An amortizing bond is a bond which pays the principal not at its maturity, but prior to its maturity, according to some schedule, typically (but not necessarily) in equal amounts.
In particular, consider a floating-rate amortizing bond, which pays 25% of its principal amount each year until maturity (in 4 years from today). In addition, the bond pays a yearly coupon, where the coupon rate for each period is defined as the short rate for this period. Note that the coupon payment is calculated proportional to the principal outstanding, so for a bond of principal amount USD 100, the cash stream would look like
1 year 2 years 3 years 4 years
25+100*r1 25+75*r2 25+50*r3 25+25*r4
where r1, r2, r3, r4 are the corresponding short rates. Assume the spot rate curve given as in the previous problem:
1 year 2 years 3 years 4 years
0.5% 1% 1.4% 2.1%
Assuming also the expectation dynamics, find the price of this bond.
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