Ten-second price of a three-month ATM call and put

Question

A stock is at $100, implied volatility is $40\%$ , the interest rate is zero, and a call is struck at the money with three months to expiry. Estimate its price in your head, then the price of the matching put.

Short answer

About $8 for each. The at-the-money rule of thumb is $C \approx 0.4\,\sigma S\sqrt{T} = 0.4 \times 0.4 \times 100 \times 0.5 = 8$ (Black-Scholes gives $7.97$ ). With zero rates and $K = S$ , put-call parity gives $P = C$ .

Adapted from Crack, Heard on the Street, Q2.20, p.27; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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