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Topic Author
Posts: 23
Joined: August 6th, 2007, 11:24 pm

### Bootstrapping for Bonds and Zero Coupon Bond Price

I have the following bonds and I am trying to find the Prices of the Zero Coupon Bonds for Maturities for 0.5, 1.0, 1.5 and 2.0 Years respectively. The prices for Zero coupon has to be found through Linear Equations. I am not able to get the right Prices and would like someone to tell me where I am going wrong. Maturity Face Coupon Yield toYears Value Rate Maturity2.0 $100,000 6.00% 5.7315%2.0$ 50,000 4.00% 5.7374%1.5 $250,000 8.00% 5.4871%1.0$ 250,000 6.00% 5.2463%The approach to find the Prices was to find the Prices of the Bonds discounted using the YTM rates I get. The Bond Prices are as follows. B1 100500.6266B2 48380.39617B3 258929.0115B4 251812.6206I calculate the cash flows for each of the Bonds and I get the Present Value of the cash Flows so that I can use them in the Matrix to solve the coefficients linearly. So I get the following Equation. 2916.422619 2835.17363 2756.188168 91992.84223 = 100500.6266972.1129945 945.0036741 918.6503515 45544.62915 = 48380.396179732.971072 9473.072589 239722.9678 1 = 258929.01157308.292525 244504.3281 1 1 = 251812.6206I have four equations with coefficients that indicate P6, P12, P18 and P24 i.e. prices for 6 months, 12 months, 18 months and 24 months. To Solve the matrix I inverse the matrix and try to multiply the Matrix with RHS i.e. the price of the bonds but I am not getting the right Prices. I know I am going wrong some where in this Step and would like someone to guide me in the right direction. Inverse of Matrix looks like the one below: 0.001123954 -0.002270207 -0.000004223 -0.000004095 -0.000033595 0.000067856 0.000000126 0.000004212-0.000044306 0.000089491 0.000004338 0-0.000022399 0.000067199 0 0Now if I use the prices of the Bonds and try to multiply with this matrix I dont get the correct answer. I am not doing something right and would like to know how to solve for the four unknowns in this matrix. I need some guidance on this please. Many Thanks.From here on I am in a FIX as to how to get the prices.

cemil
Posts: 221
Joined: September 16th, 2005, 7:44 am

### Bootstrapping for Bonds and Zero Coupon Bond Price

I think you make a big mistake with bonds.The bond maturity is never 1Year, 2 year but on ly a fraction of year. So to get a zero coupon yield with the bond you need to adjusted the bond with their maturities and coupon payment.

Topic Author
Posts: 23
Joined: August 6th, 2007, 11:24 pm

### Bootstrapping for Bonds and Zero Coupon Bond Price

That is true. Bonds have half yearly payments for coupons. I have taken the prices of the bonds after discounting the coupons for the whole term of the bonds. I wanted to calculate the Bond Price for the quarters up until 2 years and my calculation shows the way I have done it. But if there is any other way where I can use matrix to solve the Problem I would be interested or alternatively let me know what may be wrong with my approach.

Topic Author
Posts: 23
Joined: August 6th, 2007, 11:24 pm

### Bootstrapping for Bonds and Zero Coupon Bond Price

I have solved the problem. The Matrix that is input for the Bootstrap linear equation has to be the face value of the coupons at each payment period. i.e. 6 months, 12 months etc. This is the future value of the coupon and should not be discounted. I get the correct Zero Coupon Bond Price for the half yearly terms upto 2 Years. I would like to know the effect of Interest Rate Shifts in the Quoted Yield Prices ? If the YTM changes would that affect the Interest Rates calculated off the Zero Coupon Bond Prices ? What would be the effect of small shifts in Interest Rates such as +/- 5 - 25 basis points
Last edited by arunseshadri on September 8th, 2007, 10:00 pm, edited 1 time in total.