I have a question regarding calibrating Hull-White (Extended Vasicek) Model to bond data. As you know, and stated in Mercurio (2005), zero coupon bond price in the Hull and White (1994);
My question is what happens if t=0? What is $f(0,0)$ in this case ? What $A(0,T)$ leads to ?
I wonder if it is possible to fit bond market data (zero and coupon bearing) to get parameters. Most of the works calibrating data using caplets/floorlets/inflation indexed swaps etc. But there is none of them in the market I'd like to work. So all I have is nominal and inflation indexed bonds.
Jarrow Yildirim has 7 parameters to price inflation indexed derivatives. By fitting these for nominal and inflation indexed bonds I'll have 4 of them. What is left is $\sigma_I$ and correlations between nominal, real and inflation. Any idea how to get those?
To give you the broad picture I need to explain that: My main goal is to price hypothetical caps by using only nominal bonds and inflation indexed bonds price data.
Any lead on this matter will be much appreciated.