Hi Alastair, You have a company with two business lines, A and B say the retail branch of a bank and a Life insurance division (common in South Africa) . You want to find the total amount of some say Market Risk capital. You go to the branch and model the loss distribution as L, then go to the Life Insurance company to try and model the loss distribution. By the time you get there the CRO gives you their risk capital number, he says "we have quantified our Market risk to be k".
Then you go back to your desk and have to answer your initial question, "what it the total amount of Market risk capital?"
You have your loss distribution from the branch L, and you decide to use Var to find the capital (for all business lines A + B) i.e F(L+k), then you remember you have the capital for the Life Insurance business line.
So u start worrying with F(L) knowing that you have k, hence F(L)+k.
P.S;-
- I have a technical mathematical proof I can post on request if that is what you are looking for.
- Let us extend the solution;-
Suppose now that the Life insurance company gave you their own loss distribution Y. You now want F(L+Y) and here follows sub-additivity. Assuming there is correlation between Market risk at the bank and at the Life division of your bank.
(I was typing this fast, feel free to ask for clarity if not clear, also you can modify example such that Y is a different risk within the same life division and hence k the capital of that risk)
Last edited by a moderator: Feb 7, 2015