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Assignment 01

Assignment 01
Assignment 01

Financial Derivatives B0300850

Assignment01

March14,2014

1.An interest rate is quoted as5%per annum with semiannual compounding.What is the equivalent rate with(a)annual compounding,(b)monthly compounding,and(c)continously compounding.

2.The6-month,12-month,18-month,24-month zero rate are4%,4.5%,4.75%and5%,with semiannual compounding.

(a)What are the rates with continuous compounding?

(b)What is the foreward rate for the6-month period beginning in18months?

(c)What is the value of a FRA that promises to pay you6%(compounded semiannually)on a principal of$1million for the6-month period starting in18months?

3.What is the2-year par yield when the zero rates are as in Problem2?What is the yield on a2-year bond that pays a coupon equal to the par yield?

4.The following table gives the prices of bonds:

Bond principal($)Time to maturity(years)Annual coupon1($)bond price($) 1000.500.098

100 1.000.095

100 1.50 6.2101

100 2.008.0104

(a)Calculate zero rate for maturities of6months,12months,18months,and24months.

(b)What are the foreward rate for the following periods:6months to12months,12months

1Half the stated coupond is assumed to be paid every six months.

to18months,abd18months to24months?

(c)What are the6months,12months,18months,and24months par yields for bonds that provide semiannual coupond payment?

(d)Estimate the price and yield of a2-year bond providing a semiannual coupond of7%per annum.

5.Portfolio A consists of a1-year zero-coupon bond with a face value of$2,000and a10-year zero-coupon with a face value of$5,000.The current yield on all bonds is10%per annum.

(a)Show that both portfolio have the same duration.

(b)Show that the percentage changes in the value of two portfolios for a0.1%per annum increase in yields are the same.

(c)What are the percentage changes in the value of the two portfolio s for a5%per annum increase in yields?

chapter3-assignment

第三章 线性分组码 习题 1.证明[n ,k ]线性分组码的最大距离为n -k +1。 2.设一个[7,4]码的生成矩阵为 1000111010010100100110 00111 0G ????? ?=?????? (1)求出该码的全部码矢; (2)求出该码的一致校验矩阵; (3)作出该码的标准阵译码表。 3.证明定理3.1.3。 4.一个[8,4]系统码,它的一致校验方程为: c 0=m 1+m 2+m 3c 1=m 0+m 1+m 2c 2=m 0+m 1+m 2c 3=m 0+m 2+m 3 式中,m 0,m 1,m 2,m 3是信息位,c 0,c 1,c 2,c 3是校验位。找出该码的G 和H ,并证明该码的最小距离为4。 5.构造第4题中码的对偶码。 6.设H 1是[n ,k ]线性分组码C 1的校验矩阵,且有奇数最小距离为d 。作一个新的码C 2,它的校 验矩阵为 12000111 1H H ?? ????? ?=???????? M L (1)证明C 2是一个(n +1,k )分组码; (2)证明C 2中每一码字的重量为偶数; (3)证明C 2码的最小重量为d +1。 7.设C 1是一个有最小距离为d 1的[n 1,k ]线性系统码,生成矩阵为G 1=[P 1I k ]。C 2是一个有最小距离为d 2的[n ,k ]线性系统码,它的生成矩阵G 2=[P 2I k ]。对满足下述一致校验矩阵 212T k n n k T p H I P I ???? ? ?=??????

