Using linear interpolation to neighboring key rates

[Regi725]

Hello everyone,

I'm new here on the board. Came across a situation in my professional setting where the idea of using linear interpolation to shock neighboring key rates when conducting a stress scenario using a key rate. Don't quite grasp this concept? Why would this be necessary, what is the logic here? Thanks very much!

 

[Matthew Graves]

I think you might need to elaborate on what you mean by "using linear interpolation to shock neighbouring key rates".

It's common to use linear interpolation to derive interest rates from a curve where the timing of the cashflow does not correspond exactly to any point on the curve. Shocking the nearest points on the curve either side of the cashflow time will both obviously have an effect on the interpolated rate. Is that what you mean?

 

[Regi725]

Hi Matthew - thanks very much for your reply!

To give you context - this has come up in an attempt to conduct a stress test. So, I would shock a 5 yr maturity by lets say 100bps. I'm okay with this. But additionally, it appears that I need to shock the neighboring key rates. Using linear interpolation to calculate the shock for these neighboring rates. This is what I'm unclear about. If I'm only testing a 5 YR maturity, is it also necessary to shock the neighboring key rates as well? Why is that?

 

[Matthew Graves]

Ah I see. I think this is about constructing a realistic scenario. Is it likely that the 5YR rate will increase by 100bps and the surrounding rates stay static? Probably not. I think linear interpolation is probably a misnomer here and rather it should be linear regression. You can estimate how the surrounding rates will move in a simplistic sense by simply calculating the beta (which is the slope of the linear regression) of the surrounding rates relative to the 5yr.

e.g. if BETA(2yr, 5yr) is 1.2 and BETA(7yr, 5yr) is 0.7 then your shocks would be 2yr: 120bps, 5yr:100bps, 7yr:70bps. That way your scenario is consistent with observed market behaviour.

 

[Regi725]

That's very helpful. Thank you!!