Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 12, Problem 59PS
a.
To determine
Test whether there is a difference in the proportion of Americans who say advertisements are honest on the basis of geographic region.
b.
To determine
Test whether there is a difference in the proportion of Americans who trust advertisements on the basis of their geographic region.
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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 12 Solutions
Basic Business Statistics, Student Value Edition
Ch. 12 - Determine the critical value of 2 with 1 degree of...Ch. 12 - Determine the critical value of 2 with 1 degree of...Ch. 12 - Use the following contingency table: a. Compute...Ch. 12 - Use the following contingency table: a. Compare...Ch. 12 - An lpsos poll asked 1,004 adults “If purchasing...Ch. 12 - Prob. 6PSCh. 12 - Prob. 7PSCh. 12 - The Society for Human Resource Management (SHRM)...Ch. 12 - What Social media tools do marketers commonly use?...Ch. 12 - Docs co-browsing have positive effects on the...
Ch. 12 - Consider a contingency table, with two rows and...Ch. 12 - Use the following contingency table: a. Compute...Ch. 12 - Use the following contingency table: a. Compute...Ch. 12 - How common are financial cost or contractual...Ch. 12 - Business sensor technology provides a way for...Ch. 12 - Prob. 16PSCh. 12 - Repeat (a) and (b) of Problem 12.16, assuming that...Ch. 12 - Prob. 18PSCh. 12 - The MSCI 2016 Survey of Women of Boards Survey...Ch. 12 - Prob. 20PSCh. 12 - Prob. 21PSCh. 12 - Prob. 22PSCh. 12 - A Gallup survey across generations of workers...Ch. 12 - How often do Facebook users post? A study by the...Ch. 12 - What makes sales leaders tick? Mercuri...Ch. 12 - PwC takes a closer look at what CEOs are looking...Ch. 12 - Using Table E.6, determine the lower-and...Ch. 12 - Using Table E.6, determine the lower-tail critical...Ch. 12 - Prob. 29PSCh. 12 - Prob. 30PSCh. 12 - Prob. 31PSCh. 12 - Prob. 32PSCh. 12 - From Problem 12.32 , at the 0.05 level of...Ch. 12 - In Problems 12.32 and 12.33, what is your...Ch. 12 - A vice president for marketing recruits 20 college...Ch. 12 - Prob. 36PSCh. 12 - Is there a difference in the satisfaction rating...Ch. 12 - The management of a hotel has the business...Ch. 12 - Prob. 39PSCh. 12 - Brand valuations are critical to CEOs, financial...Ch. 12 - A bank with a branch located in a commercial...Ch. 12 - Prob. 42PSCh. 12 - Prob. 43PSCh. 12 - Prob. 44PSCh. 12 - A pet food company has the business objective of...Ch. 12 - A hospital conducted a study of the waiting time...Ch. 12 - Prob. 47PSCh. 12 - An advertising agency has been hired by a...Ch. 12 - Prob. 49PSCh. 12 - The more costly and time consuming it is to export...Ch. 12 - Prob. 51PSCh. 12 - Prob. 52PSCh. 12 - Prob. 53PSCh. 12 - Prob. 54PSCh. 12 - Prob. 55PSCh. 12 - Prob. 56PSCh. 12 - Prob. 57PSCh. 12 - Prob. 58PSCh. 12 - Prob. 59PS
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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
- Using the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. LOADING... Click the icon to view the Home Market Value data. Question content area bottom Part 1 Construct a frequency distribution of the errors, e Subscript iei. (Type whole numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0 minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5 minus−50005000less than< e Subscript iei less than or equals≤0 21 0less than< e Subscript iei less than or equals≤50005000 9…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 Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000arrow_forwardUsing the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416plus+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. Square Feet Market Value1813 911001916 1043001842 934001814 909001836 1020002030 1085001731 877001852 960001793 893001665 884001852 1009001619 967001690 876002370 1139002373 1131001666 875002122 1161001619 946001729 863001667 871001522 833001484 798001589 814001600 871001484 825001483 787001522 877001703 942001485 820001468 881001519 882001518 885001483 765001522 844001668 909001587 810001782 912001483 812001519 1007001522 872001684 966001581 86200arrow_forward
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