Suppose the dynamics of the short rate r(t) are governed by 

where the short rate mean reverts to a drift rate θ(t), which itself reverts to a fixed mean rate θ̅, dZ_r dZ_θ = ρdt, and all other parameters are constant (k_r and k_θ are both positive). Show that the expected value of r(t) is given by (Beaglehole and Tenney, 1991)

Transcribed Image Text:

dr(t) = kr [0 (t) = r(t)]dt + or d Zr (t) (1) Zp 0+ ¹p [(¹) 0 - 0] = (¹) op