Volatility of Inverse Price - Quant Trader Interview Question
Difficulty: Medium
Category: Probability & Statistics
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Topics: stochastic-calculus, geometric-brownian-motion, volatility, ito's-lemma
Problem Description
Suppose a stock price, $S_t$ , follows a geometric Brownian motion with volatility $\sigma$ . You are tasked with analyzing a derivative whose payoff depends on the inverse of the stock price, $Y_t = 1/S_t$ . What is the volatility of $Y_t$ ?
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