Find the discount factors and linear interpolation, Mathematics

Assignment Help:

Question:

All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765), and the bond prices to 3 decimal places (e.g. 99.999).

You are given the following yields-to-maturity for semi-annually coupon paying Treasury Bonds on 31st December 2007 and 31st December 2008:

Term                              0.5yr      1yr          2yr          3yr          5yr          7yr          10yr

31 Dec 2007        3.49%     3.34%    3.05%    3.07%    3.45%    3.70%     4.04%

31 Dec 2008        0.27%     0.37%    0.76%    1.00%    1.55%    1.87%     2.25%

(1) Using linear interpolation to estimate any other required rates, find the discount factors D(t) for t = 0.5, 1.0, 1.5, ..., 10.0 for both dates.

(2) From your answers to (1), calculate the price of a constant-maturity 3-year semi-annual coupon bond1 with an annual coupon rate of 3% and the face value 100, for both 31 December 2007 and 31 December 2008. Hence analyse the price change.

(3) Again from your answers to (1), find the 6-month forward rates f(t,t+½) for t = 0.5, 1.0, 1.5, ... , 9.5 for both dates.2 (See Appendix for the explanation for forward rates.)

You are also given the following historical data on the spot 6-month rate:

Date           31/12/07        30/06/08               31/12/08                30/06/09            31/12/09

6m Rate     3.49%               2.17%                   0.27%                    0.35%                  0.20%

30/06/10    31/12/10        30/06/11               30/12/11             29/06/12            31/12/12

 0.22%          0.19%             0.10%                 0.06%                    0.16%                   0.11%

(4) Using a graph, comment on how well the market predicted the future moves of the spot 6-month rate on both dates.

(5) In general, are forward rates a good predictor of future interest rates? Briefly discuss.


Related Discussions:- Find the discount factors and linear interpolation

Algebra 1, Im having trouble with this word problem: The three Math Idol j...

Im having trouble with this word problem: The three Math Idol judges have been eliminating contestants all day! The number of one-step equations and two-step equations who have be

General solution to a differential equation, The general solution to a diff...

The general solution to a differential equation is the most common form which the solution can take and does not take any initial conditions in account. Illustration 5: y(t) =

Maths, what is the diameter of a circle

what is the diameter of a circle

Find a quadratic polynomial having a and ß, If α,β are the zeros of a Quadr...

If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.

Statistics, do we calculate midpoints from classes or from class boundaries...

do we calculate midpoints from classes or from class boundaries

Marketing of herbal products , To help Himalya herbal launch a successful m...

To help Himalya herbal launch a successful marketing campaign in the UK

Example of circle graphs, Q. Example of circle graphs? Ans. The Un...

Q. Example of circle graphs? Ans. The United States Government pays obligations annually, called "outlays". Medicare contributes to the health and well being of aged an

Definition of random variables, Q. Definition of Random Variables? Ans...

Q. Definition of Random Variables? Ans. Up to this point, we have been looking at probabilities of different events. Basically, random variables assign numbers to element

Differential equatoin, how to solve questions based on higher differential ...

how to solve questions based on higher differential equations

Integers, The Dolphins football team gained 16 yards on their first play th...

The Dolphins football team gained 16 yards on their first play then lost 11 yards on the next play. Write an addition expression to represent this situation.Find the sum an explain

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd