# Bond and Rate

Spring Semester, 2015

Derivatives

School of Economics and Finance

The University of Hong Kong

Notes on homework assignments:

Students should form groups of four to five members to work on the assignments together. Group switching is not allowed. Mandatory peer review will be carried out near the end of the semester. It is not necessary to computer-type the solution. However, the hand-written version has to be reader-friendly.

Hard copies of the solutions must be dropped in the TA’s box by 6pm of the due date. Late submission will not be accepted.

Please state clearly the names and UIDs of each member on the first page of the assignment.

Homework Assignment #3

Due: 15th April (Wednesday), 6pm

1.

A lender plans to invest $100m for 150 days, 60 days from today. (That is, if today is day 0, the loan will be initiated on day 60 and will mature on day 210.) The implied forward rate over 150 days, and hence the rate on 150-day FRA, is 2.5%. The actual interest rate over that period could be either 2.4% or 2.6%.

(a)

If the interest rate on day 60 is 2.6%, how much will the lender have to pay if the FRA is settled on day 60? How much if it is settled on day 210? (b)

If the interest rate on day 60 is 2.4%, how much will the lender have to pay if the FRA is settled on day 60? How much if it is settled on day 210?

2.

Using information in Table 7.1, complete the following:

(a)

Given the zero-coupon bond prices, compute the implied forward rates from time 1 to time 2, time 2 to time 3 and time 1 to time 3.

(b)

Calculate the implied coupon rate of a 2-year par coupon bond that will be issued at time 1.

3.

Suppose the coupon rates for 1-year, 2-year, and 3-year par coupon bonds are 5%, 5.97%, and 6.91%, respectively.

(a)

Compute the implied effective annual forward rate between year 1 and year 2 and between year 2 and year 3.

(b)

Compute the implied coupon rate for the 2-year par coupon bond that will...

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