March 31st, 2011, 7:41 pm
I'm trying to calibrate the 1factor Hull-White model to the current swapcurve. From that I've found the short-rates at future maturities:dr = (theta(t) - a*r)*dt + sigma * dzThen I've found bond prices at time t (2 to 10 years):P(t,T) = A(t,T)e-B(t ,T )r(t )Where I've used the different short-rates as r(t). The closed-form formula for discount bond options:c = P(0, s)N(h)- XP(0, T)N(h-sigma )But this is the optionprice at time 0, where P(0,s) and P(0,T) also are the time 0 values. If I use the bondprices at time zero, what is the point with the bondprices at future maturities ? I thought that the point with the model was to incorporate the termstructure ? Is the next step then to calculate the time 0 optionprices and compare them with optionprices in the market ? Anyone ?