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 8, Problem 49SE
A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample
- a. Develop a 95% confidence
interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls. - b. based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association? Explain.
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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 8 Solutions
Essentials Of Statistics For Business & Economics
Ch. 8.1 - A simple random sample of 40 items resulted in a...Ch. 8.1 - 2. A simple random sample of 50 items from a...Ch. 8.1 - A simple random sample of 60 items resulted in a...Ch. 8.1 - 4. A 95% confidence interval for a population mean...Ch. 8.1 - Data were collected on the amount spent by 64...Ch. 8.1 - Travel Taxes. In an attempt to assess total daily...Ch. 8.1 - Cost of Dog Ownership. Money reports that the...Ch. 8.1 - Studies show that massage therapy has a variety of...Ch. 8.1 - Cost to Repair Fire Damage. The mean cost to...Ch. 8.1 - 10. Costs are rising for all kinds of medical...
Ch. 8.2 - For a t distribution with 16 degrees of freedom,...Ch. 8.2 - Find the t value(s) for each of the following...Ch. 8.2 - The following sample data are from a normal...Ch. 8.2 - A simple random sample with n = 54 provided a...Ch. 8.2 - 15. Sales personnel for Skillings Distributors...Ch. 8.2 - Years to Bond Maturity. A sample containing years...Ch. 8.2 - Quality Ratings of Airports. The International Air...Ch. 8.2 - Unemployment in Older Workers. Older people often...Ch. 8.2 - Meal Cost in Hong Kong. The mean cost of a meal...Ch. 8.2 - Automobile Insurance Premiums. The average annual...Ch. 8.2 - Telemedicine. Health insurers are beginning to...Ch. 8.2 - Movie Ticket Sales. Marvel Studios motion picture...Ch. 8.3 - 23. How large a sample should be selected to...Ch. 8.3 - The range for a set of data is estimated to be 36....Ch. 8.3 - Refer to the Scheer Industries example in Section...Ch. 8.3 - Gasoline Prices. The U.S. Energy Information...Ch. 8.3 - Salaries of Business Graduates. Annual starting...Ch. 8.3 - 28. Many medical professionals believe that eating...Ch. 8.3 - 29. Customers arrive at a movie theater at the...Ch. 8.3 - Prob. 30ECh. 8.4 - A simple random sample of 400 individuals provides...Ch. 8.4 - A simple random sample of 800 elements generates a...Ch. 8.4 - In a survey, the planning value for the population...Ch. 8.4 - At 95% confidence, how large a sample should be...Ch. 8.4 - Health-Care Survey. In the spring of 2017, the...Ch. 8.4 - According to statistics reported on CNBC, a...Ch. 8.4 - Voter Sentiment. One of the questions Rasmussen...Ch. 8.4 - 38. According to Franchise business review, over...Ch. 8.4 - In 16% of all homes with a stay-at-home parent,...Ch. 8.4 - Prob. 40ECh. 8.4 - Driver’s License Rates. Fewer young people are...Ch. 8.4 - 42. A poll for the presidential campaign sampled...Ch. 8.4 - 43. The Pew Research Center Internet Project,...Ch. 8.5 - Federal Tax Return Errors. Suppose a sample of...Ch. 8.5 - Federal Government Employee Sick Hours. According...Ch. 8.5 - Web Browser Satisfaction. Internet users were...Ch. 8.5 - Speeding Drivers. In 2017, ABC News reported that...Ch. 8 - 44. A sample survey of 54 discount brokers showed...Ch. 8 - 45. A survey conducted by the American Automobile...Ch. 8 - 46. The 92 million Americans of age 50 and over...Ch. 8 - Healthy Sleep Duration. The Centers for Disease...Ch. 8 - The Health Care Cost Institute tracks health care...Ch. 8 - Obesity. Obesity is a risk factor for many health...Ch. 8 - Prob. 54SECh. 8 - 51. In developing patient appointment schedules, a...Ch. 8 - Prob. 56SECh. 8 - 53. The National Center for Education Statistics...Ch. 8 - A USA Today/CNN/Gallup survey of 369 working...Ch. 8 - Social Media Usage. The Pew Research Center has...Ch. 8 - Prob. 60SECh. 8 - The Centers for Disease Control reported the...Ch. 8 - A well-known bank credit card firm wishes to...Ch. 8 - Credit Card Ownership. Credit card ownership...Ch. 8 - 60. Although airline schedules and cost are...Ch. 8 - Driving Speeds. Huston Systems Private Limited...Ch. 8 - Prob. 66SECh. 8 - Prob. 67SECh. 8 - Prob. 68SECh. 8 - Young Professional Magazine Young Professional...Ch. 8 - Gulf Real Estate Properties Gulf Real Estate...Ch. 8 - Metropolitan Research, Inc.
Metropolitan Research,...
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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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