Hull and White (1994) proposed the following two-factor short rate model whose dynamics under the risk neutral measure are governed by 

where u has an initial value of zero and follows the process 

The parameters a,b,σ₁ and σ₂ are constants and dZ₁ dZ₂ = ρ dt, where ρ is the instantaneous correlation coefficient. Show that the zero-coupon bond price B(t,T) takes the form

Find the governing equations for α(t,T),β(t,T) and γ(t,T).

β(t,T) and γ(t,T) are readily found to be 

Transcribed Image Text:

dr(t) = [p(t) + u(t)ar(t)] dt + 0₁ dZ₁ (t),