Historical simulation (finance)

Historical simulation in finance's value at risk (VaR) analysis is a procedure for predicting the value at risk by 'simulating' or constructing the cumulative distribution function (CDF) of assets returns over time. Unlike parametric VaR models, historical simulation does not assume a particular distribution of the asset returns. Also, it is relatively easy to implement. However, there are a couple of shortcomings of historical simulation. First of all, it imposes a restriction on the estimation assuming that asset returns are independent and identically-distributed random variables, which is not the case: from empirical evidence, it is known that asset returns are clearly not independent, as they exhibit certain patterns such as volatility clustering. The second restriction relates to time: historical simulation applies equal weight to all returns of the whole period; this is inconsistent with the diminishing predictability of data that are further away from the present. These two shortcomings lead economists and financial experts to further develop other non-parametric, semi-parametric and parametric models.

Weighted historical simulation

Weighted historical simulation applies decreasing weights to returns that are further away from the present, which overcomes the inconsistency of historical simulation with diminishing predictability of data that are further away from the present. However, weighted historical simulation still assumes independent and identically-distributed (iid) asset returns. [1]

Filtered historical simulation

Filtered historical simulation is a semi-parametric technique in forecasting VaR. Here the returns are no longer assumed iid, rather there is an additional innovation term v is now assumed to be iid instead. This allows the means and variances to be 'filtered away', coupled with an empirically estimated CDF, it becomes a more realistic model in predicting VaR.[2]

See also

References

  1. ↑ Boudoukh, J.; Richardson, M.; Whitelaw, R. (1998). "The Best of Both Worlds". Risk 11: 64–67.
  2. ↑ Barone-Adesi, G.; Giannopoulos, K.; Vosper, L. (1999). "VaR Without Correlations for Portfolios of Derivatives Securities". Journal of Futures Markets 19: 583–602. doi:10.1002/(SICI)1096-9934(199908)19:5<583::AID-FUT5>3.0.CO;2-S.

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