1 练习
1. 2010/1/12 u-zcbs现货价格（单位面值）
2011 年 1 月 6 日和 2011 年 1 月 9 日到期，分别为 0.97 和 0.91。

2. 一个债券市场由三个面值为 90 的 zcbs 组成，
120 和 45，期限为 1、2 和 3 年，价格为 83、99 和 34

3. 考虑面值等于 100 的 c 债券，年息票

fB(0; 1) = 0:9;B(0; 2) = 0:89g

SPS1
= fi (0; 1) = 0:02;我 (0; 2) = 0:021;我 (0; 3) = 0:021;我 (0; 4) = 0:022;我 (0; 5) = 0:025g

SPS2
= fi (0; 1) = 0:019;我 (0; 2) = 0:02;我 (0; 3) = 0:021;我 (0; 4) = 0:022;我 (0; 5) = 0:023g

5. A Floater 有单位面值，期限 5 年，半月票

SPS1= fi (0; 1) = 0:02;我 (0; 2) = 0:021;我 (0; 3) = 0:021;我 (0; 4) = 0:022;我 (0; 5) = 0:025g
(0.01;0.01;0.011;0.011;0.0105;0.0105;0.0125;0.0125;0.0185:0.0185)

1 Exercises
1. The spot prices at 1/12/2010 of the u-zcbs (with unit nominal value)
with maturity 1/6/2011 and 1/9/2011, are 0.97 and 0.91 respectively.
Determine the price of the forward u-zcb that assures the no-arbitrage
assumption, given the previous spot prices. (0.938)

2. A bond market is composed by three zcbs with nominal values 90,
120 and 45, maturities 1, 2 and 3 years and with prices 83, 99 and 34
respectively. Determine the term structure of spot prices, of implied
prices, of the spot interest rates, of the forward interest rates, of the
spot yields and of the forward yields. (spot prices f0:92; 0:825; 0:755g,
forward prices f0:92; 0:897; 0:915g, spot rates f0:0869; 0:1; 0:0982g, for-
ward rates f0:0869; 0:115; 0:093g, spot yields f0:083; 0:096; 0:094g, for-
ward yields f0:083; 0:1087; 0:089g)

3. Consider a c-bond with nominal value equal to 100, annual coupon
equal to 10 with six-montly payments and maturity after 2 years.
Given the term structure of spot prices
fB(0; 1) = 0:9;B(0; 2) = 0:89g
compute the price of the c-bond. (107.175)4. A Basis swap contract ( oating versus oating) exchange the oating
leg computed on the term structure SPS1:
SPS1
= fi (0; 1) = 0:02; i (0; 2) = 0:021; i (0; 3) = 0:021; i (0; 4) = 0:022; i (0; 5) = 0:025g
with the oating leg computed on the term structure SPS2 and a
SPS2
= fi (0; 1) = 0:019; i (0; 2) = 0:02; i (0; 3) = 0:021; i (0; 4) = 0:022; i (0; 5) = 0:023g
Determine the spread S assuring the no-arbitrage assumption. (0.001849)

5. A Floater with unit nominal value, maturity 5 years, semestral coupons
and xed coupon (annual) 0.02, refunds 1:2 at maturity.
Determine the coupon’s plan given the following term structure of
interest rates SPS1:

SPS1= fi (0; 1) = 0:02; i (0; 2) = 0:021; i (0; 3) = 0:021; i (0; 4) = 0:022; i (0; 5) = 0:025g
(0.01;0.01;0.011;0.011;0.0105;0.0105;0.0125;0.0125;0.0185:0.0185)

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