Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Textbook Question
Chapter 5.CR, Problem 30CR
Find and interpret the present value of the annuity in Exercise 29.
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Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
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Chapter 5 Solutions
Mathematics: A Practical Odyssey
Ch. 5.1 - In Exercises 1-4, find the number of days....Ch. 5.1 - In Exercises 1-4, find the number of days. a.July1...Ch. 5.1 - In Exercises 1-4, find the number of days....Ch. 5.1 - In Exercises 1-4, find the number of days....Ch. 5.1 - In Exercises 5-10, find the simple interest of the...Ch. 5.1 - In Exercises 5-10, find the simple interest of the...Ch. 5.1 - In Exercises 5-10, find the simple interest of the...Ch. 5.1 - In Exercises 5-10, find the simple interest of the...Ch. 5.1 - In Exercises 5-10, find the simple interest of the...Ch. 5.1 - In Exercises 5-10, find the simple interest of the...
Ch. 5.1 - In Exercises 11-14, find the future value of the...Ch. 5.1 - In Exercises 11-14, find the future value of the...Ch. 5.1 - In Exercises 11-14, find the future value of the...Ch. 5.1 - In Exercises 11-14, find the future value of the...Ch. 5.1 - In Exercises 1520, find the maturity value of the...Ch. 5.1 - In Exercises 15-20, find the maturity value of the...Ch. 5.1 - In Exercises 15-20, find the maturity value of the...Ch. 5.1 - In Exercises 15-20, find the maturity value of the...Ch. 5.1 - In Exercises 15-20, find the maturity value of the...Ch. 5.1 - In Exercise 15-20, find the maturity value of the...Ch. 5.1 - In Exercises 21-26 find the present value of the...Ch. 5.1 - In Exercises 21-26 find the present value of the...Ch. 5.1 - In Exercises 21-26 find the present value of the...Ch. 5.1 - In Exercises 21-26 find the present value of the...Ch. 5.1 - In Exercises 2126 find the present value of the...Ch. 5.1 - In Exercises 2126 find the present value of the...Ch. 5.1 - If you borrow 1,000 at 8.5 interest and the loan...Ch. 5.1 - If you borrow 1,700 at 5.25 interest and the loan...Ch. 5.1 - The Square Wheel Bicycle store has found that they...Ch. 5.1 - Ernie Bilko has a business idea. He wants to rent...Ch. 5.1 - Alice Cohen buys a two-year-old Honda from...Ch. 5.1 - Seven Lundgren buys a three-year-old Chevrolet...Ch. 5.1 - Ray and Teresa Martinez buy a used car from...Ch. 5.1 - Dick Davis buys a five-year-old used Toyota from...Ch. 5.1 - In exercise 3536, use the following information....Ch. 5.1 - In exercise 3536, use the following information....Ch. 5.1 - The activity on Stuart Ratners Visa account for...Ch. 5.1 - The activity on Marny Zells MasterCard account for...Ch. 5.1 - The activity on Denise Hellings Sears account for...Ch. 5.1 - The activity on Charlie Wilsons Visa account for...Ch. 5.1 - Prob. 41ECh. 5.1 - George and Peggy Fulwider bought a house from...Ch. 5.1 - Prob. 43ECh. 5.1 - Sam Needham bought a house from Sheri Silva for...Ch. 5.1 - You have maxed out your credit card and owe 5,000....Ch. 5.1 - You have maxed out your credit card and owe 5,500....Ch. 5.1 - You have maxed out your credit card and owe 5,000....Ch. 5.1 - 46. You have maxed out your credit card and owe...Ch. 5.1 - Could Exercise 512 all be done with the Simple...Ch. 5.1 - Prob. 50ECh. 5.2 - In Exercises 1-6, find the periodic rate that...Ch. 5.2 - In Exercises 1-6, find the periodic rate that...Ch. 5.2 - In Exercises 1-6, find the periodic rate that...Ch. 5.2 - In Exercises 1-6, find the periodic rate that...Ch. 5.2 - In Exercises 1-6, find the periodic rate that...Ch. 5.2 - In Exercises 1-6, find the periodic rate that...Ch. 5.2 - In Exercises7-10, fincl the number of periods that...Ch. 5.2 - In Exercises7-10, fincl the number of periods that...Ch. 5.2 - In Exercises7-10, fincl the number of periods that...Ch. 5.2 - In Exercises7-10, fincl the number of periods that...Ch. 5.2 - In Exercise 11-16, a find and b interpret the...Ch. 5.2 - In Exercise 11-16, a find and b interpret the...Ch. 5.2 - In Exercise 11-16, a find and b interpret the...Ch. 5.2 - In Exercise 11-16, a find and b interpret