PRACT STAT W/ ACCESS 6MO LOOSELEAF
4th Edition
ISBN: 9781319215361
Author: BALDI
Publisher: Macmillan Higher Education
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Question
Chapter 6, Problem 6.1AYK
To determine
To identify: whether the study in the problem is observational or experimental.
Expert Solution & Answer
Answer to Problem 6.1AYK
The particular study is observational study.
Explanation of Solution
The study aims to determine percentage of adults whose right cerebral hemisphere is larger than left hemisphere. On a group of people aged 20 and older representing American adult population, brain imaging is done. Afterwards each scan is analyzed to decide which part of brain is larger.
The above study is an observational study and not experimental study.
This is because an observational study measures variable of interest (percentage of adults with larger right hemisphere) but does not influence the results. In an experimental study, a particular treatment is applied to a group of people and compared with control group (group where in no treatment is applied).
Here since brain imaging is done for every member without influencing the response, it is not an experimental study.
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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 6 Solutions
PRACT STAT W/ ACCESS 6MO LOOSELEAF
Ch. 6 - Prob. 6.1AYKCh. 6 - Prob. 6.2AYKCh. 6 - Prob. 6.3AYKCh. 6 - Prob. 6.4AYKCh. 6 - Prob. 6.5AYKCh. 6 - Prob. 6.6AYKCh. 6 - Prob. 6.7AYKCh. 6 - Prob. 6.8AYKCh. 6 - Prob. 6.9AYKCh. 6 - Prob. 6.10AYK
Ch. 6 - Prob. 6.11AYKCh. 6 - Prob. 6.12AYKCh. 6 - Prob. 6.13AYKCh. 6 - Prob. 6.14AYKCh. 6 - Prob. 6.15CYSCh. 6 - Prob. 6.16CYSCh. 6 - Prob. 6.17CYSCh. 6 - Prob. 6.18CYSCh. 6 - Prob. 6.19CYSCh. 6 - Prob. 6.20CYSCh. 6 - Prob. 6.21CYSCh. 6 - Prob. 6.22CYSCh. 6 - Prob. 6.23CYSCh. 6 - Prob. 6.24CYSCh. 6 - Prob. 6.25ECh. 6 - Prob. 6.26ECh. 6 - Prob. 6.27ECh. 6 - Prob. 6.28ECh. 6 - Prob. 6.29ECh. 6 - Prob. 6.30ECh. 6 - Prob. 6.31ECh. 6 - Prob. 6.32ECh. 6 - Prob. 6.33ECh. 6 - Prob. 6.34ECh. 6 - Prob. 6.35ECh. 6 - Prob. 6.36ECh. 6 - Prob. 6.37ECh. 6 - Prob. 6.38ECh. 6 - Prob. 6.39ECh. 6 - Prob. 6.40ECh. 6 - Prob. 6.41ECh. 6 - Prob. 6.42ECh. 6 - Prob. 6.43E
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