Hi,I need to simulate a trajectory of the short interest rate using Hull-White one factor model, I know that I can use this discretization of the formula:r(t)=r(t-1)+(theta(t)-a*r(t-1))*dt+sigma*sqrt(dt)*(random_normal_std)but the computational cost is quite expensive because I need to calculate theta.Knowing that the short rate in this model is normally distribuited I can calculate it as:r(t)=mean+sqrt(variance)*(random_normal_std)however I'm a little bit confused, which are the formulas for mean and variance? They are supposed to depend on r(t-1) but I don't find the exact expression...Another question: which is the starting point of the simulation? I mean, which is r(0)? Is it the euribor 1d?

http://www.wilmott.com/messageview.cfm? ... adid=97063 - your threadThe way I see it for Vasicek, HW... etc. ur supposed to model the whole yield curve. Each of the points of the yield curve today at t=0 makes up your r(0). When you simulate, your simulated values should follow the general shape of the original yield curve, with all the simulated random points going sometimes above sometimes below sometimes at the original points of the yield curve. Each pillar of yield curve, you ought to model separately theta, mean reversion and vol.

I don't undersatand your answer... is my second approchr(t)=mean+sqrt(variance)*(random_normal_std)a valid one?

I found mean and variance in Brigo Mercurio - Interest rate models ed. 2006, 3.37Is it correct to use as r(s) r(t-1)?

If all you need is r(T) at some terminal point T, another approach might be to just make draws of thatusing the exact SDE solution, which is discussed in this thread

That means I have to calculate theta (thing I want to avoid)!I only want to know if my approch is correct... are the formulas I suggested correct?

guess you can do that - but it wouldn't be very HW now would it? How you gonna collapse theta and previous rate in one variable called mean? when theta is dependent also on the yield curve gradient and volatility etc.?