the...Ch. 5.2 - In Exercise 11-16, a find and b interpret the...Ch. 5.2 - In Exercise 11-16, a find and b interpret the...Ch. 5.2 - In Exercise 17-20, a find and b interpret the...Ch. 5.2 - In Exercise 17-20, a find and b interpret the...Ch. 5.2 - In Exercise 17-20, a find and b interpret the...Ch. 5.2 - In Exercise 17-20, a find and b interpret the...Ch. 5.2 - In the Exercises21 and 22, find and interpret the...Ch. 5.2 - In the Exercises 21 and 22, find and interpret the...Ch. 5.2 - In the Exercise 2326, a find and b interpret the...Ch. 5.2 - In the Exercise 24, find and interpret the present...Ch. 5.2 - In Exercises 23-26, a find and b interpret the...Ch. 5.2 - In Exercises 23-26, a find and b interpret the...Ch. 5.2 - 10,000 is deposited in an account in which it...Ch. 5.2 - 20,000 is deposited in an account in which it...Ch. 5.2 - 15,000 is deposited in an account in which it...Ch. 5.2 - 30,000 is deposited in an account in which it...Ch. 5.2 - Donald Trumptobe decided to build his own dynasty....Ch. 5.2 - How much would Donald Trumptobe in Exercise 31...Ch. 5.2 - Donald Trumptobe in Exercise 31 predicts that in...Ch. 5.2 - Donald Trumptobe in Exercise 31 predicts that in...Ch. 5.2 - When Jason Levy was born, his grandparents...Ch. 5.2 - When Alana Cooper was born, her grandparents...Ch. 5.2 - For Exercises 3740, note the following...Ch. 5.2 - For Exercises 37-40, note the following...Ch. 5.2 - For Exercises 37-40, note the following...Ch. 5.2 - For Exercises 37-40, note the following...Ch. 5.2 - For Exercises 41-46, note the following...Ch. 5.2 - For Exercises 41-46, note the following...Ch. 5.2 - For Exercises 41-46, note the following...Ch. 5.2 - For Exercises 41-46, note the following...Ch. 5.2 - For Exercises 41-46, note the following...Ch. 5.2 - For Exercises 41-46, note the following...Ch. 5.2 - Recently, Bank of the West offered six-month CDs...Ch. 5.2 - Recently, Bank of the West offered six-month CDs...Ch. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Exercises 5762 refer to Benjamin Franklins gift,...Ch. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Explain how compound interest is based on simple...Ch. 5.2 - Why is there no work involved in finding the...Ch. 5.2 - Why is there no work involved in finding the...Ch. 5.2 - Which should be higher: the annual yield of a...Ch. 5.2 - Why should the annual yield of a given compound...Ch. 5.2 - Explain the difference between simple interest and...Ch. 5.2 - If money earns compound interest, why must the...Ch. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Prob. 73ECh. 5.2 - Prob. 75ECh. 5.2 - If 1,000 is deposited into an account that earns 5...Ch. 5.2 - Do the following.Give the number of periods and...Ch. 5.2 - Do the following.Give the number of periods and...Ch. 5.2 - If you invest 10,000 at 8.125 interest compounded...Ch. 5.2 - If you invest 15,000 at 938 interest compounded...Ch. 5.3 - In Exercises 1-14, find the future value of the...Ch. 5.3 - In Exercises 1-14, find the future value of the...Ch. 5.3 - In Exercises 1-14, find the future value of the...Ch. 5.3 - In Exercises 1-14, find the future value of the...Ch. 5.3 - On September 8, Bert Sarkis started an annuity. He...Ch. 5.3 - On August 19, Rachael Westlake started an annuity....Ch. 5.3 - On September 23, Ginny Homer started an annuity....Ch. 5.3 - On September 19, Lynn Alright started an annuity....Ch. 5.3 - Pat Gilbert recently set up a TDA to save for her...Ch. 5.3 - Dick recently set up a TDA to save for his...Ch. 5.3 - Sam Whitney recently set up a TDA to save for his...Ch. 5.3 - Art Dull recently set up a TDA to save for his...Ch. 5.3 - Prob. 13ECh. 5.3 - In exercises 13-18, a find and b interpret the...Ch. 5.3 - In exercises 13-18, a find and b interpret the...Ch. 5.3 - Prob. 16ECh. 5.3 - In exercises 13-18, a find and b interpret the...Ch. 5.3 - In exercises 13-18, a find and b interpret the...Ch. 5.3 - In Exercises 19-24, find the monthly payment that...Ch. 5.3 - In Exercises 19-24, find the monthly payment that...Ch. 5.3 - In Exercise 19-24, find the monthly payment that...Ch. 5.3 - In Exercise 19-24, find the