Bond Price by Monte Carlo

fingist · October 7th, 2004, 10:14 am

I know how to price a bond using HW Affine Term Structure Model using Formulas. But how do one could use Monte Carlo for the same? Any paper, link or idea is most welcome.I am trying to do it using Excel and VBA.

ppauper · October 7th, 2004, 12:48 pm

fingist · November 2nd, 2004, 2:23 pm

I generated r according to dr= (theta(t)-a*r)dt+ sig*sqrt(dt)*ZThus r(i,j) is the interest developed according to HW at 'i'th time stepand 'j'th scenario. For discounting, I took discount factor as dt period discount i.e d(i,j) = 1/(1+r(i,j)*dt)Then I averaged it, I am not getting consistant result for the bond price.I meant it is not converging. Could anyone help me?

fingist · November 3rd, 2004, 9:00 am

I just wanted to know whether my approach is correct? could any one help me?

fingist · November 3rd, 2004, 1:47 pm

I am getting confused. Is the bond price has to be calculated using the below formula?P(t,T)=A(t,T)*exp(-B(t,T)*r(t) where dr = (theta(t)-a*r)*dt+sig*dW by Monte Carlo.or simply P(0,T) = product( d(0,1)*d(1,2)*...*d(T-1,T)) where d(i,j) = 1/(1+r(i,j)*dt)basically, I can generate the r, but I dont know how to discount it to get thebond price. Moreover, P(0,T) can be derived from yield curve. Will it be same when I calculate using Monte Carlo Simulation also? Will it depend on a - the mean reversion parameter?

fingist · November 4th, 2004, 11:20 am

I hope in such a large forum, somebody could give me an idea.