# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

10 Pages

### mws_gen_int_txt_simpson3by8

Course: MATERIALS 102, Spring 2012
School: Georgia Tech
Rating:

Word Count: 1444

#### Document Preview

07.08 Simpson Chapter 3/8 Rule for Integration After reading this chapter, you should be able to 1. derive the formula for Simpsons 3/8 rule of integration, 2. use Simpsons 3/8 rule it to solve integrals, 3. develop the formula for multiple-segment Simpsons 3/8 rule of integration, 4. use multiple-segment Simpsons 3/8 rule of integration to solve integrals, 5. compare true error formulas for multiple-segment...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Georgia >> Georgia Tech >> MATERIALS 102

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
07.08 Simpson Chapter 3/8 Rule for Integration After reading this chapter, you should be able to 1. derive the formula for Simpsons 3/8 rule of integration, 2. use Simpsons 3/8 rule it to solve integrals, 3. develop the formula for multiple-segment Simpsons 3/8 rule of integration, 4. use multiple-segment Simpsons 3/8 rule of integration to solve integrals, 5. compare true error formulas for multiple-segment Simpsons 1/3 rule and multiplesegment Simpsons 3/8 rule, and 6. use a combination of Simpsons 1/3 rule and Simpsons 3/8 rule to approximate integrals. Introduction The main objective of this chapter is to develop appropriate formulas for approximating the integral of the form b I= f ( x)dx (1) a Most (if not all) of the developed formulas for integration are based on a simple concept of approximating a given function f ( x) by a simpler function (usually a polynomial function) f i ( x) , where i represents the order of the polynomial function. In Chapter 07.03, Simpsons 1/3 rule for integration was derived by approximating the integrand f ( x ) with a 2nd order (quadratic) polynomial function. f 2 ( x ) f 2 ( x ) = a 0 + a1 x + a 2 x 2 (2) 07.08.1 07.08.2 Chapter 07.08 ~ Figure 1 f ( x ) Cubic function. In a similar fashion, Simpson 3/8 rule for integration can be derived by approximating the given function f ( x) with the 3rd order (cubic) polynomial f 3 ( x ) f 3 ( x ) = a0 + a1 x + a 2 x 2 + a 3 x 3 a0 a (3) 1 2 3 = {1, x, x , x } a 2 a3 which can also be symbolically represented in Figure 1. Method 1 The unknown coefficients a 0 , a1 , a 2 and a3 in Equation (3) can be obtained by substituting 4 known coordinate data points {x0 , f ( x0 )}, {x1 , f ( x1 )}, {x 2 , f ( x 2 )} and {x3 , f ( x3 )} into Equation (3) as follows. 2 2 f ( x 0 ) = a 0 + a1 x0 + a 2 x0 + a3 x 0 f ( x1 ) = a 0 + a1 x1 + a 2 x12 + a3 x12 (4) 2 2 f ( x 2 ) = a 0 + a1 x 2 + a 2 x 2 + a3 x 2 2 2 f ( x3 ) = a 0 + a1 x3 + a 2 x3 + a3 x3 Equation (4) can be expressed in matrix notation as Simpson 3/8 Rule for Integration 2 3 1 x 0 x0 x 0 a 0 f ( x 0 ) 2 3 1 x1 x1 x1 a1 = f ( x1 ) 2 3 1 x 2 x 2 x 2 a 2 f ( x 2 ) 2 3 1 x3 x3 x3 a3 f ( x3 ) The above Equation can symbolically be represented as (5) [ A] 44 a 41 = f 41 Thus, a1 a 1 a = 2 = [ A] f a3 a 4 07.08.3 (5) (6) (7) Substituting Equation (7) into Equation (3), one gets 1 f 3 ( x ) = 1, x, x 2 , x 3 [ A] f (8) As indicated in Figure 1, one has x0 = a x1 = a + h ba =a+ 3 2a + b = 3 x 2 = a + 2h (9) 2b 2a =a+ 3 a + 2b = 3 x3 = a + 3h 3b 3a =a+ 3 =b With the help from MATLAB [Ref. 2], the unknown vector a (shown in Equation 7) can