# Zero Coupon Bond Price under Hull White Model (One Factor)

While pricing Zero coupon bond using One Factor Hull White model: $$dr(t) = \left(\theta(t) - a r \right)dt + \sigma dW(t)$$

How to determine the value of $$\theta(t)$$ using real world example: $$θ(t)=F_t (0,t)+σ^2 \frac{1-e^{-2at}}{2a}$$

• This is a well-known, solved problem. See, for example, Brigo, D., & Mercurio, F. (2006). Interest Rate Models - Theory and Practice (2nd ed). Springer-Verlag Berlin Heidelberg. – stans - Reinstate Monica Aug 4 '18 at 12:18
• Hi Stans, Thanks for your comment I have read various articles and books on this but only problem which i have faced to identify F_t(0,t). If we look at real world example does it means we need to plug in here Forward rate for zero coupon bond ? If you take any real example with data that would be really useful. – Add Aug 5 '18 at 5:35
• Yes, you have to do that because that is what your specification of the drift is saying. Also, you need to be clear on what F(0,t) stands for, whether this is the forward curve of LIBOR, treasuries, munis or something else. – stans - Reinstate Monica Aug 5 '18 at 11:21
• I was able to solve the theta value, thanks for your help. However, when I am pricing ZCB there it's asking for P(0,T)/P(0,t) what should be the input for this ? – Add Aug 10 '18 at 14:27