monthly payment that...Ch. 5.3 - In Exercise 19-24, find the monthly payment that...Ch. 5.3 - In Exercise 19-24, find the monthly payment that...Ch. 5.3 - Mr. and Mrs. Gonzales set up a TDA to save for...Ch. 5.3 - Mr. and Mrs. Jackson set up a TDA to save for...Ch. 5.3 - Jeanne and Harold Kimura want to set up a TDA that...Ch. 5.3 - Susan and Bill Stamp want to set up a TDA that...Ch. 5.3 - In June 2004, Susan set up a TDA to save for...Ch. 5.3 - In June 2007, Manuel set up a TDA to save for...Ch. 5.3 - In Exercises 3134, use the following information....Ch. 5.3 - In Exercises 3134, use the following information....Ch. 5.3 - In Exercises 31-34, use the following information....Ch. 5.3 - In Exercises 3134, use the following information....Ch. 5.3 - Toni Torres wants to save 1,200 in the next two...Ch. 5.3 - Fred and Melissa Furths daughter Sally will be a...Ch. 5.3 - Anne Geyer buys some land in Utah. She agrees to...Ch. 5.3 - Chrissy Fields buys some land in Oregon. She...Ch. 5.3 - Develop a new formula for the present value of an...Ch. 5.3 - Use the formula developed in Exercise 39 to find...Ch. 5.3 - Use the formula developed in Exercise 39 to find...Ch. 5.3 - Use the formula developed in Exercise 39 to find...Ch. 5.3 - Use the formula developed in Exercise 39 to find...Ch. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Prob. 49ECh. 5.3 - For those who have completed Section 1.1: Is the...Ch. 5.3 - Answer the following questions using complete...Ch. 5.3 - Answer the following questions using complete...Ch. 5.4 - In Exercises1-6, find a the monthly payment and b...Ch. 5.4 - In Exercises1-6, find a the monthly payment and b...Ch. 5.4 - In Exercises1-6, find a the monthly payment and b...Ch. 5.4 - In Exercises1-6, find a the monthly payment and b...Ch. 5.4 - In Exercises1-6, find a the monthly payment and b...Ch. 5.4 - In Exercises1-6, find a the monthly payment and b...Ch. 5.4 - Wade Ellis buys a new car for 16,113.82. He puts...Ch. 5.4 - Guy dePrimo buys a new car for 9,837.91. He puts...Ch. 5.4 - Chris Burditt bought a house for 212,500. He put...Ch. 5.4 - Shirley Trembley bought a house for 187,600. She...Ch. 5.4 - Dennis Lamenti wants to buy a new car that costs...Ch. 5.4 - Barry Wood wants to buy a used car that costs...Ch. 5.4 - Investigate the effect of the term on simple...Ch. 5.4 - Investigate the effect of the interest rate on...Ch. 5.4 - Investigate the effect of the interest rate on...Ch. 5.4 - Some lenders offer fifteen-year home loans....Ch. 5.4 - Some lenders offer loans with biweekly payments...Ch. 5.4 - Some lenders are now offering loans with biweekly...Ch. 5.4 - Verify a the monthly payments and b the interest...Ch. 5.4 - The home loan in Exercise 19 presented two...Ch. 5.4 - Pool-N-Patio World needs to borrow 75,000 to...Ch. 5.4 - Slopes R Us needs to borrow 120,000 to increase...Ch. 5.4 - The owner of Blue Bottle Coffee is opening a...Ch. 5.4 - The Green Growery Nursery needs to borrow 48,000...Ch. 5.4 - For Exercises 2528, note the following...Ch. 5.4 - For Exercises 25-28, note the following...Ch. 5.4 - For Exercises 25-28, note the following...Ch. 5.4 - For Exercises 25-28, note the following...Ch. 5.4 - Wade Ellis buys a car for 16,113.82. He puts 10...Ch. 5.4 - Guy de Primo buys a car for 9837.91. He puts 10...Ch. 5.4 - Gary Kersting buys a house for 212,500. He puts 20...Ch. 5.4 - Shirley Trembley buys a house for 187,600. She...Ch. 5.4 - Harry and Natalie Wolf have a three-year-old loan...Ch. 5.4 - Russ and Roz Rosow have a ten-year-old loan with...Ch. 5.4 - Michael and Lynn Sullivan have a ten-year-old loan...Ch. 5.4 - Charlie and Ellen Wilson have a...Ch. 5.4 - Ray and Helen Lee bought a house for 189,500. They...Ch. 5.4 - Jack and Laurie Worthington bought a house for...Ch. 5.4 - a. If the Lees in Exercise 37 save for their...Ch. 5.4 - a. If the Worthingtons in Exercise 38 save for...Ch. 5.4 - In July 2005, Tom and Betty bought a house for...Ch. 5.4 - In August 2004, Bonnie Martin bought a house for...Ch. 5.4 - Al-Noor Koorji bought a house for 189,000. He put...Ch. 5.4 - The Franklins bought a house for 265,000. They put...Ch. 5.4 - To get your bachelors degree, you incurred 50,000...Ch. 5.4 - To get your bachelors degree, you incurred 50,000...Ch. