Suppose there are 1-, 2-, and 3-year zero-coupon bonds, with prices given by P1, P2, and P3.
Question:
Suppose that you select the 3-year bond as numeraire.
a. Explain why r(2) is a martingale, but r(1) is not.
b. The price ratio P1/P3 is a martingale. What is the interpretation of this ratio?
c. Suppose that P1/P3 and P2/P3 both follow geometric Brownian motion with zero drift, volatilies σ13 and σ23, and correlation ρ dt. What is the process followed by r(1)?
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