Kyle's Lambda Estimation - Quant Researcher Interview Question

Problem Description

Kyle's Lambda is a fundamental metric in market microstructure derived from the Kyle (1985) model, used to quantify the price impact of order flow and the cost of demanding liquidity. It posits a linear relationship between price changes and signed order flow, where the slope coefficient ($\lambda$) represents the illiquidity or depth of the market. Task Implement the function estimate_kyles_lambda to calculate the rolling Kyle's Lambda ($\lambda$) coefficient using Ordinary Least Squares (OLS)