Basic Business Statistics
14th Edition
ISBN: 9780134684840
Author: BERENSON, Mark L., Levine, David M., Szabat, Kathryn A.
Publisher: Pearson,
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Chapter 2, Problem 86PS
To determine
Write the difference between the drill down and slicer.
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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
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…
Chapter 2 Solutions
Basic Business Statistics
Ch. 2 - A categorical variable has three categories, with...Ch. 2 - The following data represent the responses to two...Ch. 2 - The following table, stored in Smartphones Sales,...Ch. 2 - The Consumer Financial Protection Bureau reports...Ch. 2 - In addition to the impact of Big Data, what...Ch. 2 - This table represents the summer power-generating...Ch. 2 - Timetric’s 2016 survey of insurance...Ch. 2 - A survey of 1,520 Americans adults asked “Do you...Ch. 2 - A study of selected Kickstarter projects showed...Ch. 2 - Do special recommendations increase ad...
Ch. 2 - Construct an ordered array, given the following...Ch. 2 - Construct an ordered array, given the following...Ch. 2 - Planning and preparing for the unexpected,...Ch. 2 - Data was collected on salaries of compliance...Ch. 2 - The file NBACost contains the total cost ($ ) for...Ch. 2 - The file Utility contains the following data about...Ch. 2 - How much time do commuters living in or near...Ch. 2 - How do the average credit scores of people living...Ch. 2 - One operation of a mill is to cut pieces of steel...Ch. 2 - Call centers today play an important role in...Ch. 2 - The financial service call centre in problem 2.20...Ch. 2 - The file Bulbs contains the life (in hours) of a...Ch. 2 - The file Drink Contains the following data for the...Ch. 2 - A survey of online shoppers revealed that in 2015...Ch. 2 - How do college students spend their day? The 2016...Ch. 2 - The Energy Information Administration reported the...Ch. 2 - The Consumer Financial Protection Bureau reports...Ch. 2 - The following table indicates the percentage of...Ch. 2 - Timetric’s 2016 survey of insurance...Ch. 2 - A survey of 1,520 American adults asked “Do you...Ch. 2 - A study of selected Kickstarter projects showed...Ch. 2 - Do special recommendations increase ad...Ch. 2 - Construct a stern-and-leaf display, given the...Ch. 2 - Construct an ordered array, given the following...Ch. 2 - The following is a stern-and0-leaf display...Ch. 2 - The file NBACost contains the total cost in$ for...Ch. 2 - The file MobileSpeed contains the overall download...Ch. 2 - The file Utility contains the following data about...Ch. 2 - As player salaries have increases, the cost of...Ch. 2 - The following histogram and cumulative percentage...Ch. 2 - How much time do Americans living in cities spend...Ch. 2 - How do the average credit scores of people living...Ch. 2 - One operation of a mill is to cut pieces of steel...Ch. 2 - Call centers today play an important role in...Ch. 2 - The financial service call center in problem 2.44...Ch. 2 - The file Bulbs contains the life (in hours) of a...Ch. 2 - The data stored in Drink represents the amount of...Ch. 2 - The following is a set of data from a sample of...Ch. 2 - The following is a series of annual sales...Ch. 2 - Movie companies need to predict the gross receipts...Ch. 2 - Data were collected on the typical cost of dining...Ch. 2 - The file Mobile contains the overall download and...Ch. 2 - A Pew Research Center survey found a noticeable...Ch. 2 - How have stocks performed in the past? The...Ch. 2 - The file NewHomeSales contains the number of new...Ch. 2 - The file Movie Attendance 16 contains the yearly...Ch. 2 - The Super Bowl is a big viewing event watched by...Ch. 2 - Using the sample of retirement funds stored in...Ch. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 60PSCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 62PSCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 64PSCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 66PSCh. 2 - Prob. 67PSCh. 2 - Prob. 68PSCh. 2 - Prob. 71PSCh. 2 - Prob. 72PSCh. 2 - Examine the following visualization, adapted from...Ch. 2 - Prob. 75PSCh. 2 - Prob. 76PSCh. 2 - How do histograms and polygons differ in...Ch. 2 - Why would you construct a summary table?Ch. 2 - What are the advantages and disadvantage of using...Ch. 2 - Compare and contrast the bar chart for categorical...Ch. 2 - What is the difference between a time-series plot...Ch. 2 - Why is it said that the main feature of a Pareto...Ch. 2 - What are the three different ways to break down...Ch. 2 - How can a multidimensional table differ from a...Ch. 2 - What type of insights can you gain from a...Ch. 2 - Prob. 86PSCh. 2 - What is the difference between a time-series plot...Ch. 2 - The following table shown in the TextbookCosts...Ch. 2 - The following table represents the market share...Ch. 2 - B2B marketers in North America were surveyed about...Ch. 2 - The owner of a restaurant that services...Ch. 2 - Suppose that the owner of the restaurant in...Ch. 2 - The following data represents the pounds per...Ch. 2 - The Air Travel Consumer Report, a monthly product...Ch. 2 - One of the major measures of the quality of...Ch. 2 - The file DomesticBeer Contains the percentage...Ch. 2 - Prob. 97PSCh. 2 - The file CDRate contains the yields for one-year...Ch. 2 - The file CEO 2016 includes the total compensation...Ch. 2 - Prob. 100PSCh. 2 - What was the average price of a room at two-star,...Ch. 2 - The file Protein contains calorie and cholesterol...Ch. 2 - The file Natural Gas contains the U.S. monthly...Ch. 2 - The data stored in Drink represent the amount of...Ch. 2 - Prob. 105PSCh. 2 - A/B testing allows business to test a new design...Ch. 2 - Referring to the results from Problem 2.100 on...
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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.)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_forwardUsing 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_forward
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