2023年12月21日发(作者：)
圣才电子书
十万种考研考证电子书、题库视频学习平台4.2 课后习题详解一、问答题1. 一个银行的利率报价为每年14％，每季度复利一次。在以下不同的复利机制下对应的利率是多少?（a）连续复利；（b）一年复利一次。A bank quotes you an interest rate of 14% per annum with quarterly
compounding. What is the equivalent rate with (a) continuous compounding and
(b) annual compounding?答：(a)等价的连续复利利率为：，即每年13.76％。(b)按年计复利的利率为：，即每年14.75％。2. LIBOR与LIBID的含义是什么?哪一个更高?What is meant by LIBOR and LIBID. Which is higher?答：LIBOR是伦敦同业银行拆出利率，它是一家银行提供给其他银行资金所要求的利率。LIBID是伦敦同业银行拆入利率，它是一家银行愿意接受的从其他银行借款的利率。一般情况下，LIBOR比LIBID高。3. 6个月期与一年期的零息利率均为10％。一个剩余期限还有18个月，券息利率为8％（刚刚付过半年一次的利息）的债券，收益率为10.4％的债券价格为多少?18个月的零息利率为多少?这里的所有利率均为每半年复利一次利率。 1 / 20
圣才电子书
十万种考研考证电子书、题库视频学习平台The six-month and one-year zero rates are both 10% per annum. For a bond
that lasts 18 months and pays a coupon of 8% per annum (with a coupon
payment having just been made), the yield is 10.4% per annum. What is the
bond’s price? What is the 18-month zero rate? All rates are quoted with
semiannual compounding.答：考虑票面价值为100美元的债券。由于要求收益率为每年10.4%，按半年计息，债券价格应该等于未来现金流以半年5.2％的贴现率折现得到。即价格为：如果18个月的即期利率是R，价格也应该等于未来现金流按照相应的即期利率折现得到。则有：从而得到R=10.42%。4. 一个投资者在年初投入1000美元，年末收入1100美元。计算投资在不同复利机制下的收益率：（a）一年复利一次，（b）一年复利2次，（c）每月复利一次以及（d）连续复利。An investor receives $1,100 in one year in return for an investment of $1,000
now. Calculate the percentage return per annum with a) Annual compounding, b)
Semiannual compounding, c) Monthly compounding and d) Continuous
compounding.答：（a）按年计复利，回报率为 2 / 20，即每年10％。
圣才电子书
十万种考研考证电子书、题库视频学习平台，可化简为：，即回报率为每年9.76％。（b）按半年计复利，设回报率为R，则（c）按月计复利，设回报率为R，则，可化简为：=1.00797，则R=0.0957，即回报率为9.57％。（d）按连续复利计，设回报率为R，则9.53％。，则R=0.0953，即回报率为5. 假设连续复利的零息利率如表4-1所示：表4-1计算第2季度、第3季度、第4季度、第5季度和第6季度的远期利率。Suppose that Zero interest rates with continuous compounding are as
follows：Calculate forward interest rates for the second，third，fourth，fifth．and
sixth quarters 3 / 20
圣才电子书
十万种考研考证电子书、题库视频学习平台答：与上题同理，可得按连续复利计算的远期利率如下：第二季度：8.4％；第三季度：8.8％；第四季度：8.8％；第五季度：9.0％；第六季度：9.2％。6. 假如零息利率如练习题5所示，一个3个月期限的固定利率为9.5%的FRA价值为多少？这里FRA的面值为1000000美元，起始日期为1年以后，利率复利为每季度一次。Assuming that zero rates are as in Problem 4-5, what is the value of an FRA
that enables the holder to earn 9.5% for a three-month period starting in one year
on a principal of $1, 000, 000 ? The interest rate is expressed with quarterly
compounding.答：连续复利时，远期利率为9.0%；每季度复利时，远期利率为9.102%。由复习笔记中方程（4-9）知，FRA的价值为：[1000000×0.25×(0.095-0.09102)]e-0086×125=893.56（美元）。7. 利率期限结构向上倾斜，将以下变量按大小排列。（a）5年期零息利率；（b）5年期带息债券（coupon bearing bond）的收益率；（c）将来从第5年到第5年零3个月期间的远期利率。当利率期限结构向下倾斜，结果会如何变化?The term structure is upward sloping. Put the following in order of magnitude:a. The five-year zero rate 4 / 20
圣才电子书
十万种考研考证电子书、题库视频学习平台b. The yield on a five-year coupon-bearing bondc. The forward rate corresponding to the period between 5 and 5.25 years in
the future. What is the answer to this question when the term structure is
downward sloping?答：当利率期限结构是向上倾斜时：c>a>b；当利率期限结构是向下倾斜时：b>a>c。8.从久期你知道债券组合对于利率有什么样的敏感度？久期有什么局限性？What does duration tell you about the sensitivity of a bond portfolio to
interest rates. What are the limitations of the duration measure?答：久期描述了关于债券组合价值的收益率曲线的轻微平移。债券组合价值下降的百分比等于其久期乘以在轻微平移中，利率上升的值。但久期也有限制性，它只适用于收益率曲线的轻微平行移动。9. 与年利率15%，并按月复利等价的连续复利的年利率是多少？What rate of interest with continuous compounding is equivalent to 15% per
annum with monthly compounding?答：设利率为R，有：可化简为： 5 / 20
圣才电子书
十万种考研考证电子书、题库视频学习平台因此，年利率为14.91%。10. 一个存款账号以每年12%的连续复利利率来计算利息，但利息每个季度付出一次，则10000美元存款对应于每季度的利息为多少？A deposit account pays 12% per annum with continuous compounding, but
interest is actually paid quarterly. How much interest will be paid each quarter on
a $10,000 deposit?答：设按季度复利的等效利率为R，有：即：因此每季度支付的利息为：11. 假定6个月期、12个月期、18个月期、24个月期和30个月期的零息利率分别为每年4％、4.2％、4.4％、4.6％和4.8％，利率以连续复利为计。估计一个面值为100美元的债券的价格，假定此债券在第30个月后到期，债券息票利率为每年4％，每半年付息一次。Suppose that 6-month, 12-month. 18-month, 24-month, and 30-month zero
rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per anent with continuous compounding
respectively. Estimate the cash price of a bond with a face value of 100 that will
6 / 20
