'forward curve steeping'..??

[Sahil Puri]

Hi, I got this question and I'm not able to figure out how to start, also the correlation dosen't seem to have any effect on the question (but that just seems incorrect intuitively )

b) Consider a process for the spot price ft for an asset defined by the SDEs

dyt= −aytdt + η(t)dUt

dzt= −bzt dt+λ(t)dVt

ft = φ(t)+yt+zt

dUtdVt = ρdt

with φ(t) chosen to fit forward prices of the asset today.

In order to incorporate forward curve steepening in the model, should correlation ρ be positive or negative?

Also, how are the mean reversion parameters a and b likely to compare with each other?

Alternatively, have a look at the assignment.

Thanks everyone. I really hope this assignment helps me get ready for MFE.

Regards,
Sahil Puri

 

[tim]

I don't know the math behind it but it looks like G2++ setting to me. The rho in your content is often heard as having something to do with "humps" in the vol term structure. Brigo's book (ch4) should have some useful information for you.
If you want, you can build the machinary to calibrate the model to real market data; then find two (or more) historical dates where one day's forward curve is "more steepen" than the other day. Calibrate the model on these days to both caps and swaptions volatilities. Compare the parameters in these settings should give you some sense.