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Difficulty: Hard
Category: Finance
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Topics: stochastic-calculus, ornstein-uhlenbeck, variance, mean-reversion, probability
A mean-reverting trading strategy uses a process modeled by the Ornstein-Uhlenbeck process: $dX_t = -\theta X_t dt + \sigma dW_t$, where $X_t$ represents the deviation from the mean, $\theta > 0$ is the rate of mean reversion, $\sigma > 0$ is the volatility, and $dW_t$ is a standard Wiener process. What is the long-run variance of $X_t$ as $t \to \infty$?
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