Consider the SDE for the spot rate rt

(a) Show that

9Suppose we brought in another equation containing B(t, U):

(b) What do these two equations imply for the conditional mean and variance of spot rate as s†’ˆž?
(c) Suppose the market price of interest rate risk is constant at λ (i.e., the Girsanov transformation adjusts the drift by σλ). Using the bond price function given in the text, show that the drift and diffusion parameters for a bond that matures at time s are given by

(d) What happens to bond price volatility as maturity approaches? Is this expected?
(e) What happens to the drift coefficient as maturity approaches? Is this expected?
(f) Finally, what is the drift and diffusion parameter for a bond-with very long-maturity, s†’ˆž?

Transcribed Image Text:

ar,-α (m-rt) dt + ơdWİ (18.47) (18.48) log Be,u)-logB.S), ks (1846) F(t, u,s) = S- u (18.49) σλ