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Hard · Mental Math & Estimation · Quant Trader interview question · options, mental-math, approximation, volatility, trading
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.