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 1 0 10, and that P2 P3 is a martingale following a geometric Brownian process with annual standard deviation 2 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 2 2 12 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)

Question: 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

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).

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