Financial Models in Excel
Exam, F65
April 2009
Exam
F65: Financial Models in Excel Copenhagen Business School 1. April 2009
Open book exam, 4 hours
Own computers allowed
General information You must hand in your solution in Excel spreadsheet format. You must hand in 2 copies at floppy disks or CD-ROMs. Each of the exercises has been given an individual weight. These indicate to the student how much time should be used on each exercise. However, the final grade will not rely on these weights only, but might be affected by the overall impression. The design of the exercise is such that even though you are not able to answer a question, you might be able to answer the subsequent questions. If you do not think this is so, you should make assumptions that enable you to proceed. Remember to save frequently.
Page 1 of 5
Exam, F65
April 2009
Exercise 1: Bond pricing (25%)
Consider the following bond market, where time is years to payment:
Payments Time: Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 1 104 4 4 4 4 2 0 104 4 4 4 3 0 0 104 4 4 4 0 0 0 104 4 5 0 0 0 0 104
The prices of the bonds are:
Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 Prices 102.0 102.0 101.5 96.9 100.1
Question 1.a Determine the five zero-coupon interest rates in the market. Question 1.b Price Bond A which pays 58 after 2 years and 54 after 4 years. You suspect that the prices of some of the bonds are too inaccurate, and decide to estimate a linear term structure of the form:
nt = α 0 + α1t
Question 1.c Estimate the two parameters of the linear term structure specification above such that the sum of squared pricing errors of the five original bonds is minimized. Price Bond A using the result. Consider the following specification instead:
α 0 + α1t nt = β 0 + β1 (t − 3)
for 0 ≤ t < 3 for 3 ≤ t
Question 1.d Estimate the parameters in the new term structure specification with the restriction that the approximation must be continuous at t = 3. Show the term structure in a chart.
Page 2 of 5
April 2009
Exam
F65: Financial Models in Excel Copenhagen Business School 1. April 2009
Open book exam, 4 hours
Own computers allowed
General information You must hand in your solution in Excel spreadsheet format. You must hand in 2 copies at floppy disks or CD-ROMs. Each of the exercises has been given an individual weight. These indicate to the student how much time should be used on each exercise. However, the final grade will not rely on these weights only, but might be affected by the overall impression. The design of the exercise is such that even though you are not able to answer a question, you might be able to answer the subsequent questions. If you do not think this is so, you should make assumptions that enable you to proceed. Remember to save frequently.
Page 1 of 5
Exam, F65
April 2009
Exercise 1: Bond pricing (25%)
Consider the following bond market, where time is years to payment:
Payments Time: Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 1 104 4 4 4 4 2 0 104 4 4 4 3 0 0 104 4 4 4 0 0 0 104 4 5 0 0 0 0 104
The prices of the bonds are:
Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 Prices 102.0 102.0 101.5 96.9 100.1
Question 1.a Determine the five zero-coupon interest rates in the market. Question 1.b Price Bond A which pays 58 after 2 years and 54 after 4 years. You suspect that the prices of some of the bonds are too inaccurate, and decide to estimate a linear term structure of the form:
nt = α 0 + α1t
Question 1.c Estimate the two parameters of the linear term structure specification above such that the sum of squared pricing errors of the five original bonds is minimized. Price Bond A using the result. Consider the following specification instead:
α 0 + α1t nt = β 0 + β1 (t − 3)
for 0 ≤ t < 3 for 3 ≤ t
Question 1.d Estimate the parameters in the new term structure specification with the restriction that the approximation must be continuous at t = 3. Show the term structure in a chart.
Page 2 of 5