be solved for symbolically. { } Method 2 Using Lagrange interpolation, the cubic polynomial function f 3 ( x ) that passes through 4 data points (see Figure 1) can be explicitly given as 07.08.4 Chapter 07.08 ( x x1 ) ( x x 2 ) ( x x3 ) ( x x0 ) ( x x 2 ) ( x x3 ) f ( x0 ) + f ( x1 ) ( x0 x1 ) ( x0 x 2 ) ( x0 x3 ) ( x1 x0 ) ( x1 x 2 ) ( x1 x3 ) ( x x0 ) ( x x1 ) ( x x3 ) ( x x0 ) ( x x1 ) ( x x 2 ) + f ( x3 ) + f ( x3 ) ( x 2 x0 ) ( x 2 x1 ) ( x2 x3 ) ( x3 x0 ) ( x3 x1 ) ( x3 x 2 ) f3 ( x) = (10) Simpsons 3/8 Rule for Integration Substituting the form of f 3 ( x ) from Method (1) or Method (2), b I = f ( x ) dx a b f 3 ( x ) dx a = (b a) { f ( x0 ) + 3 f ( x1 ) + 3 f ( x2 ) + f ( x3 )} 8 (11) Since ba 3 b a = 3h and Equation (11) becomes 3h I { f ( x 0 ) + 3 f ( x1 ) + 3 f ( x 2 ) + f ( x3 )} 8 Note the 3/8 in the formula, and hence the name of method as the Simpsons 3/8 rule. The true error in Simpson 3/8 rule can be derived as [Ref. 1] (b a) 5 Et = f ( ) , where a b 6480 Example 1 The vertical distance covered by a rocket from x = 8 to x = 30 seconds is given by 30 140000 s = 2000 ln 9.8 x dx 140000 2100t 8 Use Simpson 3/8 rule to find the approximate value of the integral. h= (12) (13) Simpson 3/8 Rule for Integration Solution ba n ba = 3 30 8 = 3 = 7.3333 3h I { f ( x 0 ) + 3 f ( x1 ) + 3 f ( x 2 ) + f ( x3 )} 8 x0 = 8 h= 140000 f ( x0 ) = 2000 ln 9.8 8 140000 2100 8 = 177.2667 x = x + h 0 1 = 8 + 7.3333 = 15.3333 140000 f ( x1 ) = 2000 ln 9.8 15.3333 140000 2100 15.3333 = 372.4629 x = x + 2h 0 2 = 8 + 2(7.3333) = 22.6666 140000 f ( x 2 ) = 2000 ln 9.8 22.6666 140000 2100 22.6666 = 608.8976 07.08.5 07.08.6 Chapter 07.08 x = x + 3h 0 3 = 8 + 3(7.3333) = 30 140000 f ( x3 ) = 2000 ln 9.8 30 140000 2100 30 = 901.6740 Applying Equation (12), one has 3 I = 7.3333 {177.2667 + 3 372.4629 + 3 608.8976 + 901.6740} 8 = 11063.3104 The exact answer can be computed as I exact = 11061.34 Multiple Segments for Simpson 3/8 Rule Using n = number of equal segments, the width h can be defined as ba h= (14) n The number of segments need to be an integer multiple of 3 as a single application of Simpson 3/8 rule requires 3 segments. The integral shown in Equation (1) can be expressed as b I = f ( x ) dx a b f 3 ( x ) dx a x3 xn = b x6 f ( x ) dx + f ( x ) dx + ........ + f ( x ) dx 3 x0 = a 3 x3 3 Using Simpson 3/8 rule (See Equation 12) into Equation (15), one gets 3h f ( x0 ) + 3 f ( x1 ) + 3 f ( x 2 ) + f ( x3 ) + f ( x3 ) + 3 f ( x 4 ) + 3 f ( x5 ) + f ( x 6 ) I= 8 + ..... + ( f x n 3 ) + 3 f ( x n 2 ) + 3 f ( x n 1 ) + f ( x n ) = (15) xn 3 n 2 n 1 n 3 3h f ( x 0 ) + 3 f ( xi ) + 3 f ( xi ) + 2 f ( xi ) + f ( x n ) 8 i =1, 4 , 7 ,.. i = 2 , 5,8,.. i =3, 6, 9 ,.. Example 2 The vertical distance covered by a rocket from x = 8 to x = 30 seconds is given by (16) (17) Simpson 3/8 Rule for Integration 07.08.7 30 140000 s = 2000 ln 9.8 x dx 140000 2100t 8 Use Simpson 3/8 multiple segments rule with six segments to estimate the vertical distance. Solution In this example, one has (see Equation 14): 30 8 h= = 3.6666 6 { x0 , f ( x0 )} = {8,177.2667} { x1 , f ( x1 )} = {11.6666,270.4104} where x1 = x0 + h = 8 + 3.6666 = 11.6666 { x2 , f ( x2 )} = {15.3333,372.4629} where x2 = x0 + 2h = 15.3333 { x3 , f ( x3 )} = {19,484.7455} where x3 = x0 + 3h = 19 { x4 , f ( x4 )} = { 22.6666,608.8976} where x4 = x0 + 4h = 22.6666 { x5 , f ( x5 )} = { 26.3333,746.9870} where x5 = x0 + 5h = 26.3333 { x6 , f ( x6 )} = {30,901.6740} where x6 = x0 + 6h = 30 Applying Equation (17), one obtains: n 2= 4 n 1= 5 n 3= 3 3 I = ( 3.6666 ) 177.2667 + 3 f ( xi ) + 3 f ( xi ) + 2 f ( xi ) + 901.6740 8 i =1, 4,.. i = 2, 5,.. i =3, 6 ,.. = (1.3750 ){177.2667 + 3( 270.4104 + 608.8976) + 3( 372.4629 + 746.9870 ) + 2( 484.7455) + 901.6740} = 11,601.4696 Example 3 Compute I= b =30 140,000 2000 ln 140,000 2100 x 9.8xdx, a =8 using Simpson 1/3 rule (with n1 = 4), and Simpson 3/8 rule (with n2 = 3). Solution The segment width is ba h= n ba = n1 + n2 30 8 = ( 4 + 3) = 3.1429 07.08.8 Chapter 07.08 x0 = a = 8 x1 = x0 + 1h = 8 + 3.1429 = 11.1429 x 2 = x0 + 2h = 8 + 2( 3.1429 ) = 14.2857 Simpson' s 1/3 rule x3 = x0 + 3h = 8 + 3( 3.1429 ) = 17.4286 x 4 = x0 + 4h = 8 + 4( 3.1429 ) = 20.5714 x5 = x0 + 5h = 8 + 5( 3.1429 ) = 23.7143 x6 = x0 + 6h = 8 + 6( 3.1429) = 26.8571 x7 = x0 + 7 h = 8 + 7( 3.1429) = 30 140,000 f ( x 0 = 8) = 2000 ln 9.8 8 = 177.2667 140,000 2100 8 Similarly: f ( x1 = 11.1429) = 256.5863 f ( x2 ) = 342.3241 f ( x3 ) = 435.2749 f ( x4 ) = 536.3909 f ( x5 ) = 646.8260 f ( x6 ) = 767.9978 f ( x7 ) = 901.6740 For multiple segments ( n1 = first 4 segments) , using Simpson 1/3 rule, one obtains (See Equation 19): n1 1=3 n1 2 = 2 h I 1 = f ( x0 ) + 4 f ( xi ) + 2 f ( xi ) + f x n1 3 i =1, 3,... i = 2 ,... () 3.1429 = {177.2667 + 4( 256.5863 + 435.2749 ) + 2( 342.3241) + 536.3909} 3 = 4364.1197 For multiple segments ( n2 = last 3 segments) , using Simpson 3/8 rule, one obtains (See Equation 17): n2 2 =1 n2 1= 2 n2 3=0 3h I 2 = f ( x0 ) + 3 f ( xi ) + 3 f ( xi ) + 2 f ( xi ) + f x n1 8 i =1, 3,... i = 2 ,... i = 3, 6,... // () 3 = 3.1429 {177.2667 + 3( 256.5863) + 3( 342.3241) + ( no contribution ) + 435.2749} 8 = 6697.2748 The mixed (combined) Simpson 1/3 and 3/8 rules give Simpson 3/8 Rule for Integration 07.08.9 I = I1 + I 2 = 4364.1197 + 6697.2748 = 11,061.3946 Comparing the truncated error of Simpson 1/3 rule ( b a ) 5 f ( ) (18) Et = 2880 With Simpson 3/8 rule (See Equation 12), it seems to offer slightly more accurate answer than the former. However, the cost associated with Simpson 3/8 rule (using 3rd order polynomial function) is significantly higher than the one associated with Simpson 1/3 rule (using 2nd order polynomial function). The number of multiple segments that can be used in the conjunction with Simpson 1/3 rule is 2, 4, 6, 8, (any even numbers). h I 1 = { f ( x0 ) + 4 f ( x1 ) + f ( x 2 ) + f ( x 2 ) + 4 f ( x3 ) + f ( x 4 ) + ..... + f ( x n 2 ) + 4 f ( x n 1 ) + f ( x n ) } 3 n 1 n 2 h = f ( x 0 ) + 4 f ( x i ) + 2 f ( xi ) + f ( x n ) (19) 3 i =1, 3,... i = 2 , 4 , 6... However, Simpson 3/8 rule can be used with the number of segments equal to 3,6,9,12,.. (can be certain odd or even numbers that are multiples of 3). If the user wishes to use, say 7 segments, then the mixed Simpson 1/3 rule (for the first 4 segments), and Simpson 3/8 rule (for the last 3 segments) would be appropriate. Computer Algorithm for Mixed Simpson 1/3 and 3/8 Rule for Integration Based on the earlier discussion on (single and multiple segments) Simpson 1/3 and 3/8 rules, the following pseudo step-by-step mixed Simpson rules can be given as Step 1 User inputs information, such as f ( x) = integrand n1 = number of segments in conjunction with Simpson 1/3 rule (a