🤖 AI Summary
Historical simulation is often mistakenly regarded as assumption-free, yet it implicitly relies on strong and unspecified modeling assumptions. This study provides the first unified parametric framework for modeling asset returns that encompasses standard historical simulation, filtered historical simulation, and shifted historical simulation. By systematically reconstructing these methods through the extraction of realized innovations from historical data, the paper explicitly uncovers their underlying assumptions. The analysis demonstrates that these approaches impose far more stringent structural requirements on the model than commonly acknowledged, thereby significantly advancing the theoretical understanding of Value-at-Risk (VaR) estimation methodologies.
📝 Abstract
Historical Simulation (HS) and its extensions form a popular class of methods for estimating Value-at-Risk for portfolios of financial assets based on historical data. In this note, we seek to unify several ideas and models from throughout the literature into a single modeling framework. By explicitly defining a parametric model form for the asset returns and extracting the realized increments of the driving innovation process from historical data, we are able to reproduce the Historical Simulation, filtered Historical Simulation, and displaced Historical Simulation methods. This shows beyond a doubt that these methods need more underlying assumptions than what is often alluded to.