Volatility Skew and Term Structure

A simple Black-Scholes-Merton model uses one volatility for every strike. Real premiums do not fit that flat picture, so each contract implies its own volatility. Plot IV upward and strike across, at one expiry. The shape shows which strikes carry higher or lower IV.

A downward slope means lower strikes have higher IV than higher strikes. Index traders call it put skew or a smirk. "Near the money" means a strike close to the index level. The wings are strikes far away on either side. A smile has higher IV on both wings. A rising skew has higher IV at higher strikes. The shape depends on the underlying, the expiry, any event and the moment you look. A NIFTY chain does not follow one fixed curve.

A portfolio owner can buy an out-of-the-money Put, one with a strike below today's price, to guard against a large fall. If many people want that protection, its premium rises against other contracts, and the model turns that premium into a higher IV. The seller takes the other side. A richer quote does not remove the seller's chance of a large loss.

Hedging demand, fear of sudden gaps, the chance of everyone selling together, and the pay sellers ask for that risk can all add to downside skew. Call demand and supply can shape the other wing. These are reasonable explanations for a shape. The curve alone does not prove any of them. Open interest does not show who holds what or why.

Be precise about "Puts have higher IV". It usually compares a lower-strike OTM Put with a higher-strike OTM Call. For a European Call and Put with the same underlying, strike and expiry, put-call parity ties their price gap to spot, strike, time, interest and dividends. These last two are often called carry. With consistent carry and parity-respecting prices, the model gives both the same IV. A gap on a real screen is more likely quote timing, wide spreads, a stale trade or a different calculation.

Fix one underlying, one expiry and one timestamp. Check the bid, which is the price buyers offer, and the ask, which is the price sellers want. The last trade may be old, and the midpoint is arithmetic, not a fill. IV from the bid can differ from IV from the ask, so a wide spread makes one displayed IV less useful.

Moneyness says where a strike sits against spot or the forward price. A simple comparison takes a Put and a Call the same distance either side of spot, if you say so. A forward-based comparison uses strike divided by forward. Another common one uses the same absolute Delta, the local price sensitivity to the underlying. Each answers a different question and may pick different strikes.

Keep IV differences apart from premium differences. Our model uses NIFTY 25,000, 30 calendar days, 6% yearly interest and a 1% continuous dividend yield. The 24,000 Put at 21% IV costs about ₹194.06 per unit. The 26,000 Call at 17% costs about ₹170.96. Strike, type, carry and IV all feed those prices, so the gap is not pure skew. To isolate IV, reprice the same contract with every other input fixed.

Now the 25,000 Call and Put, both at 18% IV. Their premiums still differ: ₹565.99 and ₹463.55. The ₹102.44 gap is the parity relationship at work under our carry inputs. Our rate is a teaching input and not NSE's displayed-IV method. Check a provider's model, inputs and quote convention before comparing its numbers with another source.

For term structure, change the expiry and keep the comparison rule the same. An at-the-money-forward comparison uses a strike near each expiry's forward price. The forward is the delivery price for that horizon under its carry inputs, and it differs by expiry. Holding one strike number does not hold its forward moneyness.

An expiry's IV covers the whole stretch from now to that expiry. A 60-day IV is not the volatility of days 31 to 60 alone. It is also a yearly rate. A 20% IV does not mean an expected 20% move in 60 days. To compare uncertainty built up over time, square the decimal IV and multiply by years left. That is total implied variance, written IV² × T.

Take hypothetical comparable readings at 30, 60 and 90 days of 18%, 20% and 21% yearly IV. Using days divided by 365, their total variances are about 0.002663, 0.006575 and 0.010874. The yearly rate and the built-up variance answer different questions. More time can add variance even while the yearly rate falls.

Differences in total variance also give a rough forward volatility between two expiries. Subtract the earlier total from the later, divide by the extra years, and take the square root. For 30 to 60 days that gives about 21.82%. This assumes a tidy variance-budget model. An ATM-IV calculation is not a tradable forward quote and not a forecast of realised volatility. A negative difference means check the data and assumptions. A few ATM points cannot certify an arbitrage-free surface.

An upward term structure has lower yearly IV at short expiries and higher IV at long ones. A downward or inverted one is the reverse. Traders sometimes call these contango and backwardation. Here the words describe option IV across maturities. They are not the prices of volatility futures.

A separate front-loaded example uses 28%, 24% and 22% yearly IV at 30, 60 and 90 days. Its total variance still rises: about 0.006444, 0.009468 and 0.011934. The short expiry has the higher yearly rate. The long expiry holds more total variance. So a downward slope does not mean later options carry less total uncertainty.

A scheduled event hits expiries differently. In a simple example, take an 18% baseline yearly volatility and one independent event with a 6% log-return standard deviation on day 20. The 30, 60 and 90-day expiries all include it. The same event variance spreads over more time in longer contracts, so yearly IV comes to about 27.60%, 23.30% and 21.68%. The 6% is an assumed event size. It is not a promised jump, and it is not a yearly rate.

An expiry before the event leaves it out. One after includes it. That can make a step or a hump, especially when later horizons dilute the event. Real curves also carry other risks and flows. An upward curve does not certify calm. An inversion does not predict a crash. A hump does not give the date of a shock. After the event, remaining IV can fall, stay high or rise as the outlook changes.

A spread adds up the premiums and exposures of its legs. A vertical uses two strikes in one expiry, so it crosses the skew. A calendar usually uses one strike at two expiries, so it crosses the term structure. Work out the net debit or credit from the actual leg premiums. Lower IV does not by itself mean a cheaper rupee premium. Put and Call spreads of equal width need not collect the same credit.

Vega is a leg's local price sensitivity to a one-point change in yearly IV. In a calendar with a long far option and a short near option, add the long leg's Vega effect and subtract the short leg's. Near the money, that often leaves positive net Vega, but the two expiries can move by different amounts. Neither an upward nor a downward curve guarantees a good entry or a profit. Spot, time, changing Greeks and execution also count.

A bull Put spread is short a higher-strike Put and long a lower-strike Put. Say the lower wing gets richer. Your hedge gains. But if the short leg's adverse repricing outweighs that gain, the spread loses. "Skew steepened" does not settle the result. You need both IV changes and both sensitivities. The figure holds NIFTY, time and carry fixed on a short 24,000 Put and long 23,000 Put. Starting from IVs of 21% and 24%, the model cost to close is ₹114.55. If the IVs move to 24% and 28%, the cost to close rises by ₹10.89. If they move to 22% and 29%, it falls by ₹48.77. The gap between the two IVs widens in both cases, with opposite results.

Before expiry, a spread's market value responds to more than its final payoff. An expiry payoff diagram shows outcomes at settlement. It does not promise the same value along the way. Margin is not a loss cap, gaps can defeat planned exits, and spreads and charges change what you can actually get. When a calendar's near leg ends, any long option left over has its own exposure. The next lesson follows one event through time to explain IV crush, and why direction alone does not decide an option buyer's result.