multiple of 2 (any even numbers) n2 = number of segments in conjunction with Simpson 3/8 rule (a multiple of 3) Step 2 Compute n = n1 + n 2 ba h= n 07.08.10 Chapter 07.08 x0 = a x1 = a + 1h x 2 = a + 2h . . xi = a + ih . . x n = a + nh = b Step 3 Compute result from multiple-segment Simpson 1/3 rule (See Equation 19) n1 1 n1 2 h I 1 = f ( x0 ) + 4 f ( xi ) + 2 f ( xi ) + f x n1 3 i =1, 3,... i = 2 , 4 , 6... Step 4 Compute result from multiple segment Simpson 3/8 rule (See Equation 17) n2 2 n2 1 n2 3 3h ( x 0 ) + 3 f ( x i ) + 3 f ( x i ) + 2 f ( x i ) + f x n2 I 2 = f 8 i =1, 4 , 7... i = 2 , 5,8... i = 3, 6, 9 ,... Step 5 I I1 + I 2 and print out the final approximated answer for I . () () SIMPSONS 3/8 RULE FOR INTEGRATION Topic Simpson 3/8 Rule for Integration Summary Textbook Chapter of Simpsons 3/8 Rule for Integration Major General Engineering Authors Duc Nguyen Date April 15, 2012 Web Site http://numericalmethods.eng.usf.edu (19, repeated) (17, repeated) (20)
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Georgia Tech - MATERIALS - 102
Georgia Tech - MATERIALS - 102
Practice Final - Problem 4
Georgia Tech - MATERIALS - 102
Georgia Tech - MATERIALS - 102
If you have any questions, contact the REGISTRAR'S OFFICE at the appropriate location listed below:Administrative Services Building65 Davidson Road Room 200LPiscataway,NJ 08854-8096(732) 445-3220Armitage Hall311 North 5th StreetCamden, NJ 08102-149
Georgia Tech - MATERIALS - 102
Solutions to HW # 66-1 (a) Acceptable alternatives are those having a PW(15%) 0.Alt I: PW (15%) = \$100,000 + \$15,200(P/A, 15%, 12) + \$10,000(P/F, 15%, 12)= \$15,738Alt II: PW(15%) = \$152,000 + \$31,900 (P/A, 15%,12)= \$20,917Alt III: PW(15%) = \$184,000
Georgia Tech - MATERIALS - 102
Solutions to HW # 77-6Basis = \$120,000(a)(b)BV1 = \$120,000 \$11,000 = \$ 109,000(c)7-8d 2 = (\$120,000 \$10,000)/10 = \$ 11,000BV10 = \$120,000 \$11,000(10) = \$10,000Basis = \$60,000 and SVN = \$12,000. Find d3 and BV5.(a)d3 = dk =B SVN \$60,000 \$12,00
Georgia Tech - MATERIALS - 102
Solutions to HW # 89.1Defender (old lift truck):Using the outsider viewpoint, the investment value of the old lift truck is its current market value.Defender: PW(20%) = \$7,000 \$8,000(P/A, 20%, 5) = \$30,925Challenger: PW(20%) = \$22,000 \$5,100(P/A, 20%
Georgia Tech - MATERIALS - 102
14: 332: 375Elements of Electrical Engineering LabExperiment 1Basic Laws of Electrical EngineeringGroup A1. Member 12. Member 23. Member 3Lab Section: 1Lab Instructor: Jatin DabholkarDate of Experiment: February 7, 2011Due Date of Lab Report: F
Rutgers - HIST - 151
History &amp; NewsOp-EdRepublicans &amp; Democrats UniteThe Republicans AND the Democrats have equal blame. American society istired off all the bickering and fighting. They want something done; not just A dissing B, Bdissing A.What must be created is an en
Rutgers - HIST - 151
History &amp; NewsOp-EdUS Over OthersProviding aid would seem like the the proper action for the U.S. at this point, especiallyconsidering our impact up until now. That said, I definitely agree with most of you thatwe need to take care of our economy and
Rutgers - HIST - 151
History &amp; NewsOp-EdPublic Education in World AffairsIn general it is important for people to be well educated as to important situations going aroundthe world but as I wrote in my op-ed, any type of rally about Americans would be futile. Ingeneral, i
