Vega: Implied Volatility & Event-Driven Pricing

Start with a premium. A pricing model turns the underlying level, strike, time, interest rate, dividend and volatility into a premium. To find IV, fix the other inputs and work backwards from the premium to the volatility that reproduces it. A higher IV means the contract prices in bigger swings. It does not say whether NIFTY will rise or fall.

Realised volatility measures the swings that actually happened over a stated period. Historical volatility is the same idea computed from a past sample and scaled to a year. IV comes from option prices; historical volatility comes from past returns. To compare them, match the underlying, the period and the method. Yesterday’s swings do not settle tomorrow’s.

India VIX is a third measure. NSE calculates it from NIFTY option bid and ask prices, as yearly volatility expected over the next 30 calendar days. It blends many contracts. It is not the IV of our one strike and expiry, and it is not realised volatility. A VIX of 20 does not promise a 20% move in 30 days. A one-point rise in VIX does not mean a one-point rise in this Call’s IV.

Even one contract gives different IVs depending on whether you use its bid, its ask or an old last traded price. Fitting a model to a premium and getting that premium back is calibration. It is not proof that the option is cheap or dear. We come back to quotes and fills at the end.

The inputs: NIFTY 25,000, strike 25,000, 30 calendar days left. The model is Black–Scholes–Merton, or BSM, for European options, which can be exercised only at expiry. Interest rate 6% a year, dividend yield 1% a year, volatility 18% a year. The formula takes time as 30/365 years and volatility as the decimal 0.18. The yield is a modelling assumption, not a dated dividend schedule.

These inputs give a Call premium of ₹565.99 and a Put premium of ₹463.55 per unit. Both have Vega of about ₹28.41 per unit for each percentage point of IV. Moving IV from 18% to 19% is one percentage point (0.18 to 0.19 as a decimal). So the premium rises by about ₹28.41 per bought unit, with spot, strike, time, rate and yield unchanged.

A relative 1% rise is different. One per cent of 18% is 0.18 points, so the new IV is 18.18%, not 19%. The estimate is only about ₹5.11 per unit. When a platform says “Vega for a 1% move”, check two things: is it one point or a relative change, and is the figure per unit or per position?

In this BSM model, a bought Call and a bought Put both have positive Vega. A small rise in IV raises either premium. Selling to open reverses it: a sold Call and a sold Put both have negative Vega. Selling an option you already own to close it is a different transaction from opening a new short position.

Contract type, direction and Vega sign are three separate questions. A bought Call is bullish and a bought Put is bearish, yet both have positive Vega. A sold Call is bearish and a sold Put bullish, yet both have negative Vega. Positive Vega does not mean “NIFTY will rise”.

Take 65 units per position, a teaching quantity; check the real lot size of the contract you trade. Vega × +65 gives about +₹1,846.74 per volatility point for either bought option. Vega × −65 gives −₹1,846.74 for either short position. If IV falls instead, each sign reverses.

Vega is a slope at the starting point, like the gradient of a road at one spot. For a small change in IV alone, multiply Vega by the number of points. For a bigger change, or when spot and time also move, price the option again with all the new inputs.

Raise volatility from 18% to 20% and hold the rest fixed. Vega estimates +₹56.82 per unit. Full repricing gives Call ₹622.83 and Put ₹520.39, a rise of about ₹56.84 for either. For 65 bought units the estimate is +₹3,693.49 and the full reprice is +₹3,694.52. Close, for this small change.

Fix NIFTY, time and the other inputs, and change only the strike. In the 30-day comparison, Vega is largest near the money. The 24,000 Call is in the money and the 24,000 Put is out of the money, yet they have equal Vega when their volatility input matches.

“At the money has the highest Vega” is a handy shorthand, not an exact rule. With these inputs the true peak sits slightly above 25,000, at about 25,136, because of interest, yield and volatility. That exact strike need not be a listed contract. We use round strikes for teaching.

Now keep spot and strike at 25,000 and change the time left. Vega is about ₹5.22 per point at one day, ₹13.79 at seven days, ₹28.41 at 30 days and ₹48.59 at 90 days. More time means more rupee Vega here. Other strikes or inputs can change that ranking, so compare like with like.

Before a policy announcement, option premiums may price in the uncertainty. Once the news is out, IV can drop sharply. Traders call this an IV crush. Company earnings raise the same question for that company’s stock options. Neither a rise before nor a fall after is guaranteed. The news can leave uncertainty higher.

Take our 25,000 Call at ₹565.99. Picture two alternative next days. In both, 29 days are left and volatility falls from 18% to 14%. These are two possible outcomes from the same start, not two steps of one path.

Portfolio Vega adds each leg’s Vega times its signed quantity: positive for bought, negative for short. The total answers one question: what if every leg’s IV shifts by the same small amount? It does not cover every possible market change.

Buy 65 of our 25,000 Call and sell 65 of the matching Put, same expiry and inputs. The equal Vegas cancel, so net Vega is zero. The Deltas do not cancel: the position keeps about +64.95 units of bullish exposure, and it carries the short Put’s obligations. Zero Vega is not zero risk.

First pin down the underlying, Call or Put, strike, expiry and exercise style. Then make sure the premium and the underlying were captured at the same time, and check which model the screen uses. A spot-based formula is not a futures-based one: feeding a futures quote into the spot formula miscounts carry. A precise Greek can still rest on uncertain inputs.

The bid is the price buyers show; the ask is the price sellers show. The midpoint is their average, not a promised fill, and the last traded price can be stale. Size matters too: an order can fill partly or not at all. IV from the bid and IV from the ask are different readings. Vega predicts neither the spread nor the price at which you can exit.

A separate example. A bought Call fills at ₹570 and later sells at ₹560. For 65 units the result is (₹560 − ₹570) × 65 = −₹650 before charges. Subtract charges once. The fills already include the spread and slippage, so do not deduct those again. Keep three things apart: a model reprice, a displayed quote and a realised result.

A constant-volatility model simplifies markets that have events, jumps and a changing volatility surface. A scenario holds only for its chosen inputs. It is not a confidence interval, a quote or a forecast. Use Vega to ask how exposed a position is to volatility, next to its other exposures.

Three Greeks so far: Delta for the underlying level, Theta for time, Vega for volatility. Next is Gamma: how Delta itself changes as NIFTY moves. It explains why a hedge that fits today can fail after a bigger move. The later IV, skew and IV-crush lessons go deeper into volatility.