Pricing options in Indian markets

Eleven chapters derived prices for an abstraction. This one lists what the abstraction leaves out, and the omissions are not small.

The contract, as SEBI specifies it

Index options are European and cash settled. The exchange's specification says the contracts "shall be European styled which can be exercised only on the expiration date," with final settlement in cash against the index's closing price in the normal market. So chapters 1, 2 and 6 apply directly — no early-exercise correction, no delivery.

Premium style. SEBI directs that "the Exchanges shall introduce premium style index options," meaning the buyer pays the premium in cash rather than running it as a daily mark-to-market. Since 1 February 2025 the upfront margin requirement also includes net option premium payable at client level.

Stock options may be either style. SEBI permits exchanges to introduce "Premium Settled American / European Style Stock Options", so the exercise style is a contract term to look up rather than assume — and chapter 5 showed what that right can be worth.

Maturities run long. Index option contracts on Nifty and SENSEX may have maturities of up to five years, with eight semi-annual contracts, three serial monthly and three quarterly contracts. Chapter 10's point about vega applies here: a five-year option is a volatility instrument, and chapter 7's single-interest-rate assumption is doing much more work over five years than over thirty days.

Weekly expiries are now limited. From 20 November 2024, weekly contracts are available on only one benchmark index for each exchange. Chapter 9 explains why that was a consequential restriction: weekly at-the-money options carry the highest gamma and the fastest decay in the market.

Lot sizes, and why the hedge is lumpy

The model holds 0.5609 units of the index. The market trades lots.

For index derivatives, SEBI requires that a contract have a value of not less than ₹15 lakh at introduction, and that the lot size be fixed so the contract value on the day of review is within ₹15 lakh and ₹20 lakh, as "a multiple of 5, provided the lot size is not less than 10" — effective for contracts introduced after 20 November 2024. Exchanges review lot sizes every six months on the average closing price of the prior month, with at least two weeks' notice, and a lot size must be the same for an underlying across exchanges.

For stock derivatives the band is lower: contract value within ₹5 lakh and ₹10 lakh, lot size a multiple of 25 and not less than 50 — with a fallback to multiples of 5 and a minimum of 10 where 50 units would exceed ₹10 lakh.

What that does to chapter 8's hedge. At an index of 24,000, the ₹15–20 lakh band implies a lot of roughly 60 to 80 units. A single short call with a delta of 0.5609 and a lot of 75 carries 42.07 units of exposure, and the hedging instrument comes in the same lot of 75. The available hedges are zero or 75 units against a requirement of 42 — a position that cannot be delta hedged at all, only over- or under-hedged.

And the strike grid is finite too. Each maturity must carry "a minimum of three strikes (in the money, at the money and out of the money)", and for long-dated index options SEBI's framework sets a strike scheme between 1–1–1 and 5–1–5 with intervals designed to give at least 5% coverage either side of the index. So chapter 11's smile is sampled, not continuous, and the far strikes where the skew is steepest are exactly the ones with the fewest quotes and the widest spreads.

Securities transaction tax, which rose on 1 April 2026

Chapter 9's breakeven of 175.9 points assumed costless rebalancing. Here is the main statutory cost, under the Finance Act 2004 as modified by the Finance Act 2026:

Taxable transaction	From 1 April 2026	Up to 31 March 2026	Paid by	Charged on
Sale of an option	0.15%	0.10%	Seller	the option premium
Sale of an option, where exercised	0.15%	0.125%	Purchaser	the intrinsic value
Sale of a futures contract	0.05%	0.02%	Seller	the traded price

Three features of that table matter more than the rates themselves.

The increases are large and recent. Option-sale STT rose by half, from 0.10% to 0.15%. Futures STT rose by 150%, from 0.02% to 0.05% — and futures are the hedging instrument of chapters 8 and 9. Every rebalance of a delta hedge now costs two and a half times what it did before 1 April 2026.

The base differs by leg. On a sale, the tax is on the premium — a small number. On exercise, it is on the intrinsic value, which is a different and potentially much larger number, and it is the purchaser who pays. A 24,000 call exercised with the index at 24,500 on a lot of 75 has intrinsic value of ₹37,500, so the purchaser pays ₹56.25. Modest here, and it scales with how deep in the money the option finishes.

It falls on the seller for the premium leg. So the hedging seller of chapters 8 and 9 pays STT on every option sold and on every futures leg sold, while the buyer pays only on exercise. That is a structural tilt: hedged option selling is the tax-heaviest activity in the chain, which is part of why implied volatility sits above realised.

And the aggregate shows where this is going. SEBI's data has individual traders' STT rising more than five-fold from ₹1,291 crore in FY22 to ₹6,645 crore in FY26, lifting STT's share of their transaction costs from 13% to 27% while brokerage fell from 52% to 44%. Total transaction costs were about ₹25,000 crore in each of FY25 and FY26. That was all before the April 2026 rate increase, which raises the dominant component again.

Margin, which the model does not have

The replicating portfolio of chapters 3 to 6 is self-financing. A real short option position is not.

Initial margin covers a 99% one-day VaR. For index products the price scan range is six standard deviations scaled up, subject to at least 9.30% of the underlying price — SEBI states it as "SIX standard deviations (6σ) or 9.30% of the underlying value, whichever is higher." The volatility scan range is 25% of annualised EWMA volatility, subject to a minimum of 4%. For index options with more than nine months' residual maturity the price scan range is at least 17.7%.

Margins are scaled up for a minimum two-day liquidation horizon. Clearing corporations estimate an appropriate margin period of risk, "subject to a minimum of 2 days", and scale the price scan range accordingly.