Rutgers - HIST - 151
History &amp; NewsOp-Ed2012 Presidential election &amp; GOP DebatesFor my Op-Ed I wrote about the 2012 Presidential election and the current GOPdebates. As you all know the Republican Party is currently seeking a suitable candidatefor the 2012 election. It i
Rutgers - HIST - 151
History &amp; NewsOp-EdSOPA and PIPABackground: SOPA and PIPA are U.S. bills created with the intention of eliminatingwebsites engaged in piracy. However, the explanation of what intellectual propertyinfringement is is incredibly vague.Critique: In shor
Rutgers - HIST - 151
History &amp; NewsOp-EdExpensive Athletic ProgramsIn regards to this weeks article about &quot;Rutger's Football&quot; I read it with mixed emotions.As a student athlete at Rutger's I witness firsthand the vast benefits that Rutger'sfootball program and players re
Rutgers - HIST - 151
History &amp; NewsOp-EdDeparture of our Rutgers head football coach, Greg SchianoI think that Schiano had given so much to this university that he earned the right to move on ifhe saw fit. I completely agree with you that the manner which he is leaving in
Rutgers - HIST - 151
History &amp; NewsOp-EdAiding OthersWith all of the turmoil within our own country, it is hard to imagine that we can afford to helpother countries with their own political, social, and economic issues. I do agree that undercertain circumstances, typical
Rutgers - HIST - 151
History &amp; NewsOp-EdPerceptions of CountriesI thought this week's Op-Ed was quite interesting, especially because I can relate to thesituaiton myself while also seeing the benefits of understanding the events that are occurring inEgypt. The interviews
Rutgers - HIST - 151
History &amp; NewsOp-EdAmerican Public Knowledge on Domestic &amp; Foreign MattersI also have also noticed the vast amount of &quot;clueless&quot; people out there in regards to manycurrent events both foreign and domestic. As the grease truck video accurately portray,
Rutgers - HIST - 151
History &amp; NewsOp-EdCultural Differences in Egyptian Revolution StrategyThis week I discussed cultural differences should play a role in how the United Statesdevelops a policy for the revolution in Egypt. It's very easy for most Americans to feel like
Rutgers - HIST - 151
History &amp; NewsOp-EdEgypts Future StabilityIn reference to the article &quot;Economic Crisis Adds Dangers on Egypt's New Political Path&quot;, I seea lot of disappointment and lack of hope in terms of Egypt's future stability. The country mayhave succeeded in a
Rutgers - HIST - 151
History &amp; NewsOp-EdAmerican Public Knowledge of Foreign MattersI wrote about the knowledge of the American Public on foreign matters in the Middle East; theveil on the American Public.According to passerby interviews and class polls conducted at Rutg
Rutgers - HIST - 151
History &amp; NewsOp-EdCensorship of InternetThe United States has long opposed the practices of censorship of the internet such asthose in China and Iran. Then they decide to do the same?People backlashed against the bills. The biggest online protest ev
Rutgers - HIST - 151
History &amp; NewsOp-EdSOPA/PIPA &amp; GOP Primary with IranI think that you can tie Iran into the discussions of both the GOP primary andSOPA/PIPA bills. There is greater emphasis being placed on this election cycle as amake, or break vote for the health of
