Question

30. Which of the following is true? A. Both forward and futures contracts are traded on exchanges Porward contracts are traded on exchanges, but futures contracts are not. Futures contracts are traded on exchanges, but forward contracts are not. D: Neither futures contracts nor forward contracts are traded on exchanges. 2. Long answer questions (25 points) Note: write down the necessary st eps; round the answer to two decimal points, e g . 0.45%. (1) The following table gives the prices of bonds Principal(s) Time to ManrityAnual Coupon(S Bond Price (S) ors) 0.5 1.0 100 0.0 0.0 6.2 98 95 102 100 100 1.5 Half the stated coupon is paid every six months a) (7 points) Calculate zero rates (with continuous compounding) for maturities of 6 months, 12 months and 18 months. (8 points) What are the forward rates (with continuous compounding) for the periods: 6 months to 12 months? b) 12 months to 18 months?

Answer 1

30). Option c - Futures contracts are traded on exchanges but forward contracts are traded OTC.

2-1).

a). Zero rate for 6 months: Use the zero-coupon bond with 6 months maturity.

Discrete rate R: 98 = 100/(1+R)^1

R = 2.04%

Continuously compounded rate Rc = ln(1+R) = ln(1+2.04%) = 2.02% (for 6 months)

Zero rate for 12 months: Use the zero-coupon bond with 12 months maturity.

Discrete rate R: 95 = 100/(1+R)^1

R = 5.26%

Continuously compounded rate Rc = ln(1+R) = ln(1+5.26%) = 5.13%

Zero rate for 18 months:

For the 18 month coupon bond, annual coupon is 6.2 so coupon rate is 6.2/100 = 6.2%

If continuously compounded rate is z then

102 = 3.1/(1+2.02%) + 3.1/(1+ 5.13%) + (100+3.1)exp(-z)

102 - 3.0386 - 2.9487 = 103.1 exp(-z)

96.0126 = 103.1 exp(-z)

exp(-z) = 0.9313

z = 7.12% (rate for 18 months)

b). Forward rate from 6 to 12 months - 6f12

(1+z12)^2 = (1+6f12)*(1+z6)

(1+5.13%)^2 = (1+6f12)*(1+2.02%)

1.0833 = 1 + 6f12

6f12 = 8.33%

Forward rate from 12 to 18 months - 12f18

(1 +z18)^2 = (1+ 12f18)*(1+z18)

(1+7.12%)^2 = (1+12f18)*(1+5.13%)

1.0915 = 1 + 12f18

12f18 = 9.15%