Business Statistics: A First Course (8th Edition)
8th Edition
ISBN: 9780135177785
Author: David M. Levine, Kathryn A. Szabat, David F. Stephan
Publisher: PEARSON
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Chapter 2, Problem 2.25AC
(a)
To determine
To construct:A bar, a pie, doughnut and a Pareto chart from the given data set.
(b)
To determine
To explain:The best graphical method for the given data.
(c)
To determine
To discuss:The conclusion could be made from the given dataset.
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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
Business Statistics: A First Course (8th Edition)
Ch. 2 - Prob. 2.1LBCh. 2 - The following data represent the responses to two...Ch. 2 - Prob. 2.3ACCh. 2 - Prob. 2.5ACCh. 2 - Prob. 2.6ACCh. 2 - Prob. 2.7ACCh. 2 - Prob. 2.8ACCh. 2 - Prob. 2.10ACCh. 2 - Prob. 2.11LBCh. 2 - Prob. 2.12LB
Ch. 2 - Prob. 2.14LBCh. 2 - The file UTILITY contains the following data about...Ch. 2 - One operation of a mill to cut pieces of steel...Ch. 2 - Prob. 2.21ACCh. 2 - Prob. 2.23ACCh. 2 - Prob. 2.25ACCh. 2 - Prob. 2.26ACCh. 2 - The following table indicates the percentage of...Ch. 2 - Prob. 2.29ACCh. 2 - Prob. 2.30ACCh. 2 - Prob. 2.31ACCh. 2 - Prob. 2.32ACCh. 2 - Prob. 2.33LBCh. 2 - Prob. 2.34LBCh. 2 - Prob. 2.35ACCh. 2 - The file UTILITY contains the following data about...Ch. 2 - Prob. 2.39ACCh. 2 - Prob. 2.43ACCh. 2 - The data stored in DRINK represents the amount of...Ch. 2 - Prob. 2.48LBCh. 2 - Prob. 2.49LBCh. 2 - Prob. 2.50ACCh. 2 - Data were collected on the typical cost of dining...Ch. 2 - Prob. 2.53ACCh. 2 - Prob. 2.54ACCh. 2 - Prob. 2.55ACCh. 2 - Prob. 2.56ACCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 2.59ACCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 2.62ACCh. 2 - Prob. 2.70ACCh. 2 - Prob. 2.71ACCh. 2 - Prob. 2.72ACCh. 2 - Prob. 2.73ACCh. 2 - Prob. 2.75ACCh. 2 - Prob. 2.76ACCh. 2 - Prob. 2.77CYUCh. 2 - Prob. 2.78CYUCh. 2 - What are the advantages and disadvantages of using...Ch. 2 - Compare and contrast the bar chart for categorical...Ch. 2 - Prob. 2.81CYUCh. 2 - Prob. 2.82CYUCh. 2 - What are the three different ways to break down...Ch. 2 - How can a multidimensional table differ from a...Ch. 2 - Prob. 2.85CYUCh. 2 - Prob. 2.89CRPCh. 2 - The owner of a restaurant that serves...Ch. 2 - Suppose that the owner of the restaurant in...Ch. 2 - Prob. 2.94CRPCh. 2 - One of the major measures of the quality of...Ch. 2 - Prob. 2.103CRPCh. 2 - Prob. 2.104CRPCh. 2 - Prob. 2.105CRPCh. 2 - Prob. 2.109RWE
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