Fixed Rate Government Coupon Bonds with Matlab

For example, in May 2010 the U.S. Treasury sold a bond with a coupon rate of 2 (1/8) % and a maturity date of May 31, 2015. Purchasing $1 million face amount of these bonds.

 [ (1/2) * 2, (1/8)   * 1.000.000 ] - 1.000.000 = 10.625 $

Then, on the maturity date of May 31, 2015, in addition to the coupon payment on that date, the Treasury promises to pay the bond’s face amount of $1,000,000.

Selected U.S. Treasury Bond Prices as of May 28, 2010

Since Treasury bonds promise future cash flows, discount factors can be extracted from Treasury bond prices. In fact, each of the rows of Table 1.2 can be used to write one equation that relates prices to discount factors. The equation from the 1,(1/4)' s of November 30, 2010, is

First solving method

eqn = 100.550==(100.000 + 1.25 / 2)*d()
S = solve(eqn,x,'Real',true)  
0.99925

and The equation from the 4,(7/8)' s of May 31, 2011:

d(.5) is equal to the 0.99925 and we find d(1);


4,(7/8)  is equal to 7/8 =0.875
4.875
4.875/2 =2.4375

eqn = (2.4375*.99925) + 102.4375*x==104.513 

x= .99648


and The equation from the 4,(1/2)' s of 11/30, 2011:

d(.5) is equal to the 0.99925 and d(1) is equal to the 0.99648 and
we find d(1.5)

 
4,5
4.5/2 =2.25

 eqn= (2.25* .99925) + (2.25 * .99648) + (102.25*x)==105.856

d(1.5) is .99135



The law of one price

Another US Treasury bond issue, one not included in Table 1.2
 
 and The equation from the ,(3/4)' s of 11/30, 2011:

3/4=0.75
0.75/2=0.375

eqn= (.375* .99925)+(.375* .99648)+(100.375* .99135)
price might be 100.255

 Bruce Tuckman, Angel Serrat - Fixed Income Securities: Tools for Today's Markets 53-55