Whitepaper: Stabilizing Monte Carlo VaR Results
How to achieve Stable VaR results when using Monte-Carlo Simulation
This Whitepaper addresses one of the most debated issues in Risk Management – The Stability of Monte-Carlo VaR Results. As Risk practitioners are acutely aware, Monte-Carlo is a preferred method when valuing non-linear, path-dependent instruments including complex derivatives. However, unstable VaR results is a very pervasive issue due to the inherent sampling variation in Monte-Carlo. The assumption made by this model about the stochastic process due to its dependence on random sampling leaves it vulnerable to unstable results. The variance in end results can sometimes be so huge, that it renders Risk Management meaningless for most decision-makers.
There are several parameters that determine how stable the VaR results are:
This Whitepaper shows how unstable the VaR numbers can be, and how as we increase the number of simulations (we’ve used RiskEdge Software for this analysis), the stability of VaR results improves by a factor of SQRT (N); where N is the number of times the simulations have been increased by.
We have used a simple linear portfolio to analyze this issue, and we show how the variance in results reduces (per 100 iterations) as we increase the simulations gradually from 1,000 to 100,000. Conditional EWMA method was used to calculate Volatility, along with 95th percentile Confidence Level, and 1-day Holding period.
We analyzed variance reduction / stability improvement using Relative Standard Deviation (RSD) for 3 VaR measures – Portfolio VaR, Individual (or Asset) VaR, and Component (or Contribution) VaR. The results indicate that the variance reduction is broadly in line with SQRT (N) formula.
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