Rutgers - HIST - 151
History &amp; NewsOp-EdIranian-American RelationsFor my Op-ed, I chose to address the decaying Iranian- American relations. I view theongoing encounter with Iran as a second Cold War and attempted to briefly compareand contrast it against the Cold War wi
Rutgers - HIST - 151
History &amp; NewsOp-EdAmerican intervention in LibyaThe Professors in the video discussed the American intervention in Libya, classifying it as asuccess only in the sense that Gaddafi is gone. They realized that it showed that America's onlytactic is mi
Rutgers - HIST - 151
History &amp; NewsOp-EdOccupy Wall Street MovementMy Op-Ed focused on the the Occupy Wall Street Movement and how in the pastpeople have also taken part in social movements with a similar style. The Occupy WallStreet Movement was one that was supported,
Rutgers - FIN - 420
CHAPTER 19Volatility SmilesProblem 19.8.A stock price is currently \$20. Tomorrow, news is expected to be announced that will eitherincrease the price by \$5 or decrease the price by \$5. What are the problems in using BlackScholes to value one-month op
Rutgers - FIN - 420
CHAPTER 18Binomial Trees in PracticePractice QuestionsProblem 18.8.Consider an option that pays off the amount by which the final stock price exceeds theaverage stock price achieved during the life of the option. Can this be valued from abinomial tr
Rutgers - FIN - 420
CHAPTER 12Introduction to Binomial TreesPractice QuestionsProblem 12.8.Consider the situation in which stock price movements during the life of a European optionare governed by a two-step binomial tree. Explain why it is not possible to set up a posi
Rutgers - FIN - 420
CHAPTER 1IntroductionPractice QuestionsProblem 1.8.Suppose you own 5,000 shares that are worth \$25 each. How can put options be used toprovide you with insurance against a decline in the value of your holding over the next fourmonths?You should buy
Rutgers - FIN - 420
F&amp;O HW Assignment #2, Select SolutionsProf Harvey Poniachek, Spring 2012Problem 3.16.The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standarddeviation of monthly changes in the futures price
Rutgers - FIN - 420
Prof Harvey Poniachek, F&amp;O, Spring 2012Ch 4 Select Problems &amp; SolutionsProblem 4.8.The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond thatwill pay coupons of \$4 every six months currently sells for \$94.84. A tw
Rutgers - FIN - 420
F&amp;O, Select Problems &amp; Solutions, Ch 5Prof Harvey Poniachek, Spring 2012Problem 5.8.Is the futures price of a stock index greater than or less than the expected future value of theindex? Explain your answer.The futures price of a stock index is alway
Rutgers - FIN - 420
Prof Harvey Poniachek, F&amp;O, Spring 2012Select Problems &amp; Solutions, Ch 6Problem 6.8.The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded return (on an actual/365basis) does an investor earn on the Treasury bill for the
Rutgers - FIN - 420
CHAPTER 7SwapsPracticeQuestionsProblem 7.8.Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts.At the start of the swap, both contracts have a value of approximately zero. As time passes, it islikely that
Rutgers - FIN - 420
CHAPTER 24Weather, Energy, and Insurance DerivativesPractices QuestionsProblem 24.8.HDD and CDD can be regarded as payoffs from options on temperature. Explain thisstatement.HDD is max(65 A, 0) where A is the average of the maximum and minimum tempe
