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October 22, 2008
FRM問題-你問我答(九)


老師請教您,以下這篇來自Schweser 2008年版FRM Study Notes Book 4p.41,幫我翻譯一下。

Time-Scaling In the Pareto Severity Model

AIM 58.4: Explain the time- scaling in the Pareto Severity Model and its implications.

The square root of time rule is a well- known approximation in risk management. The rule allows for the approximation of multi- period VAR measures from single Period VAR measures by adjusting by the square root of time. This rule is based on the central limit theorem, which also holds for Pareto models when certain adjustments are made. For Pareto models ( OpVAR ), time scaling will follow a l/α-root as opposed to1/2- root ( i.e., t^0.5time scaling for VAR. Note that α can be any number greater than 0, but does a better job of modeling actual VAR when values are small ( e.g.,1). In the case of the Pareto model, typical values for α imply that the threat of losses due to operational risk increases very quickly, and notably faster than the result of the square- root- rule . Briefly stated, as time increases operational risk significantly increases.

 

答覆:

這篇是在說「柏拉圖損失金額模型(Pareto Severity Model)的時間比例調整(Time-Scaling)」

AIM58.4:解釋柏拉圖損失金額模型的時間比例調整與其意涵

時間平方根規則是風險管理有名的趨近值。該規則以時間的平方根調整單期VAR為多期VAR的趨近值。此規則是根據中央極限理論。柏拉圖模型的調整也可根據中央極限理論。柏拉圖模型(作業VAR)的時間比例調整使用1/α次方,而非1/2次方(亦即t^0.5)來調整VAR。注意α可以是大於0的任一數,但是當α很小時(例如1),在模擬實際VAR時很有效。柏拉圖模型的典型α值隱含因為作業風險的損失增加得非常快,而且比平方根規則的結果還快。簡言之,隨著時間的增加,作業風險大幅增加。

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