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Fifi Essay

  • Submitted by: anonymous
  • on April 4, 2014
  • Category: Miscellaneous
  • Length: 1,049 words

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Below is an essay on "Fifi" from Anti Essays, your source for research papers, essays, and term paper examples.

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 *...

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