There is no separate short option minimum charge, but there is extreme loss margin, and on expiry day an additional 2% ELM on short options — applying to open shorts at the start of the day and to shorts opened during it that expire that day.

What that costs the model. Three things the formula never priced:

Funding. Margin is capital that earns a deposit rate while the position earns an option's return. For a market maker running thousands of contracts, this is a real and continuous charge.

Procyclicality. Margin rises when volatility rises, which is when a short option position is already losing. The margin call arrives at the worst moment by construction — the Financial institutions subject's forced-selling mechanism, applied to a derivatives book.

Minimum viable size. Chapter 8's observation sharpened: delta hedging requires holding two positions, each with its own margin and its own lot. Below a certain account size the strategy is not merely approximate, it is unavailable.

Corporate actions, which rewrite the contract

A stock option is written on a share whose terms can change. SEBI's rule is a principle followed by formulas.

The principle. The basis for any adjustment "shall be such that the value of the position of the market participants on cum and ex-date for corporate action shall continue to remain the same as far as possible", which "will facilitate in retaining the relative status of positions viz. in-the-money, at-the-money and out-of-money." Adjustments are carried out on the last day the security trades cum, and apply to all open, exercised and assigned positions.

What gets adjusted: strike price, position, and market lot or multiplier — any or all, depending on the action.

The formulas. For a bonus in ratio $A{:}B$ the adjustment factor is $(A+B)/B$; for splits and consolidations in ratio $A{:}B$ it is $A/B$. The new strike is the old strike divided by the factor; the new lot and the new position are the old ones multiplied by it.

For a rights issue of ratio $A{:}B$ at issue price $S$, the factor is $(P-E)/P$ where $P$ is the spot price on the last cum date and $E = (P-S) \times A/(A+B)$ — and here the strike is multiplied by the factor while the lot is divided by it.

Four weeks' notice is required for any change in contract specifications, with narrower exceptions for index constituent changes on merger or demerger.

The dividend rule, which is the one that catches people

Dividends get a bright line, and it is worth quoting exactly:

Dividends which are below 2% of the market value of the underlying stock would be deemed to be ordinary dividends and no adjustment in the Strike Price would be made for ordinary dividends. For extra-ordinary dividends, at or above 2% of the market value of the underlying stock, the adjustment in derivatives shall be carried out.

Read what that means for a call holder. On the ex-date the share price falls by roughly the dividend. If the dividend is ordinary — below 2% — nothing is adjusted, so the option holder absorbs the fall and receives nothing in return. The dividend goes to the shareholder, and the call holder is not one.

This is chapter 7's no-dividend assumption, with a regulatory threshold attached. The formula assumes no dividends; the market handles large ones by adjusting the contract and small ones by not adjusting at all.

Working the problem

A 2,400 call on a stock at 2,400, lot size 500, delta 0.56. A dividend of ₹40 a share is declared.

Step 1 — which side of the line.

$\frac{40}{2{,}400} = 1.67\%$

Below 2%, so this is an ordinary dividend. No adjustment is made — strike stays 2,400, lot stays 500, position unchanged.

Step 2 — what happens to the share. On the ex-date the share trades without the right to the ₹40, so it falls by roughly that amount, to about ₹2,360.

Step 3 — what happens to you. Delta 0.56 against a 40-point fall:

$0.56 \times 40 \times 500 = ₹11{,}200 \text{ lost, per lot}$

And nothing arrives to offset it. A shareholder is made whole by the dividend; you are not. The option's price simply falls, and the contract is working exactly as specified.

Step 4 — the correct response is before the fact, not after. The dividend was announced; the ex-date is known. An option's price already reflects expected dividends over its life, because the market prices the forward rather than the spot. So the loss is not a surprise to the market — it is a surprise only to a holder who priced the option as if the share paid nothing, which is what chapter 6's formula does unless you adjust it. Before buying a stock option, check the ex-dates inside its life.

Step 5 — if the dividend were ₹60.

$\frac{60}{2{,}400} = 2.5\%$

At or above 2%, so it is extraordinary and an adjustment is carried out. The adjustment preserves position value across the cum and ex dates and keeps the relative moneyness — so the strike is reduced, and the holder is not left absorbing the price fall. You are protected from a ₹60 dividend and not from a ₹40 one, and the only difference is which side of a stated percentage it falls on.

Which is the right note to end the subject on. Chapters 1 to 11 derived what an option is worth, from arbitrage, replication and a limit. Every one of those results is correct and none of them tells you that a 1.67% dividend costs you ₹11,200 a lot while a 2.5% one costs you nothing. The model gives you the price; the contract decides what you own. Both have to be read.

The point

Indian index options are European, cash settled and premium style, so chapters 1 to 6 apply without an early-exercise correction — but the contract adds terms the model has no room for. Lot sizes are pegged to a ₹15–20 lakh contract value for indices and ₹5–10 lakh for stocks, which makes an exact delta hedge unavailable to a single-lot position; strikes are a finite grid, thinnest where the skew is steepest; margin is a 99% one-day VaR with a floor of 9.30% of underlying value, rising with volatility and carrying an extra 2% on expiry day. Securities transaction tax rose on 1 April 2026 to 0.15% on option premium and 0.05% on futures — the hedging leg up 150% — against SEBI data showing STT already at 27% of individuals' transaction costs. And corporate actions rewrite the contract by formula, except for dividends below 2% of market value, where nothing is adjusted and the option holder absorbs the ex-date fall.