Options: basics and payoffs

Options are the part of the syllabus that separates candidates who memorise from candidates who understand. The exam will give you a strike, a premium and a settlement price and ask for profit, break-even or moneyness. Each has a fixed recipe. Learn the four basic positions here and every strategy in chapter 6 becomes a sum of them.

The contract and its parties

An option gives its buyer (holder) the right, without the obligation, to buy or sell the underlying at a fixed strike price (exercise price) on or before the expiry date. A call is the right to buy; a put is the right to sell. The buyer pays a premium up front to the seller (writer), who keeps it whatever happens and is obliged to deliver on the option if the buyer exercises.

• European options can be exercised only on the expiry date. All index and stock options on Indian exchanges are European.
• American options can be exercised on any trading day up to expiry. They are worth at least as much as an equivalent European option.

Premiums are quoted per unit of underlying. A Nifty option quoted at ₹150 costs 150 × 75 = ₹11,250 per lot. The buyer's maximum loss is this premium; the writer's maximum gain is this premium, and the writer posts margin because the loss can be far larger.

Moneyness, intrinsic value and time value

Moneyness describes where the strike sits relative to the current spot price S.

• Call: in the money (ITM) if S > K, at the money (ATM) if S = K, out of the money (OTM) if S < K.
• Put: ITM if S < K, ATM if S = K, OTM if S > K.

Intrinsic value is what the option would be worth if exercised right now; it is never negative. Time value is the extra the market pays for the chance that the option becomes more valuable before expiry. It is highest for ATM options, falls as the option goes deep ITM or OTM, and decays to zero on expiry, when the premium equals intrinsic value exactly.

The four basic payoffs

Payoff at expiry depends on the settlement price S_T. The formulas below are per unit; multiply by lot size for rupees.

The short positions are exact mirror images: short call profit = premium − max(S_T − K, 0); short put profit = premium − max(K − S_T, 0). Break-even points are the same as for the buyer.

• Long call: bullish. Loss capped at premium; profit unlimited above break-even.
• Short call: neutral to bearish. Gain capped at premium; loss unlimited as the underlying rises.
• Long put: bearish. Loss capped at premium; profit grows as the underlying falls, up to K − premium if it goes to zero.
• Short put: neutral to bullish. Gain capped at premium; loss up to K − premium if the underlying goes to zero.

Note the shape: the buyer loses the full premium everywhere at or below the strike, starts recovering it above the strike, and crosses zero at break-even. The writer's line is the reflection. The same table for a 24,000 put bought at ₹140 would show break-even at 23,860 and a profit of (24,000 − 23,500 − 140) × 75 = ₹27,000 if Nifty settles at 23,500.

Exercise, assignment and settlement

Because Indian options are European, exercise happens only at expiry, and it is automatic: the clearing corporation exercises every ITM option on behalf of the buyer at the final settlement price. Index options settle in cash for the intrinsic value. Stock options that expire ITM result in physical delivery: a long ITM call must take delivery of the shares and pay the strike; a long ITM put must deliver shares. The writer who is assigned takes the opposite side. A buyer who does not want delivery must square off before expiry. Premium is settled on T+1 in cash, and the writer's margin is released when the position is closed or settled.

A quick exam heuristic: for any option question, first write down K, premium and S_T, then compute intrinsic value at S_T, then subtract (buyer) or add (writer) the premium, then multiply by the lot. The order never changes.