Paper: arXiv 2605.10066

Authors: Björn Löfdahl Grelsson

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.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a valuable theoretical unification of Historical Simulation variations by casting them within a explicit parametric innovation model. While it effectively clarifies hidden modeling assumptions mathematically, it lacks extensive empirical backtesting and statistical validation on live portfolio datasets.

Research Flowchart

  flowchart TD
    A["Research Goal: Unify Historical Simulation (HS) methods into a single framework"] --> B["Data/Inputs: Historical asset returns & market data"]
    B --> C["Define parametric model for asset returns & extract innovation increments"]
    C --> D["Computational Process: Map innovations to HS, Filtered HS, & Displaced HS"]
    D --> E["Findings: Proves HS methods require strong underlying parametric assumptions"]

Cited References (18)

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  2. Evaluation of Value-at-Risk Models Using Historical Data (1996)
  3. Value at Risk (2000)
  4. Market Risk Analysis, Volume IV : Value-at-Risk Models (2008)
  5. Risk and Portfolio Analysis: Principles and Methods (2012)
  6. Risk and Asset Allocation (2005)
  7. The Hidden Dangers of Historical Simulation (2006)
  8. An overview of value at risk (1997)
and 10 more
  1. Displaced relative changes in historical simulation: Application to risk measures of interest rates with phases of negative rates (2017)
  2. How to choose the return model for market risk? Getting towards a right magnitude of stressed VaR (2019)
  3. Value at risk when daily changes in market variables are not normally distributed (1998)
  4. VaR without Correlations for Portfolios of Derivative Securities (1999)
  5. Nonlinear Time Series: Nonparametric and Parametric Methods (2003)
  6. Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances (1992) — link
  7. Generalized Autoregressive Conditional Heteroskedasticity (1986)
  8. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation (1982)
  9. Stochastic Calculus for Finance II : Continuous-Time Models (2004)
  10. Options, Futures, and Other Derivatives (2018)

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.