Variance of Integrated Brownian Bridge - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
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Topics: probability, stochastic-calculus, brownian-motion, integral, variance
Problem Description
A quant trader is designing a novel trading strategy that relies on the properties of Brownian bridges. A key component of their model involves calculating the integral of a standard Brownian bridge.
Let $B_t$ be a standard Brownian Bridge from 0 to 0 over the interval $0, 1$. What is the variance of the random variable $X = \int_0^1 B_t dt$?
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