NISM-Series-X-A: Investment Adviser (Level 1) · Understanding Derivatives

Options Contracts and Payoffs for NISM Series X-A

Updated 11 October 2026 · Fact-checked

An option gives the buyer the right, but not the obligation, to buy (call) or sell (put) an underlying at a fixed strike price on or before expiry, in return for a premium. To solve payoff questions, compute intrinsic value at expiry, then subtract the premium paid for a buyer or add it for a seller.

Understand Options Contracts and Payoffs

An option is a contract between a buyer and a seller (the writer). The buyer pays a price called the premium and gets a right. The writer receives the premium and takes on an obligation. This is the key asymmetry: the buyer has a right, the writer has an obligation.

A call option gives the buyer the right to buy the underlying at the strike price (exercise price). You buy a call when you expect the price to rise. A put option gives the buyer the right to sell the underlying at the strike price. You buy a put when you expect the price to fall.

On exercise style: a European option can be exercised only on the expiry date. An American option can be exercised at any time up to expiry. Index options and stock options on Indian exchanges are European style.

Moneyness tells you whether exercising now would give a gain. A call is in the money (ITM) when spot is above strike, at the money (ATM) when spot equals strike, and out of the money (OTM) when spot is below strike. For a put, it is reversed: ITM when spot is below strike, OTM when spot is above strike.

The premium has two parts: intrinsic value (the gain if exercised now, never below zero) and time value (the rest). An OTM or ATM option has zero intrinsic value, so its whole premium is time value. The buyer's loss is limited to the premium. A call buyer's profit is unlimited in theory. A call writer's loss is unlimited in theory, while the writer's maximum gain is the premium. A put buyer's maximum profit is limited, because the price cannot fall below zero.

Key formulas to remember

Call payoff to buyer at expiry: Max(S − K, 0); S is spot price at expiry, K is strike. Net profit = payoff − premium.
Put payoff to buyer at expiry: Max(K − S, 0); Net profit = payoff − premium.
Writer's payoff: Writer's profit = − (buyer's payoff) + premium; Writer's result is the exact opposite of the buyer's. Options are a zero-sum game before costs.
Break-even, call: Strike + Premium; Same for buyer and writer. Above this the call buyer gains.
Break-even, put: Strike − Premium; Below this the put buyer gains.
Intrinsic value: Call: Max(S − K, 0); Put: Max(K − S, 0); Premium = intrinsic value + time value.
Maximum loss and gain: Buyer: loss = premium. Call writer: gain = premium.; Call buyer gain and call writer loss are unlimited in theory. Put gain and loss are limited by the price falling to zero.

How to solve Options Contracts and Payoffs questions

Use the same sequence for any payoff or terminology question on options.

1Identify the position: long call, short call, long put or short put. Ask who has the right and who has the obligation.
2Note the strike (K), premium and the spot price (S) given.
3Decide moneyness: compare S with K, remembering that puts work in reverse to calls.
4Compute the buyer's payoff: Max(S − K, 0) for a call or Max(K − S, 0) for a put.
5Subtract the premium to get the buyer's net profit. For the writer, reverse the sign of the buyer's net result.
6Multiply by lot size or number of units only if the question asks for total profit or loss.
7Check against limits: buyer's loss cannot exceed the premium, and the writer's gain cannot exceed the premium.

Quickest way: Premium and break-even shortcut

When to use it: Use when the question asks for net profit, break-even or maximum loss on a single option.

Find the break-even first: strike + premium for a call, strike − premium for a put.
If spot is on the losing side of strike, the buyer's loss is the full premium.
Otherwise net profit = distance of spot beyond break-even.
For the writer, flip the sign.
Eliminate options that show a buyer's loss larger than the premium.

Common mistakes in Options Contracts and Payoffs

Treating a put as ITM when spot is above strike.
You apply the call rule to puts.
Fix: For a put, ITM means spot is below strike. Ask: would I gain by selling at the strike?
Forgetting to subtract the premium from the buyer's payoff.
You stop at Max(S − K, 0).
Fix: Payoff is not profit. Always compute net profit = payoff − premium when the premium is given.
Saying the buyer of an option has an obligation to perform.
You mix up buyer and writer.
Fix: The buyer holds the right. Only the writer is obliged if the buyer exercises.
Calling an ITM option's entire premium time value.
You ignore intrinsic value.
Fix: Time value = premium − intrinsic value. Only ATM and OTM options are all time value.
Mixing up American and European options.
The names suggest geography.
Fix: European: exercise only at expiry. American: any time up to expiry.
Putting the break-even of a put at strike + premium.
You reuse the call formula.
Fix: Put break-even is strike − premium.

Worked examples

Example 1

An investor buys a call option with strike ₹500 on a share at a premium of ₹20. At expiry the share closes at ₹545. What is the net profit per share, and what is the break-even?

Show the solution

Position: long call. K = 500, premium = 20, S = 545.
Payoff = Max(545 − 500, 0) = ₹45.
Net profit = 45 − 20 = ₹25.
Break-even = 500 + 20 = ₹520.

Answer: Net profit is ₹25 per share and break-even is ₹520.

Example 2

A trader writes a put option with strike ₹1,200 and receives a premium of ₹30. At expiry the underlying is at ₹1,150. What is the writer's profit or loss per unit?

Show the solution

Position: short put. K = 1,200, premium received = 30, S = 1,150.
Buyer's payoff = Max(1,200 − 1,150, 0) = ₹50.
Writer pays 50 and received 30.
Writer's result = 30 − 50 = −₹20.
Check: break-even = 1,200 − 30 = ₹1,170. Spot is below it, so the writer loses.

Answer: The writer makes a loss of ₹20 per unit.

Exam tips

Practise moneyness for puts. Examiners often use puts to catch the call-rule reflex.
Read whether the question asks for payoff or net profit. They differ by the premium.
Remember that maximum loss for any buyer equals the premium, and maximum gain for any writer equals the premium.
Negative marking applies, so skip only if you cannot remove two options. Use break-even to eliminate wrong choices.
Do not confuse exercise style with the right: American and European options differ in timing, not in call or put.

Practice questions from Understanding Derivatives

Options Contracts and Payoffs in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Options Contracts and Payoffs: frequently asked questions

What is the difference between American and European options?

A European option can be exercised only on its expiry date. An American option can be exercised on any day up to and including expiry. Index and stock options on Indian exchanges are European style.

How do I know if an option is in the money, at the money or out of the money?

Compare spot with strike. A call is ITM when spot is above strike and OTM when below. A put is ITM when spot is below strike and OTM when above. Both are ATM when spot equals strike.

What is the maximum loss for an option buyer?

It is the premium paid. The buyer can simply let the option expire if it is not profitable, so the loss cannot exceed that amount.

Who receives the premium in an option contract?

The writer (seller) receives the premium from the buyer at the time the contract is made. The writer keeps it whether or not the option is exercised.