NuclearPhynance Archive

I am looking at the risk of a large fixed income portfolio

that includes options (swaptions, caps, exotics) in addition

to simple products (e.g. treasuries). Currently the risk is

represented in a fairly standard way -- I have a delta strip

for the portfolio for a number of maturities, vega matrix (vol

sensitivity for each maturity, tenor), and spread risk (e.g.

swap spread to treasuries). I'd like to represent this risk in terms

of a small number of simple, intuitive factors.



For the rate part, I can just look at the three PCA factors (shift,

slope, curvature). What could be done to simplify vol

sensitivity? I am not sure running PCA on the whole vol matrix is

a good idea. Is there a way to represent ATM cap/swaption vol

matrix movement in terms of intuitively simple factors, similar

to the way PCA does it for rates? I am looking at the ATM vols

only, making an assumption that skew is more stable over time.

Thanks, Brain.

I've seen this done in FX, but not IR. The basic factors are ATM vol, Strangle and Risk Reversal, say at 0.25/0.75 delta. You measure these at each tenor, then assume parallel shifts in each.

Interesting question brain.



It wasn't very intuitive, but we used to have a PCA for the ATM IR vol surface, with an East/West factor to show movements across underlying tenor. Main issue was that it took forever to run, don't remember the last time I looked at it, but will try to dig something up this weekend.



Aaron, was the FX PCA done on Comp vol or breakeven?

EDIT: Maybe [url=/Show%20Post.aspx?PostIDKey=96818]this thread[/url] is of use? 



I have seen PCA used for a swaption vol surface by CS; will have a look for the piece and send it on if I can find it.

Thanks folks.



bsycheng, thanks, thinking of what you said -- it this somewhat equivalent

to having the first pca vector correspond to the parallel shifts

of the entire vol surface, and to have two more factors,

one expressing a slope in the tenor dimension, and the other

expressing a slope in the maturity dimension, so that

we have something like

sigma(t,T) = F1(t,T) + F2(t) +F3(T) ?



Jungle, aaron, thanks for your help.

brain.

Couldn't find anything sorry, but it was a 3 factor model as you describe.

bsycheng,



no worries, and thanks.

brain