Binomial Analysis Tree Efb344

Assignment Part B | John Smith

Assignment Part B

EFB344 Risk Management and Derivatives

Due: 12/10/15

Semester 2 2015

Assignment Part B |

1 Task 1: Interest Rate Derivatives

For the completion of Task 1, Table 1, was provided detailing Maturity and Swap Zero Rate. All rates

in the table provided are quoted nominal annual with semi-annual compounding.

Maturity

6 Month

1 Year

2 Year

3 Year

4 Year

5 Year

Swap Zero Rate

2.210%

2.039%

2.040%

2.127%

2.380%

2.532%

Table 1 Swap Zero Rates

1.1 Task 1 a

Calculate the one-year forward rates out to year five.

Assumptions:

1. Only calculating one-year forward rates for values provided on table e.g. 1 year, 2 year etc.

As all Swap Zero Rates are given, Equation 1 Forward Rate Equation can be used.

=

− −1 −1

− −1

Equation 1 Forward Rate Equation

Where,

Rf = Forward Rate

R = Swap Zero Rate

T = Maturity

Using the forward rate between Year 1 and Year 2 as an example.

2 2 − 1 1

2 − 1

2.040 × 2 − 2.039 × 1

=

2−1

= 2.041%

2 =

Using Microsoft Excel to complete for all years.

Maturity

6 Month

1 Year

2 Year

3 Year

4 Year

5 Year

Swap Zero Rate

2.210%

2.039%

2.040%

2.127%

2.380%

2.532%

Forward Rate

1.868%

2.041%

2.301%

3.139%

3.140%

Table 2 Forward Rates

1

Assignment Part B |

1.2 Task 1 b

Find the Swap rate (rounded to 3 decimal places) for a 3 year fixed for floating swap.

Firstly using Equation 2 Linear Interpolation Equation to gain all mid-year points.

= −0.5 + ( +0.5 − −0.5 )

− −0.5

+0.5 − −0.5

Equation 2 Linear Interpolation Equation

Using year 1.5 as an example to get the Swap Zero Rate.

1.5 = 1 + (2 − 1 )

1.5 − 1

2 − 1

= 2.039 + (2.040 − 2.039)

1.5 − 1

2−1

= 2.040%

This value is the same as 2 year due to the closeness of values between 1 Year.

The table below shows completed Sway Zero Rate and Forward Rate for all whole and mid-year

points.

Calculating 6 month forward rate for...