Stats: Data And Models Plus Mylab Statistics With Pearson Etext -- Access Card Package (5th Edition)
5th Edition
ISBN: 9780135256213
Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock
Publisher: PEARSON
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Chapter 4, Problem 22E
a.
To determine
Find the summary statistic that is used to summarize the centre of the distribution and spread of the distribution.
b.
To determine
Identify the number of potential outliers in the data set.
c.
To determine
Draw the box plot for the given information.
d.
To determine
Describe the features of the distribution of number of campsites.
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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 4 Solutions
Stats: Data And Models Plus Mylab Statistics With Pearson Etext -- Access Card Package (5th Edition)
Ch. 4.1 - The Bureau of Transportation Statistics of the...Ch. 4.1 - The Bureau of Transportation Statistics of the...Ch. 4.1 - Prob. 3JCCh. 4 - Prob. 1ECh. 4 - Prob. 2ECh. 4 - 3. Fuel economy The boxplot shows the fuel economy...Ch. 4 - 4. Prisons 2014 In a way, boxplots are the...Ch. 4 - Load factors 2017 by month Here is a display of...Ch. 4 - Load factors 2017 by year Here is a display of the...Ch. 4 - Prob. 7E
Ch. 4 - Load factors 2017 by year again The box plots of...Ch. 4 - Prob. 9ECh. 4 - Load factors 2017 over time, a second look Here is...Ch. 4 - Prob. 11ECh. 4 - Prob. 12ECh. 4 - 15. Cost of living 2016, selected cities To help...Ch. 4 - Prob. 16ECh. 4 - 17. Rock concert deaths Crowd Management...Ch. 4 - Slalom times 2018 The Men’s Giant Slalom skiing...Ch. 4 - Prob. 19ECh. 4 - Prob. 20ECh. 4 - Prob. 21ECh. 4 - Prob. 22ECh. 4 - Prob. 23ECh. 4 - Prob. 24ECh. 4 - Prob. 25ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Prob. 29ECh. 4 - 30. Ozone Ozone levels (in parts per billion, ppb)...Ch. 4 - Prob. 31ECh. 4 - 32. Eye and hair color A survey of 1021 school-age...Ch. 4 - Prob. 33ECh. 4 - 34. Vineyards Here are summary statistics for the...Ch. 4 - 35. Caffeine A student study of the effects of...Ch. 4 - Prob. 36ECh. 4 - Prob. 37ECh. 4 - Prob. 38ECh. 4 - Prob. 39ECh. 4 - Prob. 40ECh. 4 - Prob. 41ECh. 4 - Prob. 42ECh. 4 - Prob. 43ECh. 4 - Prob. 44ECh. 4 - Prob. 45ECh. 4 - Prob. 46ECh. 4 - Prob. 47ECh. 4 - 48. Rainmakers The table lists the amounts of...Ch. 4 - Prob. 49ECh. 4 - Prob. 50ECh. 4 - Prob. 51ECh. 4 - Prob. 52ECh. 4 - 13. Pizza prices by city (Data in Pizza prices)...
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