12. Assume the same bonds and numeraire as in the previous question. Suppose that P1/P3 is a martingale following a geometric Brownian process with annual standard deviation σ1= 0.10, and that P2/P3 is a martingale following a geometric Brownian process with annual standard deviation σ2 = 0.05. The correlation between the two processes is 0.9.

a. Verify by simulation that the drift per unit time for (P1/P3)/(P2/P3) is

σ2 2

− ρσ1σ2.

b. Discuss the implications of the answer to

(a) if you are pricing a claim, such as a swaption, for which the payoff depends upon both r(1) and r(2).