0
$\begingroup$

I saw some threads about reducing dimensionality of IR risk strips, e.g. PCA and risk bucketing.

However, I did not find a satisfying answer to that yet. Therefore, I decided to formulate a similar problem: Suppose I have an IR par risk strip S with N buckets and want to find a smaller subset P of S such that the corresponding delta P&L's are as close as possible. This may be approached via PCA and/or VaR minimizing techniques. However, note that I do not want to fix the subset P in advance, rather the reduced buckets in P should be variables too. Hence, find reduced buckets P and a function f, which aggregates the par risks of S to the reduced par risk strip P, providing a best fit w.r.t to delta P&L of P and S.

I would start with a PCA analysis: Construct NxN Covariance Matrix, find eigenvalues and eigenvectors. I could look at "critical nodes" in PC 1,...,PC N and these may be candidates for P. Let's take the simplest and most erroneous example (just to be on the same page): Suppose the whole yield curve movement could be explained by PC 1, then P would be a singleton (I could choose any of the nodes of S). Also, the function f would be trivial too: Just multiply S with the first eigenvector. This would aggregate all the risks from S to the singleton P.

How could we then incorporate other PCA's to define a subset P and a reasonable function f?

Once having defined (P,f), I can of course transform the reduced par risk strip P to other desired risk models via Jacobians etc and also use VaR minimizing techniques etc.

Maybe you have a completely different approach and can elaborate? The above is just a first guess.

Improve this question
$\endgroup$
6
  • $\begingroup$ Is any reason behind that you want to use the PCA? Isn't the PCA for mainly seeing important component not reducing dimension? $\endgroup$
    – Cloud Cho
    Commented Nov 7, 2023 at 1:10
  • $\begingroup$ Well, as I said, it's a first guess and I would be happy to read about different/easier approaches. Obviously, some degree of correlation/volatility between buckets need to be taken into account. $\endgroup$
    – SI7
    Commented Nov 7, 2023 at 7:58
  • $\begingroup$ Do you want the PnL error to be minimised over time? i.e. youy have to define your buckets P with in sample data, and then keep the same P buckets for out of sample data over the next, say 100 days. and assert that your buckets are the best representation of the dimension reduction to capture the smallest pnl error? $\endgroup$
    – Attack68 ♦
    Commented Nov 7, 2023 at 9:38
  • $\begingroup$ PCA will not be allowed under your deffinition of P, since P is a subset of S. Any PCA is not a subset of S, it is an object that is some linear combination of all the elements in S. $\endgroup$
    – Attack68 ♦
    Commented Nov 7, 2023 at 10:45
  • $\begingroup$ I would target something like in your first comment above. Let’s make it easier: We probably all agree that 7y and 8y par swaps have more or less a beta=1 relationship (in OLS sense). Hence I can aggregate the 7y bucket into the 8y bucket without loosing significant accuracy in delta P&L explain. But 8y and 20y will not have a similarly strong relationship, hence we cannot aggregate the 8y into the 20. (but obviously the 19y into the 20y). How would you approach the risk bucketing into a smaller subset of nodes? $\endgroup$
    – SI7
    Commented Nov 7, 2023 at 18:28

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.