Introduction To Probability And Statistics
15th Edition
ISBN: 9781337554428
Author: Mendenhall, William.
Publisher: Cengage Learning,
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Chapter 1.3, Problem 12E
To determine
Compare between dot plot chart and stem and leaf chart.
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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
Introduction To Probability And Statistics
Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...
Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Parking on Campus Six vehicles selected from a...Ch. 1.1 - Past U.S. Presidents A data set gives the ages at...Ch. 1.1 - Voter Attitudes You are a candidate for your state...Ch. 1.1 - Cancer Survival Times A researcher wants to...Ch. 1.1 - New Teaching Methods A researcher wants to know...Ch. 1.2 - Pie and Bar Charts The data in Exercises 13...Ch. 1.2 - Pie and Bar Charts The data in Exercises 13...Ch. 1.2 - Pie and Bar Charts The data in Exercises 13...Ch. 1.2 - Groups of People Fifty people are grouped into...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Back to Work How long does it take you to adjust...Ch. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.3 - DotplotsConstruct a dotplot for the data given in...Ch. 1.3 - DotplotsConstruct a dotplot for the data given in...Ch. 1.3 - Stem and Leaf I Construct a stem and leaf plot for...Ch. 1.3 - Stem and Leaf I Construct a stem and leaf plot for...Ch. 1.3 - Stem and Leaf I Construct a stem and leaf plot for...Ch. 1.3 - Stem and Leaf II Use the following set of data...Ch. 1.3 - Stem and Leaf II Use the following set of data...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Comparing Graphs A discrete variable can take on...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Calcium Contents The calcium content (Ca)of a...Ch. 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 - American Presidents The following table lists the...Ch. 1.4 - Graphing Relative Frequency Histograms Construct a...Ch. 1.4 - Graphing Relative Frequency Histograms Construct a...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Class Boundaries In Exercises 912, use the...Ch. 1.4 - Class Boundaries In Exercises 912, use the...Ch. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Relative Frequency Histogram I Construct a...Ch. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - A Recurring Illness The length of time (in months)...Ch. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Student Heights The self-reported heights of 105...Ch. 1.4 - Prob. 33ECh. 1 - Quantitative or Qualitative? Identify each...Ch. 1 - Symmetric or Skewed? Do you expect the...Ch. 1 - Continuous or Discrete? Identify each variable as...Ch. 1 - Continuous or Discrete, again Identify each...Ch. 1 - World Lakes A lake is a body of water surrounded...Ch. 1 - Prob. 6RWYLCh. 1 - Election Results The 2016 election was a race in...Ch. 1 - Prob. 8RWYLCh. 1 - Prob. 9RWYLCh. 1 - Pulse Rates A group of 50 biomedical students...Ch. 1 - Prob. 11RWYLCh. 1 - Prob. 12RWYLCh. 1 - Gasoline Tax The following are the 2017 state...Ch. 1 - Prob. 14RWYLCh. 1 - Prob. 15RWYLCh. 1 - Prob. 16RWYLCh. 1 - Kentucky Derby The following data set shows the...Ch. 1 - Prob. 18RWYLCh. 1 - Old Faithful The following data are the waiting...Ch. 1 - Prob. 20RWYLCh. 1 - Prob. 1CSCh. 1 - Prob. 2CS
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