Hull White 1FM usage of Bond Price Formula

Cleo1 · March 18th, 2013, 3:47 pm

Hi,I'm currently struggeling with the problem that I don't know how to use the equation for bond prices in the HullWhite 1Factor Model.In Hull 2012 the bond function looks as the following:A(t,T) = P(0,T)/P(0,t)*EXP(-B(t,T)*dlogP(0;t)/dt-[sigma^2[EXP(-aT)-EXP(at)]^2*EXP(2at)-1]/(4a^3)I'm not sure how I can put this into excel, so that I can use the formula by already having the interest rate simulated.BRCleo

Cleo1 · March 23rd, 2013, 10:50 am

the tricky point is defining P(0,T), P(0,t). Are these the parameters that I would finally like to calculate which means the final discount factors of the bond.dlog P(0,t)/dt equals the Forwardrate F(0,t), thus can this also be calculated by bootstrapping and finally forward calculation of a simple swap rate?

Culverin · March 23rd, 2013, 4:02 pm

It seems you will need to find a textbook that works thru Affine Term Structure Model.

daveangel · March 23rd, 2013, 5:50 pm

P(0,T) is the zero coupon bond with maturity T. P(0,t) is the price of the zero coupon with maturity t. at t=0, you can observe the prices of zero coupon bonds with different maturities T= T1, T2 etc. so invert your equation such that you writeP(0,T) = A(0,T) *exp(B(0,T)/d(logP(0;t=0)/dt etc now if I remember there are expressions for A() and B() and you will need to estimate a and sigma and i think a parameter b.

Cleo1 · April 24th, 2013, 5:15 am

Thanks for your response.In a next step I would like to estimate a, sigma and b which I would like to do by just having 1 interest curve as an input as I would like to keep it simple