本次代写主要为金融数学相关的Homework

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。
确定保证无套利的远期 u-zcb 的价格
假设,鉴于之前的现货价格。 (0.938)

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
分别。确定现货价格的期限结构,隐含
价格、即期利率、远期利率、
即期收益率和远期收益率。 (现货价格 f0:92;0:825;0:755g,
远期价格 f0:92; 0:897; 0:915g,即期费率 f0:0869; 0:1; 0:0982g,对于-
病房费率 f0:0869; 0:115; 0:093g,现货产量 f0:083; 0:096; 0:094g,为-
病房产量 f0:083; 0:1087; 0:089g)

3. 考虑面值等于 100 的 c 债券,年息票
等于 10,每 6 个月付款一次,2 年后到期。
鉴于现货价格的期限结构
fB(0; 1) = 0:9;B(0; 2) = 0:89g
计算 c 债券的价格。 (107.175)4。基础掉期合约(oating 对 oating)交换 oating
在期限结构 SPS1 上计算的边:
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
使用期限结构 SPS2 和 a
点差
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
确定确保无套利假设的价差 S。 (0.001849)

5. A Floater 有单位面值,期限 5 年,半月票
和固定息票(每年)0.02,到期时1:2退款。
给定以下期限结构,确定优惠券的计划
利率 SPS1:

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
spread S
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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