OPENINTRO:STATISTICS
4th Edition
ISBN: 9781943450077
Author: OPENINTRO
Publisher: amazon.com
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Question
Chapter 1, Problem 35E
a.
To determine
Identify whether the given data are part of experimental or observational study.
a.
Expert Solution
Explanation of Solution
Observational study:
Observational study is the one where researchers observe the effect of diagnostic test or treatment without trying to modify the subjects that are or are not exposed it.
The data are collected as part of an observational study.
b.
To determine
Identify the most common dog and cat names.
b.
Expert Solution
Explanation of Solution
From the given visualization plot, the most common dog name is Lucy and the most common cat name is Luna as the proportions of those names are high when compared to other names.
c.
To determine
Identify the most common cat names than dogs.
c.
Expert Solution
Explanation of Solution
From the given visualization plot, the most common cat names are Oliver and Lily when compared to dogs.
d.
To determine
Identify the direction of relationship between the two variables and explain them.
d.
Expert Solution
Explanation of Solution
From the given visualization plot, the relationship between the two variables ‘proportion of dogs’ and ‘proportion of cats’ are positive.
It means that “As the popularity of a name for dogs increases, the popularity of names for cats also increases”.
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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 1 Solutions
OPENINTRO:STATISTICS
Ch. 1.1 - Prob. 1GPCh. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.2 - Prob. 2GPCh. 1.2 - Prob. 3GPCh. 1.2 - Prob. 4GPCh. 1.2 - Prob. 6GPCh. 1.2 - Prob. 7GPCh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4E
Ch. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.3 - Prob. 9GPCh. 1.3 - Prob. 11GPCh. 1.3 - Prob. 12GPCh. 1.3 - Prob. 13GPCh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.4 - Prob. 16GPCh. 1.4 - Prob. 17GPCh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1 - Prob. 35ECh. 1 - Prob. 36ECh. 1 - Prob. 37ECh. 1 - Prob. 38ECh. 1 - Prob. 39CECh. 1 - Prob. 40CECh. 1 - Prob. 41CECh. 1 - Prob. 42CECh. 1 - Prob. 43CECh. 1 - Prob. 44CE
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