The ATM Option Shortcut - Quant Trader Interview Question
Difficulty: Hard
Category: Mental Math & Estimation
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Topics: options, mental-math, approximation, volatility, trading
Problem Description
You're a market maker specializing in options. A client wants to buy an at-the-money (ATM) call option on a stock. You need to quickly estimate the fair price to quote. Using the approximation $C_{ATM} \approx 0.4 \cdot S \cdot \sigma \cdot \sqrt{T}$ , where
$S$ is the current stock price,
$\sigma$ is the implied volatility of the option,
$T$ is the time to expiration in years,
Estimate the price of an ATM call with $S = 100$, $\sigma = 0.20$, and $T = 0.25$ years.
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