Rutgers - FIN - 420
CHAPTER 23Credit DerivativesPractice QuestionsProblem 23.8.Suppose that the risk-free zero curve is flat at 7% per annum with continuous compoundingand that defaults can occur half way through each year in a new five-year credit defaultswap. Suppose
Rutgers - FIN - 420
Chapter 8Securitization and the Credit Crisis of 2007Practice QuestionsProblem 8.8.Why did mortgage lenders frequently not check on information provided by potentialborrowers on mortgage application forms during the 2000 to 2007 period?Subprime mort
Rutgers - FIN - 420
CHAPTER 14Employee Stock OptionsPractice QuestionsProblem 14.8.Explain how you would do the analysis to produce a chart such as the one in Figure 14.2.It would be necessary to look at returns on each stock in the sample (possibly adjusted for theret
Rutgers - FIN - 420
EXAM ON SWAPS1. Suppose that the yield curve is flat at 5% per annum with continuous compounding. Aswap with a notional principal of \$100 million in which 6% is received and six-monthLIBOR is paid will last another 15 months. Payments are exchanged eve
Rutgers - FIN - 420
CHAPTER 22Exotic Options and Other Nonstandard ProductsPractice QuestionsProblem 22.8.Describe the payoff from a portfolio consisting of a lookback call and a lookback put with thesame maturity.A lookback call provides a payoff of ST S min . A lookb
Rutgers - FIN - 420
CHAPTER 5Determination of Forward and Futures PricesPractice QuestionsProblem 5.8.Is the futures price of a stock index greater than or less than the expected future value of theindex? Explain your answer.The futures price of a stock index is always
Rutgers - FIN - 420
Prof Harvey P, Futures &amp; OptionsAssignment #1, Solutions of Select ProblemsSpring 2012Problem 2.11.A trader buys two July futures contracts on frozen orange juice. Each contract is for the deliveryof 15,000 pounds. The current futures price is 160 ce
Rutgers - FIN - 420
CHAPTER 16Futures OptionsPractice QuestionsProblem 16.8.Suppose you buy a put option contract on October gold futures with a strike price of \$900per ounce. Each contract is for the delivery of 100 ounces. What happens if you exercisewhen the October
Rutgers - FIN - 420
CHAPTER 17The Greek LettersPractice QuestionsProblem 17.8.What does it mean to assert that the theta of an option position is 0.1 when time is measuredin years? If a trader feels that neither a stock price nor its implied volatility will change,what
Rutgers - FIN - 420
CHAPTER 3Hedging Strategies Using FuturesPractice QuestionsProblem 3.8.In the Chicago Board of Trades corn futures contract, the following delivery months areavailable: March, May, July, September, and December. State the contract that should beused
Rutgers - FIN - 420
CHAPTER 21Interest Rate OptionsPractice QuestionsProblem 21.8.A bank uses Blacks model to price European bond options. Suppose that an implied pricevolatility for a 5-year option on a bond maturing in 10 years is used to price a 9-year optionon the
Rutgers - FIN - 420
CHAPTER 4Interest RatesPractice QuestionsProblem 4.8.The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bondthat will pay coupons of \$4 every six months currently sells for \$94.84. A two-year bond thatwill pay cou
Rutgers - FIN - 420