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - This is an exercise in buying a car. It involves...Ch. 5.4 - Trustworthy Savings offers a thirty-year...Ch. 5.4 - American Dream Savings Bank offers a thirty-year...Ch. 5.4 - Bank Two offers a thirty-year adjustable-rate...Ch. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - The Roths bought a house for 432,500. They paid...Ch. 5.5 - The Hoblets bought a house for 799,900. They paid...Ch. 5.5 - The Trivedis bought a house for 287,300. They paid...Ch. 5.5 - The Roschunis bought a house for 763,500. They...Ch. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.6 - Cheryl Wilcox is planning for her retirement, so...Ch. 5.6 - Prob. 2ECh. 5.6 - Dean Gooch is planning for his retirement, so he...Ch. 5.6 - Holly Krech is planning for her retirement, so she...Ch. 5.6 - a. How large a monthly payment must Cheryl Wilcox...Ch. 5.6 - Prob. 6ECh. 5.6 - a. How large a monthly payment must Dean Gooch...Ch. 5.6 - a. How large a monthly payment must Holly Krech...Ch. 5.6 - Lily Chang is planning for her retirement, so she...Ch. 5.6 - Wally Brown is planning for his retirement, so he...Ch. 5.6 - Prob. 11ECh. 5.6 - Shelly Franks is planning for her retirement, so...Ch. 5.6 - In Exercises 13-16, use the Annual Payout Annuity...Ch. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Bob Pirtle won 1 million in a state lottery. He...Ch. 5.6 - John-Paul Ramin won 2.3million in a state lottery....Ch. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.CR - Find the interest earned by a deposit of 8,140 at...Ch. 5.CR - Find the interest earned by a deposit of 10,620 at...Ch. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Find the present value of a future value of 10,250...Ch. 5.CR - Prob. 9CRCh. 5.CR - Find the future value of a deposit of 7,250 at 514...Ch. 5.CR - Prob. 11CRCh. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Prob. 15CRCh. 5.CR - Prob. 16CRCh. 5.CR - Prob. 17CRCh. 5.CR - Prob. 18CRCh. 5.CR - Prob. 19CRCh. 5.CR - Prob. 20CRCh. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - The Square Wheel Bicycle store has found that they...Ch. 5.CR - Prob. 24CRCh. 5.CR - The activity on Sue Washburns MasterCard account...Ch. 5.CR - Prob. 26CRCh. 5.CR - Prob. 27CRCh. 5.CR - Prob. 28CRCh. 5.CR - You are 32, and you have just set up an ordinary...Ch. 5.CR - Find and interpret the present value of the...Ch. 5.CR - Prob. 31CRCh. 5.CR - Prob. 32CRCh. 5.CR - Prob. 33CRCh. 5.CR - Prob. 34CRCh. 5.CR - Prob. 35CRCh. 5.CR - Prob. 36CRCh. 5.CR - Prob. 37CRCh. 5.CR - Ben Suico buys a car for 13,487.31. He puts 10...Ch. 5.CR - Prob. 39CRCh. 5.CR - Prob. 40CRCh. 5.CR - Prob. 41CRCh. 5.CR - Fred Rodgers is planning for his retirement, so he...Ch. 5.CR - Prob. 43CRCh. 5.CR - Prob. 44CRCh. 5.CR - Prob. 45CRCh. 5.CR - Prob. 46CRCh. 5.CR - Prob. 47CRCh. 5.CR - Prob. 48CRCh. 5.CR - Prob. 49CR
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- As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk. (a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let ds ≥ R − Rs with ds ≥ 0. Then make the objective function: Min 1 5 5 s = 1 ds2. Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund…arrow_forwardCalculus lll May I please have the blank lines completed, and final statement defined as a result? Thank you for the support!arrow_forwardFor each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram? A 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92 B 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91 C 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93 D 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91arrow_forward
- In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forward
- We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward
- 3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward3. Consider the polynomial equation 6-iz+7z2-iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forward
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