On the modeling assumptions of Historical Simulation for Value-at-Risk

TL;DR

This paper unifies various Historical Simulation methods for Value-at-Risk under a single parametric framework, revealing they rely on more assumptions than commonly acknowledged.

Contribution

It introduces a parametric model that reproduces multiple Historical Simulation variants, clarifying their underlying assumptions.

Findings

Historical Simulation methods can be derived from a common parametric model.

These methods depend on more assumptions than typically recognized.

The framework clarifies the modeling assumptions behind different HS variants.

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.