On October 26, 2004, PiVe International Bank, a AAA company, issued a 10-year corridor note. This note has several features that make it rather hard to price: First, it accrues a coupon only so long as a reference rate is within some bounds. The bounds themselves, however, change over time according to a given schedule. In addition, the coupon moves from fixed to floating at some point in the future. The term sheet is in Table 17.5. On October 26, the 3-month LIBOR was 2.11%, and the 6-month LIBOR was 2.24%. The swap rates for maturities up to 10 years are in Table 17.6.
(a) Obtain the discount curve Z(T) for the relevant maturities as of October 26, 2004. Make sure to plot your results in a figure and comment on them.
(b) Fit the Vasicek model or the Cox, Ingersoll, and Ross model to the discount curve obtained in Part (a).
(c) Employ a Monte Carlo simulation method to obtain the price of the security.
(d) What is the benefit for an investor from investing in these notes, compared to other available instruments? Why would you think that corridor notes are popular?
(e) Use Monte Carlo simulations to compute the sensitivity of the note to changes in interest rates (i.e. its Delta) as well as its convexity (i.e. its Gamma). Plot