Discrete VaR (September 2012, Q1)

Hi

I am struggling with some of the concepts for a discrete variable with question 1, part (c) of part (ii).

Here we are asked to find the 95% VaR and 95% TailVaR. When I write out the pdf of this, say X~f(x), I am unsure how to define X as the solution does it differently to me. I see it as follows:

Let X be the losses on default, Paa be the default probability on bond A and Pbb be the default probability on bond B, then the distribution of losses is:

• X = 0 with P = (1-Paa)*(1-Pbb) = 0.94479
• X = -53 with P = (Paa)*(1-Pbb) = 0.01817
• X = -54 with P = (1-Paa)*(Pbb) = 0.03634
• X = -107 with P = (Paa)*(Pbb) = 0.0007

Here I find that 95% VaR(X) = £53 since we are 95% confident the losses are no greater than this amount.

Moving on to TailVaR is where I am really struggling. I am working with E[L-X | X<L] and doing the following:

[SIGMA_{X<L} (L-X)] / P[X<L)
where L is the 95% VaR = -53.
​

The answer should be £55, but I am getting nowhere near this. Can someone please help me figure this out as I think I am missing something fundamental here?

Thanks in advanced.

 

Hi,

For the same question part i) (100 invested in company A), the 95% VaR is given to be zero in the report. I don't understand where that figure comes from (no explanation is given). Can anyone please try and explain?
However, for the same question in the revision notes a different answer is given.

I solved using the below approach -
At the end of the year, the 100 invested in company A; either becomes
106 --- if no default (0.9811)
0 --- if default (0.0189)
Using the formula --> t = max{x: P(X<x) <= p} where p = 0.05; I get t = 106
Hence, VaR = 100 - 106 = -6. Is this answer wrong? (this answer is given as one of the right answers in the revision notes solutions)

Thanks in advance!

 

Hi Joe,

Thanks for confirming all of the details. They were very helpful (panic over!).