(you are required to show your calculation process by Excel or MATLAB.) Let the

ID: 2382901 • Letter: #

Question

(you are required to show your calculation process by Excel or MATLAB.)

Let the price of zero-coupon bond that was given as follows:

Year to maturity zero-coupon bond price yield

1 0.9541 4.811%

2 0.8949 5.709%

3 0.8319 6.327%

4 0.7717 6.693%

Assume The bond price at maturity is 1.

Assume interest rate volatility of 0.5% of one year maturity of bonds.

1) Based model based on Ho-Lee model, Draw the binomial tree.

2) Based model based on Ho-Lee model, Draw the binomial tree by using Nelson-Ramaswamy method.

It is a zero coupon bond. The bond has been issued at discounted price. Therefore difference will indicate yield.

1. Bond with one year maturity.

0.9541 ( 1+ r) = 1.000

or ( 1+r ) = 1/0.9541 = 1.0481

or r = 1.0481- 1 = 0.0481 = 4.81%

2. Bond with 2 years maturity:

0.8949 ( 1+r )2 = 1.0000

(1+r ) 2 = 1.000/0.8949 = 1.1174

(1+r) = (1.1174)0.5

(1+r) = 1.05709

r = 1.05709 - 1 = 0.05709 = 5.709%

3.Bond with three years maturity:

0.8319 ( 1+ r)3 = 1

( 1+r )3 = 1/0.8319 = 1.20206

( 1+r ) = (1.20206)1/3

( 1+ r ) = 1.06326

r = 1.06326 = 0.06327 = 6.327%

4. Bond with 4 years maturity:

0.7717 ( 1+ r )4 = 1

( 1+r )4 = 1/0.7717= 1.29584

( 1+ r ) = (1.29584) 1/4

( 1+ r ) = 1.06693

r = 1.06693 - 1

r = 0.06693 = 6.693%

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