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Hard · Options & Greeks · Quant Trader interview question · options, local-volatility, dupire, implied-volatility
You are a quantitative trader at a top firm and need to quickly estimate the local volatility from the implied volatility surface. Given the implied volatility $σ_{imp}(K, T)$ for European call options, which of the following formulas correctly expresses the local volatility $σ_{loc}(K, T)$ in terms of $σ_{imp}(K, T)$, the strike price $K$, the time to maturity $T$, and the forward price $F$?