Essentials Of Statistics For Business & Economics
9th Edition
ISBN: 9780357045435
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: South-Western College Pub
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Textbook Question
Chapter 3.5, Problem 55E
Five observations taken for two variables follow.
- a. Develop a scatter diagram with x on the horizontal axis.
- b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
- c. Compute and interpret the sample
covariance . - d. Compute and interpret the sample
correlation coefficient .
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Students have asked these similar questions
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.)
Problem 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?
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?
2
Chapter 3 Solutions
Essentials Of Statistics For Business & Economics
Ch. 3.1 - Consider a sample with data values of 10, 20, 12,...Ch. 3.1 - Consider a sample with data values of 10, 20, 21,...Ch. 3.1 - Consider the following data and corresponding...Ch. 3.1 - Consider the following data.
What is the mean...Ch. 3.1 - Consider a sample with data values of 27, 25, 20,...Ch. 3.1 - Consider a sample with data values of 53, 55, 70,...Ch. 3.1 - eICU Waiting Times. There is a severe shortage of...Ch. 3.1 - Middle-Level Manager Salaries. Suppose that an...Ch. 3.1 - Advertising Spending. Which companies spend the...Ch. 3.1 - Advertising Spending. Which companies spend the...
Ch. 3.1 - Time Spent Watching Traditional TV. Nielsen tracks...Ch. 3.1 - Online Multiplayer Game Downloads. The creator of...Ch. 3.1 - Automobile Fuel Efficiencies. In automobile...Ch. 3.1 - Unemployment Rates by State. The U.S. Bureau of...Ch. 3.1 - Motor Oil Prices. Martinez Auto Supplies has...Ch. 3.1 - Calculating Grade Point Averages. The grade point...Ch. 3.1 - The following table shows the total return and the...Ch. 3.1 - Business School Ranking. Based on a survey of...Ch. 3.1 - Revenue Growth Rate. Annual revenue for Corning...Ch. 3.1 - Mutual Fund Comparison. Suppose that at the...Ch. 3.1 - If an asset declines in value from $5000 to $3500...Ch. 3.1 - The current value of a company is 25 million. If...Ch. 3.2 - Consider a sample with data values of 10, 20, 12,...Ch. 3.2 - Consider a sample with data values of 10, 20, 12,...Ch. 3.2 - Consider a sample with data values of 27, 25, 20,...Ch. 3.2 - Price of Unleaded Gasoline. Data collected by the...Ch. 3.2 - Round-Trip Flight Prices. The following table...Ch. 3.2 - Annual Sales Amounts. Varatta Enterprises sells...Ch. 3.2 - Air Quality Index. The Los Angeles Times regularly...Ch. 3.2 - Prob. 30ECh. 3.2 - Cellular Phone Spending. According to the 2016...Ch. 3.2 - Advertising Spend by Companies. Advertising Age...Ch. 3.2 - Amateur Golfer Scores. Scores turned in by an...Ch. 3.2 - Consistency of Running Times. The following times...Ch. 3.3 - Consider a sample with data values of 10, 20, 12,...Ch. 3.3 - Prob. 36ECh. 3.3 - Consider a sample with a mean of 30 and a standard...Ch. 3.3 - Suppose the data have a bell-shaped distribution...Ch. 3.3 - The results of a national survey showed that on...Ch. 3.3 - Price per Gallon of Gasoline. Suppose that the...Ch. 3.3 - GMAT Exam Scores. The Graduate Management...Ch. 3.3 - Many families in California are using backyard...Ch. 3.3 - Best Places to Live. Each year Money magazine...Ch. 3.3 - NCAA Basketball Game Scores. A sample of 10 NCAA...Ch. 3.3 - Prob. 45ECh. 3.4 - Consider a sample with data values of 27, 25, 20,...Ch. 3.4 - Show the boxplot for the data in exercise 46. 46....Ch. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Naples Half-Marathon Times. Naples, Florida, hosts...Ch. 3.4 - Pharmaceutical Company Sales. Annual sales, in...Ch. 3.4 - Cell Phone Companies Customer Satisfaction....Ch. 3.4 - Most Admired Companies. Fortune magazines list of...Ch. 3.4 - U.S. Border Crossings. The Bureau of...Ch. 3.5 - Five observations taken for two variables follow....Ch. 3.5 - Five observations taken for two variables follow....Ch. 3.5 - Stock Price Comparison. The file StockComparison...Ch. 3.5 - Driving Speed and Fuel Efficiency. A department of...Ch. 3.5 - Smoke Detector Use and Death Rates. Over the past...Ch. 3.5 - Stock Market Indexes Comparison. The Russell 1000...Ch. 3.5 - Best Private Colleges. A random sample of 30...Ch. 3 - Americans Dining Out. Americans tend to dine out...Ch. 3 - NCAA Football Coaches Salaries. A 2017 USA Today...Ch. 3 - Physician Office Waiting Times. The average...Ch. 3 - Worker Productivity and Insomnia. U.S. companies...Ch. 3 - Work Commuting Methods. Public transportation and...Ch. 3 - Household Incomes. The following data represent a...Ch. 3 - Prob. 69SECh. 3 - Best Hotels. Travel + Leisure magazine provides an...Ch. 3 - NFL Teams Worth. In 2014, the 32 teams in the...Ch. 3 - MLB Team Winning Percentages. Does a major league...Ch. 3 - Money Market Funds Days to Maturity. The days to...Ch. 3 - Automobile Speeds. Automobiles traveling on a road...Ch. 3 - Annual Returns for Panama Railroad Company Stock....Ch. 3 - Pelican Stores, a division of National Clothing,...Ch. 3 - Prob. 2CPCh. 3 - The pursuit of a higher education degree in...Ch. 3 - Although millions of elephants once roamed across...
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- Question 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_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_forward
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