December 7th, 2008, 10:41 am
Hi, Q: Hull-White model of stochastic, short-term interest rate is given bydr = ( a(t) - b(t) r )dt+c(t)dWWhere da/dt + 3 t a = t^2 , db/dt + t b = 2t( 1 - Exp[-3t])dc/dt + 3 t c = 5t( 1 - Exp[-5t])Q: Obtaining the stochastic interest rate for constant r(0) ?from aboveas you can see the definitions for variables a,b and c in the Hull-White model are given in First order differential equations.I tried tackling the question using the conventional method i.e. using the integrating factor to obtain a,b and c interms of t, however this hasnot been simple since I end up with the erf (error) function.I was wondering whether any of you know any other way to tackle this problem?thx.