Introductory Statistics Plus Mylab Statistics With Pearson Etext -- Access Card Package (3rd Edition)
3rd Edition
ISBN: 9780135229996
Author: Robert Gould, Rebecca Wong, Colleen N. Ryan
Publisher: PEARSON
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Chapter 1, Problem 9SE
The data in Table 1A were collected from one of the authors’ statistics classes. The first row gives the variable, and each of the other rows represents a student in the class.
TABLE 1A
Coding Explain why the variable Female, in Table 1A, is categorical, even though its values are numbers. Often, it does not make sense, or is not even possible, to add the values of a categorical variable. Does it make sense for Male? If so, what does the sum represent?
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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
Introductory Statistics Plus Mylab Statistics With Pearson Etext -- Access Card Package (3rd Edition)
Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - Coding Suppose you decided to code living...Ch. 1 - The data in Table 1A were collected from one of...Ch. 1 - Coding Students who have accumulated fewer than 30...
Ch. 1 - Facebook Wall Posts (Example 2) A student shared...Ch. 1 - Age of Marriage A student did a survey on the age...Ch. 1 - Snacks Emmanuel, a student at a Los Angeles high...Ch. 1 - Movies A sample of students were questioned to...Ch. 1 - Use the data in Table 1A to answer questions 1.15...Ch. 1 - Use the data in Table 1A to answer questions 1.15...Ch. 1 - Use the data in Table 1A to answer questions 1.15...Ch. 1 - Use the data in Table 1A to answer questions 1.15...Ch. 1 - Investigating Data (Example 4) A data set on Shark...Ch. 1 - Investigating Data Suppose a surfer wanted to...Ch. 1 - Hands (Example 5) A survey was done of men’s and...Ch. 1 - Hands-Biased A survey was done of men’s and...Ch. 1 - Finding and Using Percentages a. A statistics...Ch. 1 - Finding and Using Percentages a. A hospital...Ch. 1 - Women Find the frequency, proportion, and...Ch. 1 - Brown-Haired People Find the frequency,...Ch. 1 - Two-Way Table from Data Make a two-way table from...Ch. 1 - Two-Way Table from Data Make a two-way table from...Ch. 1 - Occupation Growth (Example 6) The 2017 World...Ch. 1 - Chocolate Sales The 2017 World Almanac and Book of...Ch. 1 - Incarceration Rates (Example 7) The table gives...Ch. 1 - Population Density The accompanying table gives...Ch. 1 - Health Insurance The accompanying table gives the...Ch. 1 - Cable TV Subscriptions The accompanying table...Ch. 1 - Percentage of Elderly The projected U.S....Ch. 1 - Marriage and Divorce The marriage and divorce...Ch. 1 - Course Enrollment Rates Two sections of statistics...Ch. 1 - Prob. 38SECh. 1 - For Exercises 1.39 through 1.44, indicate whether...Ch. 1 - For Exercises 1.39 through 1.44, indicate whether...Ch. 1 - For Exercises 1.39 through 1.44, indicate whether...Ch. 1 - For Exercises 1.39 through 1.44, indicate whether...Ch. 1 - For Exercises 1.39 through 1.44, indicate whether...Ch. 1 - For Exercises 1.39 through 1.44, indicate whether...Ch. 1 - Vitamin C and Cancer The blog NHS Choices...Ch. 1 - Aloe Vera You can find many testimonials on the...Ch. 1 - Effects of Tutoring on Math Grades (Example 8) A...Ch. 1 - Treating Depression A doctor who believes strongly...Ch. 1 - Try Exercise and Language Learning (Example 9) In...Ch. 1 - Pneumonia Vaccine for Young Children A study...Ch. 1 - Does Fish Oil Lower Asthma Risk? The New England...Ch. 1 - Association between Glycemic Load and Acne? An...Ch. 1 - Milk and Cartilage (Example 10) Cartilage is a...Ch. 1 - Autism and MMR Vaccine An article by Wakefield et...Ch. 1 - Prob. 55SECh. 1 - Effect of Confederates on Compliance A study was...Ch. 1 - A Salad a Day Keeps Stroke Away? The Harvard Heart...Ch. 1 - Does Drinking Sugary Beverages Lead to Dementia?...Ch. 1 - Secondhand Smoke Exposure and Young Children...Ch. 1 - Prob. 60CRECh. 1 - Speeding Tickets College students who were drivers...Ch. 1 - Prob. 62CRECh. 1 - Writing: Vitamin D Describe the design of a...Ch. 1 - Writing: Strokes People who have had strokes are...Ch. 1 - Yoga and High-Risk Adolescents Can mindful yoga...Ch. 1 - Neurofeedback and ADHD Some studies have indicated...Ch. 1 - Virtual Reality and Fall Risk A study was...Ch. 1 - Ear Infections Babies 6 to 23 months of age with...Ch. 1 - Effects of Light Exposure A study carried out by...Ch. 1 - Scared Straight The idea of sending delinquents to...
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