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Formula sheet/NISM Series XV: Research Analyst/Introduction to Securities Market
[ INTRODUCTION TO SECURITIES MARKET ]

Option Payoff (Buyer / Holder Perspective)

Call Payoff=max(0,ST−X)−C0\text{Call Payoff} = max(0, S_{T} - X) - C_{0}
Put Payoff=max(0,X−ST)−P0\text{Put Payoff} = max(0, X - S_{T}) - P_{0}
Variables

STS_{T}: Spot price of underlying at maturity; X: Strike / Exercise price; C0C_{0}, P0P_{0}: Upfront premium paid.

Exam note

Call is In-the-Money (ITM) when STS_{T} > X. Put is ITM when STS_{T} < X. Downside for buyer is strictly limited to premium paid.

Worked examples
Call Option Payoff and Net Profit/Loss Calculation

An equity derivative trader buys 1 lot of Nifty 50 Index Call Option with a strike price of Rs 24,000 at a premium of Rs 180. At expiration, the Nifty 50 index closes at Rs 24,450. Calculate the gross payoff, net profit/loss per unit, and total profit on the lot (Lot Size = 25 units).

Put Option Payoff and Break-even Analysis

An investor holding shares of Tata Motors buys a protective Put Option with strike price Rs 950 at a premium of Rs 35. At expiration, Tata Motors drops to Rs 870. Calculate the gross payoff, net profit per share, and the break-even price.