Dayara Pharma trades at Rs 540 on a pending approval: Rs 660 if approved, Rs 420 if not, equally likely, with ordinary 25% volatility either way over a month. Price the one-month 600 call as a mixture of the two outcomes, compare it with a single-volatility price, and say what shape the event gives implied volatility across strikes.

The 600 call is worth about Rs 31 as a mixture, against Rs 1.32 from Black-Scholes at 25%. Backing implied volatility out of the mixture prices gives about 97% at the money and less toward both wings, 62% at 390 and 55% at 720. Every strike is far above 25%, but the shape is a frown, not a smile: the event puts probability at the two outcomes and none in the middle, which no single volatility can describe.

Black-Scholes assumes tomorrow's price is spread in one smooth hump around today's. Think instead of a cricket match decided by a coin toss on the last ball: the final score sits in one of two places, never in between. Dayara's distribution in a month has two humps, one near Rs 420 and one near Rs 660, and almost nothing at Rs 540, so any single lognormal centred on Rs 540 puts its probability exactly where the stock will not be. At 25% the lognormal says a one-month standard deviation of about 7.2%, roughly Rs 39; the event moves the stock Rs 120 either way. The model cannot be fixed by a better choice of one number.

Price the call in each world and weight them. If the drug is approved the stock is at Rs 660 and the 600 call is Rs 60 in the money with a month of 25% volatility on top, worth Rs 61.98; if it is refused the stock is at Rs 420 and the 600 call is worth less than a paisa; half of each is Rs 30.99. A single Black-Scholes price at 25% from Rs 540 gives Rs 1.32, off by a factor of more than twenty. Even at the at-the-money implied volatility of the mixture, 97%, Black-Scholes gives Rs 37.77 for the 600 call, too much, because the single volatility now spreads probability too far beyond 660.

Repeat the mixture price at every strike from 390 to 720 and ask what single volatility Black-Scholes would need to match each one. Every implied volatility is far above 25%, but they are highest in the middle, about 98% at 510 and 97% at 540, and fall toward both wings, to 62% at 390 and 55% at 720: a frown, the opposite of the usual smile. The reason is in the humps. Options struck between the two outcomes are where the event matters most, since the jump decides whether they finish in or out of the money; options struck beyond 660 or below 420 need an ordinary 25% move after the jump, so they carry less event premium. Traders who see an at-the-money implied volatility far above the wings in front of a known date are looking at a binary event priced into the surface.

State the limits. The two-world model assumes the outcomes and the probability are known; in practice both are uncertain, which smooths the humps and softens the frown. Real surfaces combine this event shape with the ordinary skew of the stock, so the observed curve may be a frown on top of a downward slope. And after the decision the event premium disappears overnight: a desk long at-the-money options at 97% implied volatility the evening before has bought something that will be worth only its 25% value the next day, plus whatever the jump paid.