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Original source:Tuo End number according to the tribe public number

 

99% expected gap […] Compared with 99.6% of [… The values of risk are very close

Inspired by a quote from the “Swiss Experience” report,

At the 99% confidence level […] Expected gap on […] Corresponds to about 99.6 to 99.8 per cent var

 

review

 

For any (absolutely) continuous cumulative distribution function, strictly increment, because (VaR and TVaR) are both continuous and strictly increment, it is possible to associate any TVaR with a VaR. namely

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Consider, for example, a lognormal distribution. Since there is no simple expression for the expected shortage, monte Carlo simulations are used to approximate it. Then, the cumulative distribution function is used to obtain the association level of risk values,

> n=1e7
> TVaR_VaR_LN=function(p){
+     X=rlnorm(n)
+     E=mean(X[X>qlnorm(p)])
+     return(plnorm(E))
+ }
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For example,

> TVaR_VaR_LN (. 99) [1] of 0.9967621Copy the code

To draw it, define

> prob=c(seq(.8,.99,by=.01),.995)
> P_ln=unlist(lapply(prob,TVaR_VaR_LN))
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Now, if you look at a distribution with a lighter tail, like an exponential distribution


> P_exp=unlist(lapply(prob,TVaR_VaR_exp))
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Or thick-tailed distribution (e.g. Pareto)

 
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We have different probability levels.

 

So the heavier the tail, the higher the probability level. Therefore, in some cases, always using 99.6% VaR qppfoximate 99% TVaR may work, for example

> TVaR_VaR_exp (. 99) [1] of 0.9963071Copy the code