VWAP Execution Variance - Quant Trader Interview Question
Difficulty: Hard
Category: Market Microstructure
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Topics: VWAP, variance, brownian-motion, execution, market-microstructure
Problem Description
You are tasked with executing a VWAP (Volume Weighted Average Price) order for a large client over a single trading day, $T$. Assume the following conditions hold:
Volume arrives uniformly throughout the day.
The price of the asset follows a Brownian motion with volatility $ \sigma $.
Your execution perfectly tracks the VWAP.
Calculate the variance of the difference between your average execution price and the terminal price of the asset, $S_T$. In other words, find $VarVWAP - S_T$.
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