Volatility skew and smile

The textbook option pricing model assumes one volatility for the underlying, so every strike of the same expiry should show the same implied volatility (IV). Real markets do not work that way. If you work out the IV of every strike in a NIFTY option chain and plot them, you get a curve, not a flat line. The shape of that curve is called the volatility skew (when one side is higher) or the volatility smile (when both far ends are higher than the middle).

The skew tells you where traders are willing to pay more for options. It is one of the most useful things an option chain shows, once you know how to look.

What the NIFTY skew usually looks like

For Indian index options, the common pattern is a put skew: out-of-the-money (OTM) puts have higher IV than the at-the-money (ATM) strike, and OTM calls have the same or slightly lower IV. Here is an illustrative example with NIFTY at 25,000, for one weekly expiry (the numbers are made up to show the shape, not taken from a real day):

The left side slopes up steeply, the right side dips and then turns up slightly. That shape, a lopsided smile, is sometimes called a "smirk". It means a put 1,000 points below the price costs more than a call 1,000 points above, even though both need a similar-sized move.

Why the skew exists

• Demand for protection. Investors and funds holding shares buy index puts to protect their portfolios (see hedging with NIFTY puts). That steady demand lifts put prices, and with them put IV.
• Markets fall faster than they rise. Sharp drops tend to be quicker and more violent than rallies, and volatility usually jumps during falls. Sellers of OTM puts know that if those puts come into play, it will be in a fast, nervous market, so they charge more.
• Fat tails. Big moves happen more often than the bell curve in the model assumes. Higher IV on far strikes is how the market corrects the model for that.
• Call overwriting. Holders of shares often sell OTM calls for income, adding supply to the call side and keeping call IV down.

A live example: reading the skew from the chain

You can see the skew in prices without any IV calculation. Here is a slice of today's NIFTY chain:

Pick a put a few strikes below the money and a call the same distance above. If the put costs clearly more than the call, that difference is mostly the skew. (A small part comes from the cost of carry, because the forward price sits a little above spot.) The full option chain page shows the IV of each strike directly, so you can draw the curve yourself.

Commodities often look different. Gold can show a call-side skew when traders rush for upside exposure during uncertain times:

Compare the far call and far put prices the same way. Which side is dearer can change with the news, and that is the point: the skew shows which way the market is more afraid of a big move.

Skew, smile and term structure

• Skew is the slope across strikes for one expiry. Index options usually show a put skew; some stocks before a takeover rumour or commodities in a supply scare can show a call skew.
• Smile is when both far ends are above the middle. It is common in currencies, and in stocks just before results when a big move either way is possible.
• Term structure is how ATM IV changes from one expiry to the next. Put the skew and the term structure together and you get the "volatility surface": IV by strike and by expiry.

Near expiry, the skew usually looks steeper in IV terms, because the far strikes have very little value and a small rupee premium turns into a high IV. Do not compare a weekly skew with a monthly one number for number.

How the skew moves

The skew is not fixed. When markets fall and fear rises, put IV usually rises faster than ATM IV, so the skew steepens. In long calm rallies the skew often flattens, as fewer people pay up for protection. Around a big event, the whole curve can lift, and after it the curve can drop and change shape at the same time. Watching how the skew changes from day to day can show a change in mood before the price itself moves much, though it is not a reliable forecast.

How traders use the skew

• Choosing spreads. In a bear put spread, you buy one put and sell a lower one. With a steep put skew, the lower put you sell carries a higher IV, which helps make the spread cheaper.
• Ratio spreads. Selling two far puts against one nearer bought put collects the skew premium, but it leaves open risk on a sharp fall (see ratio spreads).
• Hedging cost. A steep skew means protective puts are expensive. Hedgers may choose closer strikes, collars or shorter periods to manage cost.
• Picking strikes for selling. Sellers of OTM puts are paid more than sellers of equally distant calls, but they also carry the risk the skew is pricing: that falls can be sudden.

A worked example: one view, two trades

A trader expects NIFTY to stay below 25,500 for the week. Using the illustrative skew above, the 25,500 call at 12.4% IV might trade around ₹25. The 24,500 put at 14.8% IV, the same distance away, might trade around ₹40. A seller collects more on the put side, but that extra ₹15 is the market's price for the extra risk of a fast fall. On a quiet week both expire worthless. On a week with a 3% drop, the put seller's loss grows quickly as IV jumps at the same time. The skew is a price, not a free gift.

Common mistakes

• Calling the skew a mispricing. It reflects real demand and real crash risk. Selling expensive puts can work for a long time and then lose heavily in one move.
• Using one IV for every strike. Payoff and Greek estimates that assume ATM IV for far strikes will understate the value of OTM puts.
• Reading near-expiry far-strike IVs literally. Tiny premiums and wide bid-ask spreads make those figures noisy.
• Ignoring liquidity. Far strikes often trade thinly; the price you see may not be the price you get. See the bid-ask spread guide.