Break-even for a call seller

Question

You sell a call option with strike $12 and collect a premium of $2.50. At what stock price at expiry do you exactly break even?

Short answer

$14.50. The seller keeps the $2.50 premium but owes $\max(S_T-12,0)$ at expiry. Setting $2.50-(S_T-12)=0$ gives $S_T = 12+2.50 = 14.50$ ; above that the short call loses money.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Market Model and Risk-Neutral Valuation
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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