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Hill Estimator for Tail Index

Hard · risk_management · Quant Researcher interview question · hill_estimator, tail_index, extreme_value_theory, heavy_tails, risk_management

Extreme Value Theory (EVT) is used in risk management to model the heavy tails of financial returns, which are poorly captured by Gaussian models. The Hill estimator provides a non-parametric method to estimate the tail index (α) of a distribution, a key parameter for quantifying tail risk. This estimator uses the largest observations in a dataset to infer the tail's shape without assuming a distribution for the entire sample. Task Implement the function hill_tail_index(data: list, k: int) -> f