Whitepapers

Stabilizing Monte Carlo VaR Results

How to achieve Stable VaR results when using Monte-Carlo Simulation

Overview

Released on June 25, 2014, this whitepaper addresses a critical issue in Risk Management: the stability of Monte-Carlo VaR results. Monte-Carlo simulation is widely used for valuing non-linear, path-dependent instruments such as complex derivatives. However, the technique often suffers from unstable VaR results due to the inherent sampling variation.

The instability of Monte-Carlo VaR results arises from the stochastic process assumption and random sampling, which can lead to significant variance. This whitepaper explores how the stability of VaR results improves with an increased number of simulations, and it demonstrates how these results can become more reliable when the number of simulations grows. Using RiskEdge Software for analysis, the study shows how variance in results diminishes as the simulation count increases from 1,000 to 100,000 iterations.

What's Inside

Key aspects covered in this whitepaper include:

The impact of random number generation, initial seed, and number of simulations on VaR stability.
How the non-linearity of the portfolio influences the variability of VaR results.
The use of the Conditional EWMA method for volatility calculation and its application to VaR analysis.
A practical demonstration of variance reduction using Relative Standard Deviation (RSD) for Portfolio VaR, Asset VaR, and Component VaR.
How the stability of VaR improves by a factor of SQRT(N) as the number of simulations increases.

This whitepaper provides valuable insights for risk practitioners seeking to enhance the reliability of their Monte-Carlo VaR models, ensuring more stable risk assessments.

Whitepapers