Plot implied volatility on the vertical axis against strike on the horizontal and you get a curve rather than a line. In Indian equity indices that curve typically slopes downward from left to right: high on the downside strikes, lowest somewhere around at-the-money, and modestly higher again at the far upside. The steep left side and the shallow right side is why practitioners call the equity shape a smirk rather than a smile. In instruments where the market fears a violent move in either direction, the two wings lift symmetrically and you get a genuine smile.

The practical consequence lands immediately on your order pad. Any structure with legs at different strikes is trading two different volatilities at once, not one. A bull call spread is buying at one point on the curve and selling at another. A strangle is selling one point on the steep side and one on the shallow side. Traders who model a spread using a single IV are misprising the position before it is even entered, and the error is largest exactly where the curve is steepest.

The first reason is demand, and it is one-sided by construction. Indian equity portfolios — mutual funds, insurers, family offices, retail SIPs — are overwhelmingly long. When those holders want protection they buy puts. Almost nobody in that population needs to buy far out-of-the-money calls, because being under-invested in a rally is an embarrassment rather than a solvency event. Persistent buying pressure on one side of the chain and none on the other shows up exactly where you would expect it: in the price of the puts, and therefore in their implied volatility.

The second reason is that markets genuinely do not fall the way they rise. Advances tend to be gradual and accumulative; declines tend to be sharp, correlated and compressed into a few sessions. A 6 per cent NIFTY drawdown can arrive across three sessions while a 6 per cent advance takes six weeks. Option sellers know this from experience, so they demand more compensation for writing a downside strike than an equidistant upside one. The skew is that compensation, expressed as volatility.

The third reason is gap risk and it is asymmetric too. Overnight news that opens a market lower is more common and more violent than news that opens it higher, and a short put has no opportunity to be managed through a gap. Add leverage into the picture — falling markets force margin calls, forced selling drives further falls — and the downside tail is genuinely fatter than the upside one. Skew is not an inefficiency waiting to be arbitraged. It is the market pricing a real asymmetry, which is the same asymmetry the black swan module is built around.

Take one expiry and pick two strikes an equal distance from spot — say 1,000 points either side of a NIFTY at 24,500. Read the implied volatility of the 23,500 put and the 25,500 call. The difference between those two figures is the skew, and reading it directly off the chain in under ten seconds is a habit worth building. A gap of a point or two is unremarkable. A gap of three or four points means the market is paying up hard for downside protection, and that usually coincides with something specific rather than with general nervousness.

What that gap does to actual rupee premiums is larger than most traders expect, because volatility enters an option price non-linearly. The table below prices both of those strikes from a standard model. The put, at an implied volatility of 15.8 per cent, comes out near ₹83. The call, at 12.6 per cent, comes out near ₹45. Same distance from spot, same expiry, and the downside strike costs close to twice the upside one. Price the call at the put’s volatility instead and it would be worth about ₹91 — the skew alone is halving it.

This is why the direction of a spread matters more than its width. A trader buying downside protection is buying the most expensive volatility on the chain. A trader selling a put spread is collecting that same rich volatility but is also taking on the risk it was pricing. Neither is a free lunch or a trap; they are the two sides of a real transfer. What is genuinely careless is comparing a call structure and a put structure on width alone and concluding that one is better value.

Fix the moneyness and vary the expiry instead. Read the at-the-money implied volatility on the current weekly contract, then the current month, then the next month, then the far month. Plot those four figures against days to expiry and you have the term structure. It answers a different question from skew: not "how does the market price a move of a given size", but "over what horizon does the market expect the uncertainty to sit". A typical calm reading might run 12.4 on the weekly, 13.1 on the current month, 13.8 on the next and 14.4 on the far month.

That upward slope is called contango and it is the ordinary state of the curve. The logic is straightforward: over a week, most of what can happen is already visible on the calendar. Over six months, elections, policy shifts, global shocks and results seasons that nobody can name yet are all inside the window. More unknowns over a longer horizon means a higher annualised volatility, so the far contracts price above the near ones. This is also why vega is larger on far-dated options, a point developed in the vega module.

Under the post-2025 F&O framework each exchange runs a single weekly index expiry, so the near end of the Indian curve has fewer points on it than it once did and those points carry heavier concentrated flow. That thinning matters when you read the curve: a single stressed weekly contract can look dramatic without much depth behind it. Check the open interest and the bid-ask on the strikes you are reading before drawing a conclusion from the near end of the term structure.

The curve inverts under stress, and the inversion is one of the cleaner signals in the volatility toolkit precisely because it does not require an opinion. When something breaks — a gap open, a global credit event, an unresolved geopolitical situation — the near-dated contracts reprice violently while the far-dated ones move much less. The weekly might jump to 28 while the next month sits at 18. That downward-sloping curve is backwardation, and what it is saying is specific: the market expects the trouble to be intense and to be soon, and expects conditions to normalise beyond it.

Backwardation therefore tends to coincide with the noisiest part of a decline rather than the start of one. It is the shape of a market that has already been hit and is scrambling for near-dated protection. Traders watch for the curve to re-steepen back into contango as one piece of evidence that the acute phase has passed — not as a signal to buy, but as an observation that the panic bid in the front contracts has drained. Reading it as a timing tool with a success rate attached is the mistake; there is no such number to quote.

The shape also changes what a calendar structure is worth. Selling a near-dated option and buying a far-dated one at the same strike is a position on the differential between two points on this curve. Opened in contango, the trader sells the cheaper volatility and buys the dearer one, which is a headwind that the faster near-leg decay has to overcome. Opened in backwardation, the differential is the other way. Either can work or fail; the point is that the curve shape is an input to the trade, not a detail to be discovered afterwards.

Every multi-leg structure inherits the shape of the curve it is built on. A bull put spread sells a strike on the steep downside portion and buys one further down where the curve is steeper still, so the credit is larger than a flat-volatility model would suggest — and so is the risk it is being paid for. A bear call spread sits on the shallow upside portion, so the credit is thinner for the same strike width. Traders who assume that a 500-point wide spread should collect the same credit on either side of the chain are ignoring the curve entirely.

The skew also moves. It steepens when protection is being scrambled for and flattens when the market is comfortable, and those changes reprice existing positions independently of the index level. A short put spread opened in a calm chain and carried into a steepening skew is marked against the trader even if NIFTY is unchanged, because the leg they are short has become relatively more expensive than the leg they are long. This is a second-order vega effect and it is the reason multi-leg positions rarely behave exactly as the entry-day payoff diagram promised.

None of this makes one side of the chain better than the other. Selling rich downside volatility is being paid for the tail that produces it, and that tail is real — the black swans module exists because the fat left side of the distribution has repeatedly done what a normal distribution says it should not. Buying cheap upside volatility gets a low price for a reason too. The useful discipline is to know which part of the curve each of your legs is standing on, and to state in advance what price action would invalidate the structure.