1) The 0.5-year zero rate is 10% and the 1-year zero rate is 12%.

a) What is the price of

(i) $1 par of a 0.5-year zero?

= 1/ (1 +0.10/2)^2*0.5

=0.952381

(ii) $1 par of a 1-year zero?

= 1/(1+0.12/2)2

= 0.889996

(iii) $100 par of a 1-year 12%-coupon bond, in the absence of arbitrage?

Annual Coupon = 12/100 *100

Semi-annual Coupon = 12/2 =6

= 6 d0.5 + 106 d1

= 6*0.952381 + 106*0.889996

= 100.0539

b) What is the dollar duration of

(i) $1 par of a 0.5-year zero?

= 0.5/(1+0.10/2)2

= 0.453515

(ii) $1 par of a 1-year zero?

= 1/(1+0.12/2)3

= 0.839619

(iii) 100 par of a 1-year 12%-coupon bond?

= 6*0.453515 + 106*0.839619

= 91.720732

c) What is the duration of

(i) $1 par of a 0.5-year zero?

= 0.5/(1+0.10/2)

= 0.476190

(ii) $1 par of a 1-year zero?

= 1/(1+0.12/2)

= 0.943396

(iii) $100 par of a 1-year 12%-coupon bond?

= 91.720732/100.0539

=0.916713

2) The current price of $1 par of a zero maturing at time 2 is $0.90

a) What is the 2-year spot rate?

=> (1+r2/2)-4 = 0.90

=> r2 = 2 (0.90-1/4 - 1)

=> 5.338%

b) What is the dollar duration of $1 par of the 2-year zero?

Dollar Duration = price * duration

= 0.90 *2/(1+0.05338/2)

= 1.7532

The current price of $1 par of a zero maturing at time 3 is $0.84

c) What is the 3-year spot rate?

=(1+r3/2)-6 = 0.84

= r3 = 2 (0.84-1/6- 1)

= 5.897%

d) What is the dollar duration of $1 par of the 3-year zero?

Dollar Duration = price * duration

= 0.84 *3/(1+0.05897/2)

= 2.447825

e) What is the dollar convexity of $1 par of the 3-year zero?

Dollar Convexity = price * convexity

= 0.84 (32+3/2)/(1+0.05897/2)2

= 8.322012

f) Using dollar duration alone, approximate the change in the value of $1,000,000 par

of the 3-year zero given an immediate decline in all discount rates of 50 basis points.

Change in value = -dollar duration *...