CHAPTER 6Interest Rate FuturesPractice QuestionsProblem 6.8.The price of a 90-day Treasury bill is quoted as 10.00. What continuously compoundedreturn (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-dayperiod?The cash
Rutgers - FIN - 420
CHAPTER 2Mechanics of Futures MarketsPractice QuestionsProblem 2.8.The party with a short position in a futures contract sometimes has options as to the preciseasset that will be delivered, where delivery will take place, when delivery will take plac
Rutgers - FIN - 420
CHAPTER 10Properties of Stock OptionsPractice QuestionsProblem 10.8.Explain why the arguments leading to putcall parity for European options cannot be used togive a similar result for American options.When early exercise is not possible, we can argu
Rutgers - FIN - 420
CHAPTER 9Mechanics of Options MarketsPractice QuestionsProblem 9.8.A corporate treasurer is designing a hedging program involving foreign currency options.What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-countermarket for
Rutgers - FIN - 420
CHAPTER 15Options on Stock Indices and CurrenciesPractice QuestionsProblem 15.8.Show that the formula in equation (15.9) for a put option to sell one unit of currency A forcurrency B at strike price K gives the same value as equation (15.8) for a cal
Rutgers - FIN - 420
CHAPTER 7SwapsPractice QuestionsProblem 7.8.Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts.At the start of the swap, both contracts have a value of approximately zero. As time passes, itis likely that
Rutgers - FIN - 420
CHAPTER 11Trading Strategies Involving OptionsPractice QuestionsProblem 11.8.Use putcall parity to relate the initial investment for a bull spread created using calls to theinitial investment for a bull spread created using puts.A bull spread using
Rutgers - FIN - 420
CHAPTER 13Valuing Stock Options: The Black-Scholes-Merton ModelPractice QuestionsProblem 13.8.A stock price is currently \$40. Assume that the expected return from the stock is 15% and itsvolatility is 25%. What is the probability distribution for the
Rutgers - FIN - 420
CHAPTER 20Value at RiskPractice QuestionsProblem 20.8.A company uses an EWMA model for forecasting volatility. It decides to change theparameter from 0.95 to 0.85. Explain the likely impact on the forecasts.2Reducing from 0.95 to 0.85 means that mo
Rutgers - FIN - 375
International capital marketWinderIntro: There are two types of international capital market investors, the institutional investorand the individual investor. The institutional investor comprise big mutual and pension funds that diversifyinvestments
Rutgers - FIN - 375
Global, Money MarketsINTRODUCTION The corporate bond market in the euro area is constantly increasing as a proportion of theinternational debt market. The main industry represented in the corporate debt market isstill financial services with a net iss
Rutgers - FIN - 375
Global, Money MarketsLong Term Credit MarketsIV. Long Term Credit MarketsA. U.S. Treasury Notes and Bonds The distinction between notes and bonds is one of original maturity:notes have an original maturity of 1-10 years; bonds have a maturitygreater
Rutgers - FIN - 375
Global, Money MarketsLong Term Credit MarketsB. Zero Coupon BondsZeroes are bonds which have no intermediate payments, and repaythe principal amount at maturity. In this respect, they are the same as T-bills, except that they are forlonger maturitie