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What is the difference between historical and Gaussian method of VaR estimation?

I know how they are calculated, but what are the pros and cons of each?

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  • $\begingroup$ Have you tried searching for this? There is a lot of info out there. $\endgroup$ – AfterWorkGuinness Oct 27 '15 at 19:11
  • $\begingroup$ I have, but didn't find anything really relevant. $\endgroup$ – luka5z Oct 27 '15 at 19:13
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Historical Simulation

Pros:

  • Easy to calculate
  • Doesn't make assumptions about distribution of returns (uses empirical distribution)
  • Can add some enhancements onto it such as giving a higher weighting to more recent returns (prevents ghosting mentioned below) or a weighting by volatility where more volatile returns get a higher weight.

Cons:

  • Assumes the past will repeat itself, doesn't consider events that it has not seen before
  • If you use the most basic historical simulation approach, as your historical window shifts, large losses or returns at the edge of the window will no longer be in your data-set and can cause a significant jump in the Var (this is called ghosting) which in very undesirable

Guassian/Parametric/Delta Normal/Variance-Covariance (has many names)

Pros:

  • Relatively easy to calculate (more work than historical, but less compared to monte carlo)

Cons:

  • Assumes returns are normally distributed, which is often incorrect
  • Assumes delta sensitivity accounts for all the risk
  • Very inaccurate for non-linear positions like options (because of above point re delta)
  • Need to compute an NxN covariance matrix for the portfolio.
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  • $\begingroup$ which one is used the most? monte carlo? $\endgroup$ – luka5z Oct 27 '15 at 19:29
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    $\begingroup$ No idea sorry. If I had to make an educated guess, historical as it is the least data and process intensive. $\endgroup$ – AfterWorkGuinness Oct 27 '15 at 19:32
  • $\begingroup$ Thanks anyway! Maybe some praticioner will input something $\endgroup$ – luka5z Oct 27 '15 at 20:05
  • $\begingroup$ But guys: in usual Monte Carlo approaches: what do you do? Estimate a covariance from historical data and sample Gaussians. There are more sophisticated approaches but in the basic case: what is the difference? $\endgroup$ – Richard Oct 28 '15 at 9:13
  • $\begingroup$ Monte Carlo simulation is quite different. Here are a couple of posts on the topic: quant.stackexchange.com/questions/17910/… and quant.stackexchange.com/questions/12592/… $\endgroup$ – AfterWorkGuinness Oct 28 '15 at 16:37

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