Assume r = X1 + X2, where the Xi are independent square-root processes under the physical probability; that is, dXi = ˆκi(θˆ

i −Xi)dt +σi

√Xi dBi for constants κˆi, θˆ

i, and σi, wherethe Bi are independent Brownian motions under the physical probability. Assume there is an SDF process M with dM M = −r dt −λ1

√X1 dB1 −λ2

√X2 dB2 +

dε

ε , where λ1 and λ2 are constants and ε is a local martingale uncorrelated with B.

(a) Show that the Xi are independent square-root processes under the risk-neutral probability corresponding to M.

(b) Calculate the risk premium of a discount bond.