STATISTICAL TECHNIQUES FOR BUSINESS AND
17th Edition
ISBN: 9781307261158
Author: Lind
Publisher: MCG/CREATE
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Chapter 2, Problem 47CE
a.
To determine
Draw a bar chart to depict the given information.
b.
To determine
Find the percentage of Country U’s total exports to Country C that is represented by two categories “Machinery” and “Electrical Machinery”.
c.
To determine
Find the percentage of the top five exported products represented by the two categories “Machinery” and “Electrical Machinery”.
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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
STATISTICAL TECHNIQUES FOR BUSINESS AND
Ch. 2 - DeCenzo Specialty Food and Beverage Company has...Ch. 2 - A pie chart shows the relative market share of...Ch. 2 - In a marketing study, 100 consumers were asked to...Ch. 2 - A total of 1,000 residents in Minnesota were asked...Ch. 2 - Two thousand frequent business travelers are asked...Ch. 2 - Wellstone Inc. produces and markets replacement...Ch. 2 - A small business consultant is investigating the...Ch. 2 - In the first quarter of last year, the 11 members...Ch. 2 - Prob. 3SRCh. 2 - A set of data consists of 38 observations. How...
Ch. 2 - A set of data consists of 45 observations between...Ch. 2 - A set of data consists of 230 observations between...Ch. 2 - A set of data contains 53 observations. The...Ch. 2 - Wachesaw Manufacturing Inc. produced the following...Ch. 2 - The Quick Change Oil Company has a number of...Ch. 2 - The manager of the BiLo Supermarket in Mt....Ch. 2 - The food services division of Cedar River...Ch. 2 - The annual imports of a selected group of...Ch. 2 - Mollys Candle Shop has several retail stores in...Ch. 2 - The following chart shows the number of patients...Ch. 2 - The following frequency distribution reports the...Ch. 2 - Prob. 18ECh. 2 - A sample of the hourly wages of 15 employees at...Ch. 2 - The following cumulative frequency and the...Ch. 2 - The cumulative frequency and the cumulative...Ch. 2 - The frequency distribution representing the number...Ch. 2 - Prob. 22ECh. 2 - Describe the similarities and differences of...Ch. 2 - Describe the similarities and differences between...Ch. 2 - Alexandra Damonte will be building a new resort in...Ch. 2 - Prob. 26CECh. 2 - A data set consists of 83 observations. How many...Ch. 2 - A data set consists of 145 observations that range...Ch. 2 - The following is the number of minutes to commute...Ch. 2 - The following data give the weekly amounts spent...Ch. 2 - A social scientist is studying the use of iPods by...Ch. 2 - David Wise handles his own investment portfolio,...Ch. 2 - You are exploring the music in your iTunes...Ch. 2 - The monthly issues of the Journal of Finance are...Ch. 2 - The following histogram shows the scores on the...Ch. 2 - The following chart summarizes the selling price...Ch. 2 - A chain of sport shops catering to beginning...Ch. 2 - The numbers of outstanding shares for 24 publicly...Ch. 2 - A recent survey showed that the typical American...Ch. 2 - Midland National Bank selected a sample of 40...Ch. 2 - Residents of the state of South Carolina earned a...Ch. 2 - A recent study of home technologies reported the...Ch. 2 - Merrill Lynch recently completed a study regarding...Ch. 2 - A total of 5.9% of the prime-time viewing audience...Ch. 2 - Refer to the following chart: a. What is the name...Ch. 2 - The following chart depicts the annual revenues,...Ch. 2 - Prob. 47CECh. 2 - Prob. 48CECh. 2 - One of the most popular candies in the United...Ch. 2 - The number of families who used the Minneapolis...Ch. 2 - Refer to the North Valley Real Estate data that...Ch. 2 - Prob. 52DACh. 2 - Refer to the Lincolnville School District bus...
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