Pay-off Profiles of Options Contracts

An option contract gives the holder the right, but not the obligation, to buy (call) or sell (put) the underlying commodity at a pre‑determined strike price (K) on the expiry date. The pay‑off is the amount received from exercising the right, irrespective of any premium paid earlier.

For a call buyer, the payoff is the excess of the spot price at expiry (S) over the strike price, if S exceeds K; otherwise the payoff is zero because the holder will let the option lapse. The opposite logic applies to a put buyer – the payoff is the excess of K over S when the market price falls below the strike.

From the perspective of the option writer (seller), the payoff is the negative of the buyer’s payoff because the writer must deliver the opposite cash flow. This sign reversal is a frequent source of confusion in the exam.

• Pay‑off is a cash‑flow at expiry, not the total profit.
• Premium paid or received is accounted for separately when computing net profit.

The writer’s payoff is simply the negative of the buyer’s payoff. For a call writer, payoff = -max{S‑K,0}; for a put writer, payoff = -max{K‑S,0}. This means the writer gains the premium upfront but faces unlimited loss for a call and limited loss for a put.

Breakeven price for a call buyer is K plus the premium paid (P). For a put buyer, breakeven is K minus the premium. These breakeven points are often plotted on payoff diagrams and are asked directly in NISM multiple‑choice questions.

Intrinsic value at expiry equals the payoff. Time value disappears at expiry, so the entire option value equals intrinsic value. Knowing this helps you answer questions that compare pre‑expiry and expiry values.

In‑the‑Money (ITM) means the option has positive intrinsic value: S > K for calls and S < K for puts. The payoff is positive and increases linearly with the distance from K.

Out‑of‑the‑Money (OTM) indicates zero intrinsic value: S ≤ K for calls and S ≥ K for puts. The payoff is zero because exercising would be disadvantageous.

At‑the‑Money (ATM) occurs when S = K. Both call and put pay‑offs are zero at expiry, but the premium is usually highest due to maximum time value. Exam questions often ask you to identify the zone given S and K values.

The premium is the price paid for the right to trade the option. It is recorded as a cost for the buyer and as income for the writer. Net profit for the buyer equals payoff minus premium, while net profit for the writer equals premium minus payoff.

Because the premium is known at the time of trade, it shifts the breakeven point. For a call buyer, breakeven = K + Premium; for a put buyer, breakeven = K – Premium. These formulas are frequently tested.

In a volatile commodity market, premiums can be high. The exam may present scenarios where a large premium makes an otherwise ITM option result in a net loss.

Option strategies such as vertical spreads, straddles and strangles are built by combining individual option pay‑offs. The resulting profile is the algebraic sum of each component’s payoff.

For example, a long straddle involves buying a call and a put with the same strike and expiry. Its payoff diagram looks like a "V" shape: profit when the spot moves far away from the strike in either direction, loss limited to the total premiums when the spot stays near the strike.

Understanding how to add pay‑offs is essential for questions that ask you to identify the strategy from a given diagram or to compute the net payoff at a particular spot price.