Question

.1.  You observe the following Treasury bills and bond prices available in Saudi Arabia Bond/Bill 

Bond/Bill principal	Time to maturity	Annual coupon	Bond price
100	0.25	0	99.2
100	0.50	0	98.3
100	0.75	0	97.2
100	1	6.2 (Quarterly payments)	102
100	1.25	6.6 (Quarterly Payments)	102.5

a) Calculate continuously compounded zero rates for maturities of 3 months, 6 months, 9 months, 12 months and 15 months. 

b) Calculate the par yield for the following bonds: 

I. A 12-month bond that pays coupons semiannually. 

II. A 12-month bond that pays coupons quarterly. 

c) What is the continuously compounded yield on the coupon-paying bonds, which mature in 1 and 1.25 years?

3. Saudi Electricity Company (SEC) arranged a syndicated loan 1 years ago. To hedge its interest rate risk, it entered into an interest rate swap with SABB, where it has agreed to pay 3% per annum and receive the three-month SAIBOR in return on a notional principal of SAR 100 million with payments being exchanged every three months. The swap has a remaining life of 15 months. You observe the following SAIBOR rates for different maturities:

Maturity	SAIBOR Rates
0.25	2.75%
0.5	2.9%
0.75	3.1%
1	3.4%
1.25	3.6%

The three-month SAIBOR rate three months ago, when the last swap payment was made, was 1.8% per annum. OIS rates are the zero rates you obtained in question 1. The swap rate and all SAIBOR rates are compounded quarterly. What is the value of the swap?

Answer 1

1. a.

It is necessary to calculate the YTMs of the bonds before calculating the continuous compounding rates. Thus, all of the YTM calculations have been attached along with the calculation of continuous compounding rates.

Continuous Compounding Rate for the bond maturing in 0.25 years

------...------- I au). - Calculating the yield to maturity for bonds YTM (Matwing in 0.25 years) ---------- Present bond Price = Face Value (ltron 8=? n =0:25 = $99.2 = $100 Face Value = $100... (trgoas Present value = $99.2 -------------------- => (itojas = $100 $99.2 1+0 = (1.00806) Yo.us 8 = 1:03265 -| 8 = 3.26502 Calculating continuous sate for bond maturing in o.as years Continuous Rate= LN(1+r) ..... ....3 In (1-03265) ---- = 3.21137 Thus, Continuous compounded rate is 3.203.%.

Continuous Compounding Rate for the bond maturing in 0.5 years.

Calculating YīM for bonds maturing in 050 years. Present Bond. Price = Face Value Clon Following values are givene Du 0. SO face value = $100 Present bond Price = $98.3 Putting values into the formula $98.3 = $100 (1+ros Cirojos = $100/$98.3 City) = (1.01729). %.5 X = 3.4878% . Calculating. Continuous compounding rate =Ln (178) = In lito.034878) = 3.42842 Thus, Continuous Compounding rate is 3.42847

Continuous Compounding Rate for the bond maturing in 0.75 years.

Calculating the YTM for bond maturing in 0.75 years Following values are given : face value = $100 Bond Price =$97.2 Time to maturity = 0.15. Putting values in the below formula Present bond Price 2 Face Value Citron __ $97.2 = $100 (+8o.rs - City 0.75 = $100 $97.2 8 = (1.0288)%0.75 -1 8= 3.859QY. Calculating Continuous compounding rate = Ln (ltr) = Lu (to.B8592 = 3.78667.

Continuous Compounding Rate for the bond maturing in 1 year.

Calculating Continuous Compounding Kata = Ln(178) = Incito.056277) 5.47SLY, . . Thus, Continuous Compounding rate is 5.475) J.

Calculating the Yield for bond maturing in 1 Year $100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment Number of Payments Yield to Maturity (YTM) -$102.0 6.2 5.6277%

Formula for 1 year rate:

Calculating the Yield for bond maturing in 1 Year 100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment Number of Payments Yield to Maturity (YTM) -102 6.2 =RATE(C10,C9,CS,C6) 12

Continuous Compounding Rate for the bond maturing in 1.25 years

W elat ng continuous compounding rate for the bond maturing in 1.25 years mate = 6.0064.4. Ccalculated). Continuous fate = ln (178) = ln (1 + 0.060064) = 5.8329y

Calculating the Yield for bond maturing in 1.25 Years $100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment (Quarterly) Number of Payments Yield to Maturity (YTM) -$102.5 6.6 6.0064%

Formula for the 1.25 year rate:

Calculating the Yield for bond maturing in 1.25 Years 100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment (Quarterly) Number of Payments Yield to Maturity (YTM) -102.5 6.6 =RATE(C10,C9,CS,C6)

1 b. The Par yield is also known as the YTM of a bond. The calculation of the par yield for the bond that pays semiannually coupon payment is shown in the attached image below:

Calculating the PAR rate or Yield for bond maturing in 1 Year $100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment Number of Payments Yield to Maturity (YTM) -$102.0 6.2 5.1225%

Formula for the Par yield (semiannual payments)

Calculating the PAR rate or Yield for bond maturin 100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment Number of Payments Yield to Maturity (YTM) -102 6.2 =RATE(C10,C9, C8, C6)

Calculation of Par yield for the bond that pays quarterly coupon payments. Certain Values are assumed to show calculations. Calculations would not be possible as there were no values given in the question.

Calculating the PAR rate or Yield for bond maturing in 1 Year $100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment (Quarterly) Number of Payments Yield to Maturity (YTM) -$102.0 6.2 5.6277%

Formula for the par yield (quarterly payments)

A Calculating the PAR rate or Yield for bond maturing in 1 Year 100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment (Quarterly) Number of Payments Yield to Maturity (YTM) -102 6.2 =RATE(C10,C9,C3, C6)

1 c) The continuous compounding yield for the bond maturing in 1 and 1.25 years will be the same as the continuous compounding yield calculated above in the attached images. For the sake of ease, the same images are also attached below.

W elat ng continuous compounding rate for the bond maturing in 1.25 years mate = 6.0064.4. Ccalculated). Continuous fate = ln (178) = ln (1 + 0.060064) = 5.8329y

Calculating the Yield for bond maturing in 1.25 Years $100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment (Quarterly) Number of Payments Yield to Maturity (YTM) -$102.5 6.6 6.0064%

Calculating the Yield for bond maturing in 1.25 Years 100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment (Quarterly) Number of Payments Yield to Maturity (YTM) -102.5 6.6 =RATE(C10,C9,CS,C6)

Continuous compounding yield for the bond maturing in 1 year:

Calculating Continuous Compounding Kata = Ln(178) = Incito.056277) 5.47SLY, . . Thus, Continuous Compounding rate is 5.475) J.

Calculating the Yield for bond maturing in 1 Year $100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment Number of Payments Yield to Maturity (YTM) -$102.0 6.2 5.6277%

Calculating the Yield for bond maturing in 1 Year 100 Face Value of the bond Time to Maturity Present Value of the Bond Coupon Payment Number of Payments Yield to Maturity (YTM) -102 6.2 =RATE(C10,C9,CS,C6) 12