Elementary Statistics: A Step By Step Approach
9th Edition
ISBN: 9780073534985
Author: Allan Bluman
Publisher: McGraw-Hill Science/Engineering/Math
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Question
Chapter 2, Problem 2.3.20RE
To determine
To draw: The pie chart.
To interpret: The graph.
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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 2 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 2.1 - Ages of Presidents at Inauguration The data...Ch. 2.1 - List five reasons for organizing data into a...Ch. 2.1 - Name the three types of frequency distributions,...Ch. 2.1 - How many classes should frequency distributions...Ch. 2.1 - What are open-ended frequency distributions? Why...Ch. 2.1 - Prob. 5ECh. 2.1 - For Exercises 58, find the class boundaries,...Ch. 2.1 - Prob. 7ECh. 2.1 - For Exercises 58, find the class boundaries,...Ch. 2.1 - Prob. 9E
Ch. 2.1 - For Exercises 912, show frequency distributions...Ch. 2.1 - Prob. 11ECh. 2.1 - For Exercises 912, show frequency distributions...Ch. 2.1 - Prob. 13ECh. 2.1 - Trust in Internet Information A survey was taken...Ch. 2.1 - Eating at Fast Food Restaurants A survey was taken...Ch. 2.1 - Ages of Dogs The ages of 20 dogs in a pet shelter...Ch. 2.1 - Prob. 17ECh. 2.1 - Stories in the Worlds Tallest Buildings The number...Ch. 2.1 - Ages of Declaration of Independence Signers The...Ch. 2.1 - Salaries of Governors Here are the salaries (in...Ch. 2.1 - Charity Donations A random sample of 30 large...Ch. 2.1 - Unclaimed Expired Prizes The number of unclaimed...Ch. 2.1 - Prob. 23ECh. 2.1 - Consumption of Natural Gas Construct a frequency...Ch. 2.1 - Average Wind Speeds A sample of 40 large cities...Ch. 2.1 - Percentage of People Who Completed 4 or More Years...Ch. 2.1 - JFK Assassination A researcher conducted a survey...Ch. 2.1 - The Value of Pi The ratio of the circumference of...Ch. 2.2 - Selling Real Estate Assume you are a realtor in...Ch. 2.2 - Do Students Need Summer Development? For 108...Ch. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Number of College Faculty The number of faculty...Ch. 2.2 - Railroad Crossing Accidents The data show the...Ch. 2.2 - NFL Salaries The salaries (in millions of dollars)...Ch. 2.2 - Prob. 7ECh. 2.2 - Costs of Utilities The frequency distribution...Ch. 2.2 - Air Pollution One of the air pollutants that is...Ch. 2.2 - Making the Grade The frequency distributions shown...Ch. 2.2 - Blood Glucose Levels The frequency distribution...Ch. 2.2 - Waiting Times The frequency distribution shows the...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Prob. 17ECh. 2.2 - Protein Grams in Fast Food The amount of protein...Ch. 2.2 - Using the histogram shown here, do the following....Ch. 2.2 - Using the results from Exercise 19. answer these...Ch. 2.2 - Math SAT Scores Shown is an ogive depicting the...Ch. 2.3 - Applying the Concepts 23 Causes of Accidental...Ch. 2.3 - Prob. 1ECh. 2.3 - Worldwide Sales of Fast Foods The worldwide sales...Ch. 2.3 - Prob. 3ECh. 2.3 - Roller Coaster Mania The World Roller Coaster...Ch. 2.3 - Prob. 5ECh. 2.3 - Violent Crimes The number of all violent crimes...Ch. 2.3 - Prob. 7ECh. 2.3 - Valentines Day Spending The data show the average...Ch. 2.3 - Prob. 9ECh. 2.3 - Reasons We Travel The following data are based on...Ch. 2.3 - Prob. 11ECh. 2.3 - Colors of Automobiles The popular car colors are...Ch. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Years of Experience The data show the number of...Ch. 2.3 - Commuting Times Fifty off-campus students were...Ch. 2.3 - Home Run Club There are 43 Major League baseball...Ch. 2.3 - Calories in Salad Dressings A listing of calories...Ch. 2.3 - Length of Major Rivers The data show the lengths...Ch. 2.3 - Math and Reading Achievement Scores The math and...Ch. 2.3 - State which type of graph (Pareto chart, time...Ch. 2.3 - State which graph (Pareto chart, time series...Ch. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Cost of Milk The graph shows the increase in the...Ch. 2.3 - U.S. Population by Age The following information...Ch. 2.3 - Prob. 27ECh. 2.3 - Trip Reimbursements The average amount requested...Ch. 2 - How People Get Their News The Brunswick Research...Ch. 2 - Mens World Hockey Champions The United States won...Ch. 2 - BUN Count The blood urea nitrogen (BUN) count of...Ch. 2 - Wind Speed The data show the average wind speed...Ch. 2 - Prob. 2.1.5RECh. 2 - Ages of the Vice Presidents at the Time of Their...Ch. 2 - Prob. 2.2.7RECh. 2 - Find the relative frequency for the frequency...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Prob. 2.3.13RECh. 2 - Calories of Nuts The data show the number of...Ch. 2 - Prob. 2.3.15RECh. 2 - AID: 1825 | 31/5/2018 16. Pet Care The data (in...Ch. 2 - Prob. 2.3.17RECh. 2 - Prob. 2.3.18RECh. 2 - Prob. 2.3.19RECh. 2 - Prob. 2.3.20RECh. 2 - Prob. 2.3.21RECh. 2 - Prob. 2.3.22RECh. 2 - Prob. 2.3.23RECh. 2 - Public Libraries The numbers of public libraries...Ch. 2 - Pain Relief The graph below shows the time it...Ch. 2 - Casino Payoffs The graph shows the payoffs...Ch. 2 - From the Data Bank located in Appendix B, choose...Ch. 2 - Prob. 2DACh. 2 - From the Data Bank, select at least 30 subjects...Ch. 2 - Prob. 4DACh. 2 - Using the data from Data Set XI in Appendix B,...Ch. 2 - Prob. 7DACh. 2 - Determine whether each statement is true or false....Ch. 2 - Prob. 2CQCh. 2 - Prob. 3CQCh. 2 - Frequency distributions can aid the researcher in...Ch. 2 - Determine whether each statement is true or false....Ch. 2 - Prob. 6CQCh. 2 - Determine whether each statement is true or false....Ch. 2 - Prob. 8CQCh. 2 - What are the boundaries for 8.68.8? a. 89 b....Ch. 2 - What graph should be used to show the relationship...Ch. 2 - Prob. 11CQCh. 2 - The three types of frequency distributions are...Ch. 2 - In a frequency distribution, the number of classes...Ch. 2 - Prob. 14CQCh. 2 - Data collected over a period of time can be...Ch. 2 - A statistical device used in exploratory data...Ch. 2 - On a Pareto chart, the frequencies should be...Ch. 2 - Housing Arrangements A questionnaire on housing...Ch. 2 - Housing Arrangements A questionnaire on housing...Ch. 2 - Prob. 20CQCh. 2 - Construct a histogram, a frequency polygon, and an...Ch. 2 - Coal Consumption The following data represent the...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Recycled Trash Construct a Pareto chart and a...Ch. 2 - Identity Thefts The results of a survey of 84...Ch. 2 - Needless Deaths of Children The New England...Ch. 2 - Prob. 27CQCh. 2 - Parking Meter Revenue In a small city the number...Ch. 2 - Prob. 29CQCh. 2 - The Great Lakes Shown are various statistics about...Ch. 2 - Teacher Strikes In Pennsylvania there were more...
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