Monte Carlo Simulation Q131.4
- Thread starter orit
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Hi Orit,
Keep in mind that, in this context of Monte Carlo simulation, the VaR is itself an estimate produced by a sample. Run a trial, get a VaR of X; run another trial, get another VaR of Y (hopefully close in value!). In this way, the VaR itself is a random variable created by a simulation with unavoidable sampling variation. So, back to our econometrics, we presume the estimate produced by the sample represents some undelying "true" population (with a true VaR that we may never know) but we recognize that, as an estimate, it has variation (dispersion) reflecting its imprecision.
So, standard error (here) is the standard deviation of the VaR (the quantile) observed in, or expected in, our sample; i.e., the higher the SE, the less precise our VaR quantile (I prefer precision over Jorion's accuracy, http://en.wikipedia.org/wiki/Accuracy_and_precision#Accuracy_versus_precision:_the_target_analogy)
Then relative error is simply to scale the SE to give it some scale context. Here is (i think) an analogy: relative error is similar to coefficient of variation http://en.wikipedia.org/wiki/Coefficient_of_variation
... with a similar purpose, to give the standard deviation (recall SE is a standard deviation) some scale context; e.g., a low SE value may look like a precise VaR, but if the VaR is (eg) smaller than the SE, then it's actually a large SE in relative terms.
I hope that helps,
Keep in mind that, in this context of Monte Carlo simulation, the VaR is itself an estimate produced by a sample. Run a trial, get a VaR of X; run another trial, get another VaR of Y (hopefully close in value!). In this way, the VaR itself is a random variable created by a simulation with unavoidable sampling variation. So, back to our econometrics, we presume the estimate produced by the sample represents some undelying "true" population (with a true VaR that we may never know) but we recognize that, as an estimate, it has variation (dispersion) reflecting its imprecision.
So, standard error (here) is the standard deviation of the VaR (the quantile) observed in, or expected in, our sample; i.e., the higher the SE, the less precise our VaR quantile (I prefer precision over Jorion's accuracy, http://en.wikipedia.org/wiki/Accuracy_and_precision#Accuracy_versus_precision:_the_target_analogy)
Then relative error is simply to scale the SE to give it some scale context. Here is (i think) an analogy: relative error is similar to coefficient of variation http://en.wikipedia.org/wiki/Coefficient_of_variation
... with a similar purpose, to give the standard deviation (recall SE is a standard deviation) some scale context; e.g., a low SE value may look like a precise VaR, but if the VaR is (eg) smaller than the SE, then it's actually a large SE in relative terms.
I hope that helps,
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