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Using Real-World Volatility Models for VaR and Expected Shortfall

Article Quant Q&A · Author: Luar86
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Summary

The discussion addresses whether maximum-likelihood estimates of a Heston stochastic-volatility model, often used in derivative pricing, can be applied to value at risk. The reply distinguishes risk-neutral calibration for pricing from real-world risk analysis and recommends modeling volatility from historical asset returns for the latter.

It outlines a workflow: fit a GARCH-family model to historical data using frequentist or Bayesian methods, simulate future returns, then estimate VaR and expected shortfall from the simulated distribution. It also notes that model choice should reflect the asset and the risk problem, since volatility behavior varies across markets. This is a broad recommendation, not a comparison of model performance; it does not establish that Heston models cannot be adapted for risk analysis or specify a particular GARCH variant, horizon, or validation method.

Key ideas

  • Derivative pricing and risk measurement generally use different probability measures and modeling objectives.
  • The response recommends fitting a GARCH-family volatility model to historical data for real-world risk analysis.
  • Maximum-likelihood or Bayesian methods can estimate model parameters before forward simulation.
  • VaR and expected shortfall can be calculated from the resulting simulated return distribution.
  • Model choice should reflect the asset’s volatility behavior and the risk question being studied.

Tags

Risk managementVolatilityStatisticsBacktesting
Full text
# Parameter estimation of Heston model for VaR using Maximum Likelihood


# Parameter estimation of Heston model for VaR using Maximum Likelihood












I found an article file that explains how to estimate the parameters of the Heston model. I want to use the parameter results to calculate the value at risk. However, after reading it, I realized that the estimation can only be done for option pricing, not for value at risk. Could you highlight the part that shows the method or explain it to me? Thank you. https://www.sciencedirect.com/science/article/abs/pii/S0304405X06001395 (Yacine Ait-Sahalia & Robert Kimmel, 2007, Maximum likelihood estimation of stochastic volatility models)

## Answer by THATS MY QUANT MY QUANTITATIVE (score 0)

https://quant.stackexchange.com/a/80863

Risk analysis i.e. VaR and CVaR typically use GARCH models and its variations for analysis since we are dealing with real-world measures. As you correctly concluded, GARCH and SV models aren't used for the same thing, the latter being for derivative pricing. The standard approach that is taught in risk management handbooks e.g. Quantitative Risk Management: Concepts, Techniques and Tools - Revised Edition, teach GARCH because GARCH is accurate in measuring historical volatility, which can be used for forward simulations to give risk levels. Using historical volatility has validity since volatility behaviour is reasonably consistent for each asset, i.e. the volatility of oil will have a lot more shocks compared to treasury bills for reasons that are unique to the asset.

If you want to do risk-analysis, the simple approach would be to take historical data of your chosen asset(s), calibrate a GARCH model using either frequentist inference (MLE) or bayesian inference (MCMC), then use the calibrated model to run forward monte-carlo simulations and calculate your expected-shortfall and VaR.

The are a plethora of different models that are used for risk management with their own strengths and weaknesses , but the general theme is that you are modelling volatility, and you want to pick a model that has similar attributes to your problem.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.