的[n 1+n 2,k]线性码,证明它有最小距离至少为d 1+d 2。 8.设一个二进制[n ,k ]码C 的G 矩阵不含全零列,将C 的所有码字排成2k ×n 的阵。 证明: (a )阵中不含有全零列; (b )阵中的每一列由2k -1个零和2k -1个1组成; (c )在一特定分量上为0的所有码字构成C 的一个子空间,问该子空间的维数是多少? 9.令是所有二进制[n ,k ]线性系统码的集合。证明非零二进制n 重V 或者恰巧含于的 ΓΓ(1)()2k n k ??个码中,或者不在的任一码中。 Γ10.证明二进制[23,12,7]Golay 码和三进制的[11,6,5]Golay 码是完备码。 11.若d 是码C 的最小重量,且为偶数,(1)/2t d =????? 。证明有两个重量均为t +1的矢量必在C 码的同一陪集中。 12.求出d =3,至多只有3个校验元的二进制码的码长n ;和d =5,至多只有8个校验元的二进 制码的码长n 。 13.计算二进制[24,12,8]扩张Golay 码的覆盖半径,及[8,4]RM 码的覆盖半径。 14.证明定理3.9.3。 15.构造三个二进制的[10,3,5]LUEP 码,其分离矢量分别为(8,2,2),(7,4,4), (6,4,4)。写出它们标准形式的G 和系统码形式的G 。 16.证明定理3.10.3。 17.构造一个具有最高码率的k =10,t =2的2-EC/AUED 码。 18.证明定理3.10.6。

solutions for assignment3

Chapter 3 Assignments P13.Consider a reliable data transfer protocol that uses only negative acknowledgments. Suppose the sender sends data infrequently. Would a NAK-only protocol be preferable to a protocol that uses ACKs? Why? Now suppose the sender has a lot of data to send and the end-to-end connection experiences few losses. In this second case, would a NAK-only protocol be preferable to a protocol that uses ACKs? Why? Answer: In a NAK only protocol, the loss of packet x is only detected by the receiver when packet x+1 is received. That is, the receivers receives x-1 and then x+1, only when x+1 is received does the receiver realize that x was missed. If there is a long delay between the transmission of x and the transmission of x+1, then it will be a long time until x can be recovered, under a NAK only protocol. On the other hand, if data is being sent often, then recovery under a NAK-only scheme could happen quickly. Moreover, if errors are infrequent, then NAKs are only occasionally sent (when needed), and ACK are never sent – a significant reduction in feedback in the NAK-only case over the ACK-only case. P23. We have said that an application may choose UDP for a transport protocol because UDP offers finer application control (than TCP) of what data is sent in a segment and when. a. Why does an application have more control of what data is sent in a segment? b. Why does an application have more control on when the segment is sent? Answer: a) Consider sending an application message over a transport protocol. With TCP, the application writes data to the connection send buffer and TCP will grab bytes without necessarily putting a single message in the TCP segment; TCP may put more or less than a singe message in a segment. UDP, on the other hand, encapsulates in a segment whatever the application gives it; so that, if the application gives UDP an application message, this message will be the payload of the UDP segment. Thus, with UDP, an application has more control of what data is sent in a segment. b) With TCP, due to flow control and congestion control, there may be significant delay from the time when an application writes data to its send buffer until when the data is given to the network layer. UDP does not have delays due to flow control and congestion control.

商务交际英语任务(assignment)

商务交际英语(二) Assignment ● You work in the Sales Department of an international company. Manuela Garcia, an important client, is visiting your company for a day. There are some changes to the itinerary you sent her last week. ● Write a letter of 120 - 140 words to Ms Garcia, using the original itinerary and your handwritten notes, informing her of the changes. Proposed itinerary for one-day visit of Manuela Garcia Wednesday 20 October 11.00 John Sallis to meet Ms Garcia at airport 11.30 Arrival at company John Sallis to give Ms Garcia an introductory tour of company 12.30 14.00 ( Carol Snape Tom McAllister Sue Smith Manuela Garcia ) 15.30 Coffee break 16.00 18.00 John Sallis to take Ms Garcia to the airport 19.30 英语老师:周俐 2012年10月17日(第七周) (作业于10月26日前上交给我)

Assignment 1

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assignment写作浅谈

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Assignment3经原

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Assignment1_OceanCarriers

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Assignment要求表(3)

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Assignment1 for chapter 1

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