Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Question
Chapter 4.2, Problem 8TY
a.
To determine
To identify: The success and the values of n, p and q.
b.
To determine
To find: The product of n and p to calculate the
c.
To determine
To find: The product of n, p and q to calculate the variance.
d.
To determine
To find: The square root of variance to calculate the standard deviation.
e.
To determine
To interpret: The results.
f.
To determine
Any unusual events.
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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
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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?
Chapter 4 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 4.1 - Prob. 1TYCh. 4.1 - Prob. 2TYCh. 4.1 - Prob. 3TYCh. 4.1 - Prob. 4TYCh. 4.1 - Prob. 5TYCh. 4.1 - Prob. 6TYCh. 4.1 - Prob. 7TYCh. 4.1 - What is a random variable? Give an example of a...Ch. 4.1 - What is a discrete probability distribution? What...Ch. 4.1 - Is the expected value of the probability...
Ch. 4.1 - What does the mean of a probability distribution...Ch. 4.1 - True or False? In Exercises 58, determine whether...Ch. 4.1 - True or False? In Exercises 58, determine whether...Ch. 4.1 - True or False? In Exercises 58, determine whether...Ch. 4.1 - True or False? In Exercises 58, determine whether...Ch. 4.1 - Graphical Analysis In Exercises 912, determine...Ch. 4.1 - Graphical Analysis In Exercises 912, determine...Ch. 4.1 - Graphical Analysis In Exercises 912, determine...Ch. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Discrete Variables and Continuous Variables In...Ch. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Constructing and Graphing Discrete Probability...Ch. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Unusual Events In Exercise 20, would it be unusual...Ch. 4.1 - Prob. 25ECh. 4.1 - Determining a Missing Probability In Exercises 25...Ch. 4.1 - Identifying Probability Distributions In Exercises...Ch. 4.1 - Identifying Probability Distributions In Exercises...Ch. 4.1 - Finding the Mean, Variance, and Standard Deviation...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Finding the Mean, Variance, and Standard Deviation...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Writing The expected value of an accountants...Ch. 4.1 - Writing In a game of chance, what is the...Ch. 4.1 - Finding an Expected Value In Exercises 37and 38,...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.2 - Prob. 1TYCh. 4.2 - Prob. 2TYCh. 4.2 - Prob. 3TYCh. 4.2 - Prob. 4TYCh. 4.2 - Prob. 5TYCh. 4.2 - Prob. 6TYCh. 4.2 - Prob. 7TYCh. 4.2 - Prob. 8TYCh. 4.2 - In a binomial experiment, what does it mean to say...Ch. 4.2 - In a binomial experiment with n trials, what does...Ch. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Mean, Variance, and Standard Deviation In...Ch. 4.2 - Mean, Variance, and Standard Deviation In...Ch. 4.2 - Mean, Variance, and Standard Deviation In...Ch. 4.2 - Mean, Variance, and Standard Deviation In...Ch. 4.2 - Prob. 11ECh. 4.2 - Identifying and Understanding Binomial Experiments...Ch. 4.2 - Identifying and Understanding Binomial Experiments...Ch. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Genetics According to a theory in genetics, when...Ch. 4.2 - Genetics Another proposed theory in genetics gives...Ch. 4.2 - Prob. 1ACh. 4.2 - Prob. 2ACh. 4.2 - For the election in Exercise 1, simulate selecting...Ch. 4.2 - Prob. 1CSCh. 4.2 - Prob. 2CSCh. 4.2 - Prob. 3CSCh. 4.3 - Prob. 1TYCh. 4.3 - Prob. 2TYCh. 4.3 - Prob. 3TYCh. 4.3 - In Exercises 14, find the indicated probability...Ch. 4.3 - Prob. 2ECh. 4.3 - In Exercises 14, find the indicated probability...Ch. 4.3 - Prob. 4ECh. 4.3 - In Exercises 58, find the indicated probability...Ch. 4.3 - Prob. 6ECh. 4.3 - In Exercises 58, find the indicated probability...Ch. 4.3 - In Exercises 58, find the indicated probability...Ch. 4.3 - Prob. 9ECh. 4.3 - In your own words, describe the difference between...Ch. 4.3 - Prob. 11ECh. 4.3 - Using a Distribution to Find Probabilities In...Ch. 4.3 - Prob. 13ECh. 4.3 - Using a Distribution to Find Probabilities In...Ch. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Using a Distribution to Find Probabilities In...Ch. 4.3 - Using a Distribution to Find Probabilities In...Ch. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Using a Distribution to Find Probabilities In...Ch. 4.3 - Prob. 25ECh. 4.3 - Using a Distribution to Find Probabilities In...Ch. 4.3 - Comparing Binomial and Poisson Distributions An...Ch. 4.3 - Hypergeometric Distribution Binomial experiments...Ch. 4.3 - Geometric Distribution: Mean and Variance In...Ch. 4.3 - Geometric Distribution: Mean and Variance In...Ch. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4 - Prob. 1UACh. 4 - Prob. 2UACh. 4 - Prob. 3UACh. 4 - Prob. 4UACh. 4 - In Exercises 1 and 2, determine whether the random...Ch. 4 - 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Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 1CTCh. 4 - Prob. 2CTCh. 4 - In Exercises 13find the indicated probabilities...Ch. 4 - Determine whether the distribution is a...Ch. 4 - The table shows the ages of students in a freshman...Ch. 4 - Prob. 6CTCh. 4 - Prob. 7CTCh. 4 - Prob. 1RSRDCh. 4 - Prob. 2RSRDCh. 4 - Prob. 3RSRDCh. 4 - In Exercises 17, consider a grocery store that can...Ch. 4 - In Exercises 17, consider a grocery store that can...Ch. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 6TCh. 4 - Prob. 5TCh. 4 - Prob. 7T
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