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

Option Payoff (Seller / Writer Perspective)

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

C0C_{0}, P0P_{0}: Premium collected upfront (maximum profit for writer); STS_{T}: Spot price at expiration. X: Strike / exercise price.

Exam note

Writer assumes theoretically unlimited downside on naked calls, and substantial downside on puts (down to STS_{T} = 0).

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.