Skip to content
All library documents

Monte Carlo VaR for Nonlinear Payoffs and Non-Normal Risk Factors

Article Quant Q&A · Author: MichaelR Collet
Read the original

Summary

The document compares Monte Carlo Value at Risk with a parametric approach. Monte Carlo methods can be useful when a portfolio contains nonlinear or path-dependent positions, such as options, mortgage-backed securities, or convertible bonds. The method simulates factor paths, reprices the instruments along those paths, and estimates portfolio VaR from the resulting return distribution. This can handle payoff features that are difficult to represent with a simple parametric return assumption or closed-form solution.

The discussion also separates simulation from the choice of factor distribution. A Monte Carlo framework need not use multivariate normal shocks: alternative stochastic models or copulas can represent fat tails and dependence in the tails. Thus, normally distributed factors reflect a modeling choice or platform limitation, not an inherent requirement of Monte Carlo. The document offers conceptual guidance rather than a comparison using data, and simulated VaR remains sensitive to the chosen factor model and pricing assumptions.

Key ideas

  • Monte Carlo VaR can reprice nonlinear instruments across simulated factor paths.
  • Path-dependent positions may require simulated paths rather than a simple return approximation.
  • A Monte Carlo framework can use non-normal factor models or copulas to represent tail behavior.
  • Multivariate normal shocks are a modeling choice rather than a requirement of Monte Carlo VaR.
  • VaR estimates depend on the selected stochastic model and instrument pricing assumptions.

Tags

Risk managementOptionsDerivatives pricingStatistics
Full text
# Monte Carlo VaR w/ Multivariate Normal vs. Parametric


# Monte Carlo VaR w/ Multivariate Normal vs. Parametric












In Aladdin's Monte Carlo VaR, the default setting for the joint distribution of factor returns is multivariate normal. Given that normal distributions do not capture the fat tails seen in empirical financial returns, what is the advantage of running a Monte Carlo VaR vs. a parametric approach?

## Answer by AlRacoon (score 2)

https://quant.stackexchange.com/a/44221

Monte Carlo VaR is good for portfolios that have instruments with non-linear payoffs, such as options and positions with embedded options (mortgage back securities, convertible bonds, etc.) It is also good for positions that have path dependency. Parametric VaR is difficult to use for these instruments in that the distribution of returns assumptions do not hold (namely normally distributed returns around an expected return). Monte Carlo VaR will produce a simulated path of returns on an underlying and reprice the non-linear and path dependent positions based on a simulated path of returns. The pricing and returns generated from those prices are then used to provide a VaR for a portfolio that contains such instruments.

## Answer by RRL (score 1)

https://quant.stackexchange.com/a/44241

Apparently that is just a limitation of Aladdin.

There is nothing to prevent you from computing VaR (as a percentile of the portfolio return distribution) using a better stochastic model for the factors that can incorporate fat tails, etc. Copula models can be used to introduce non-normality of the joint distribution (tail dependency) even if marginal distributions are normal.

In fact, much of this non-normal behavior would be difficult if not impossible to capture in a parametric approach with a closed-form solution.

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.