[SOLVED] 代写 R 


MAT 4376F/5313F

R – Value-at-Risk, Expected Shortfall
•Value-at-Risk
•Comparison of parametric and nonparametric method for Exponential distribution n=1000;
•lambda=2;
•p=seq(1,n,by=1)/(n+1);
•true.VAR=-log(p)/lambda;
•plot(p,true.VAR,type=”l”);
•X=rexp(n,lambda);
•hatlambda=1/mean(X);
•parametric.VAR=-log(p)/hatlambda;
•points(p,parametric.VAR,type=”l”,col=”blue”)
•nonparametric.VAR=sort(X,decreasing=TRUE);
•points(p,nonparametric.VAR,type=”p”,col=”red”);
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•p0=0.05;
•-log(p0)/lambda; -log(p0)/hatlambda;
•index=floor(n*p0); nonparametric.VAR[index+1];
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•Comparison of parametric and nonparametric method for Pareto distribution n=1000;
•alpha=2;
•p=seq(1,n,by=1)/(n+1);
•true.VAR=p^(-1/alpha);
•plot(p,true.VAR,type=”l”);
•U=runif(n); X=(1-U)^(-1/alpha);
•hatalpha=1/mean(log(X));
•parametric.VAR=p^(-1/hatalpha);
•points(p,parametric.VAR,type=”l”,col=”blue”)
•nonparametric.VAR=sort(X,decreasing=TRUE);
•points(p,nonparametric.VAR,type=”p”,col=”red”);
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•p0=0.05;
•p0^(-1/alpha); p0^(-1/hatalpha);
•index=floor(n*p0); nonparametric.VAR[index+1];
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•VaR for danish insurance data n=length(danish);
•p=seq(1,n,by=1)/(n+1);
•nonparametric.VAR=sort(danish,decreasing=TRUE);
•hatalpha=1/mean(log(danish));
•Pareto.method=p^(-1/hatalpha);
•Normal.method=mean(danish)+sd(danish)*qnorm(1-p);
•plot(p,Pareto.method,type=”l”);
•points(p,Normal.method,type=”l”,col=”blue”);
•points(p,nonparametric.VAR,type=”p”,col=”red”)
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n=length(danish);
•nonparametric.VAR=sort(danish,decreasing=TRUE);
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•p0=0.05;
•index=floor(n*p0);
•nonparametric.VAR[index+1]; # nonparametric method
•hatalpha=1/mean(log(danish));
•p0^(-1/hatalpha); # Pareto method
•mean(danish)+sd(danish)*qnorm(1-p0); # normal method
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•p0=0.01;
•index=floor(n*p0);
•nonparametric.VAR[index+1]; # nonparametric method
•hatalpha=1/mean(log(danish));
•p0^(-1/hatalpha); # Pareto method
•mean(danish)+sd(danish)*qnorm(1-p0); # normal method
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•Expected Shortfall
•Comparison of parametric and nonparametric method for Exponential distribution n=1000;
•lambda=2;
•p=seq(1,n,by=1)/(n+1);
•true.ES=(-log(p)+1)/lambda;
•plot(p,true.ES,type=”l”);
•X=rexp(n,lambda);
•hatlambda=1/mean(X);
•parametric.ES=(-log(p)+1)/hatlambda;
•points(p,parametric.ES,type=”l”,col=”blue”);
•nonparametric.VAR=sort(X,decreasing=TRUE);
•nonparametric.ES=NULL;
•for(i in 1:n)
•{
•value=sum(X[X>=nonparametric.VAR[i]])/n;
•nonparametric.ES=c(nonparametric.ES,value);
•}
•nonparametric.ES=(1/p)*nonparametric.ES;
•points(p,nonparametric.ES,type=”p”,col=”red”);
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•plot(p[1:30],true.ES[1:30],type=”l”);
•points(p[1:30],parametric.ES[1:30],type=”l”,col=”blue”);
•points(p[1:30],nonparametric.ES[1:30],type=”p”,col=”red”);
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