Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter 4.2, Problem 1AYU
The difference between the observed and predicted value of y is the error, or __________.
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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
Fundamentals of Statistics (5th Edition)
Ch. 4.1 - What is the difference between univariate data and...Ch. 4.1 - The _____ variable is the variable whose value can...Ch. 4.1 - A _____ _____ is a graph that shows the relation...Ch. 4.1 - What does it mean to say two variables are...Ch. 4.1 - If r = _____, then a perfect negative linear...Ch. 4.1 - True or False: If the linear correlation...Ch. 4.1 - A _____ variable is a variable that is related to...Ch. 4.1 - True or False: Correlation implies causation.Ch. 4.1 - In Problems 912, determine whether the scatter...Ch. 4.1 - In Problems 912, determine whether the scatter...
Ch. 4.1 - In Problems 912, determine whether the scatter...Ch. 4.1 - In Problems 912, determine whether the scatter...Ch. 4.1 - NW Match the linear correlation coefficient to the...Ch. 4.1 - Match the linear correlation coefficient to the...Ch. 4.1 - Prob. 15AYUCh. 4.1 - Relation between Education and Birthrate? The...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - In Problems 1720, (a) draw a scatter diagram of...Ch. 4.1 - Name the Relation, Part I For each of the...Ch. 4.1 - Prob. 22AYUCh. 4.1 - The TIMMS Exam The Trends in International...Ch. 4.1 - Prob. 24AYUCh. 4.1 - NW An Unhealthy Commute The Gallup Organization...Ch. 4.1 - Credit Scores Your Fair Isaacs Corporation (FICO)...Ch. 4.1 - Height versus Head Circumference A pediatrician...Ch. 4.1 - American Black Bears The American black bear...Ch. 4.1 - Weight of a Car versus Miles per Gallon An...Ch. 4.1 - Hurricanes The data in the next column represent...Ch. 4.1 - CEO Performance The following data represent the...Ch. 4.1 - Bear Markets A bear market in the stock market is...Ch. 4.1 - Does Size Matter? Researchers wondered whether the...Ch. 4.1 - Prob. 34AYUCh. 4.1 - Weight of a Car versus Miles per Gallon Suppose...Ch. 4.1 - American Black Bears The website that contained...Ch. 4.1 - Draw Your Data! Consider the four data sets shown...Ch. 4.1 - Predicting Winning Percentage The ultimate goal in...Ch. 4.1 - Prob. 39AYUCh. 4.1 - Lyme Disease versus Drownings Lyme disease is an...Ch. 4.1 - Prob. 41AYUCh. 4.1 - Prob. 42AYUCh. 4.1 - Crime Rate and Cell Phones The linear correlation...Ch. 4.1 - Prob. 44AYUCh. 4.1 - Influential Consider the following set of data: a....Ch. 4.1 - Prob. 46AYUCh. 4.1 - Prob. 47AYUCh. 4.1 - Prob. 48AYUCh. 4.1 - What does it mean to say that the linear...Ch. 4.1 - What does it mean if r = 0?Ch. 4.1 - Prob. 51AYUCh. 4.1 - Prob. 52AYUCh. 4.1 - Explain the difference between correlation and...Ch. 4.1 - Suppose that two variables, x and y, are...Ch. 4.2 - The difference between the observed and predicted...Ch. 4.2 - If the linear correlation between two variables is...Ch. 4.2 - Prob. 3AYUCh. 4.2 - Prob. 4AYUCh. 4.2 - For the data set a. Draw a scatter diagram....Ch. 4.2 - For the data set a. Draw a scatter diagram....Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - Prob. 9AYUCh. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - In Problems 712: a. By hand, draw a scatter...Ch. 4.2 - NW Income and Education In Problem 15 from Section...Ch. 4.2 - You Explain It! Study Time and Exam Scores After...Ch. 4.2 - Age Gap at Marriage Is there a relation between...Ch. 4.2 - You Explain It! CO2 and Energy Production The...Ch. 4.2 - NW An Unhealthy Commute (Refer to Problem 25,...Ch. 4.2 - Credit Scores (Refer to Problem 26, Section 4.1.)...Ch. 4.2 - Height versus Head Circumference (Refer to Problem...Ch. 4.2 - Prob. 20AYUCh. 4.2 - Weight of a Car versus Miles per Gallon (Refer to...Ch. 4.2 - Hurricanes (Refer to Problem 30, Section 4.1) The...Ch. 4.2 - Cola Consumption vs. Bone Density Example 5 in...Ch. 4.2 - Attending Class The following data represent the...Ch. 4.2 - CEO Performance (Refer to Problem 31 in Section...Ch. 4.2 - Bear Markets (Refer to Problem 32, Section 4.1) A...Ch. 4.2 - Male vs. Female Drivers (Refer to Problem 34,...Ch. 4.2 - Graduation Rates Go to...Ch. 4.2 - Putting It Together: Housing Prices One of the...Ch. 4.2 - Putting It Together: Smoking and Birth Weight It...Ch. 4.2 - What is a residual? What does it mean when a...Ch. 4.2 - Explain the phrase outside the scope of the model....Ch. 4.2 - Explain what each point on the least-squares...Ch. 4.3 - The _____ _____ _____, R2, measures the proportion...Ch. 4.3 - Total deviation = _____ deviation + _____...Ch. 4.3 - Match each coefficient of determination to a...Ch. 4.3 - NW The Other Old Faithful Perhaps you are familiar...Ch. 4.3 - Concrete As concrete cures, it gains strength. The...Ch. 4.3 - Prob. 7AYUCh. 4.3 - Problems 712 use the results from Problems 2530 in...Ch. 4.3 - Prob. 9AYUCh. 4.3 - Problems 712 use the results from Problems 2530 in...Ch. 4.3 - Problems 712 use the results from Problems 2530 in...Ch. 4.3 - Prob. 12AYUCh. 4.3 - Weight of a Car versus Miles per Gallon Suppose...Ch. 4.3 - American Black Bears Suppose that we find a bear...Ch. 4.3 - Putting It Together: Exam Scores The data below...Ch. 4.3 - Sullivan Survey II Go to...Ch. 4.4 - What is meant by a marginal distribution? What is...Ch. 4.4 - Refer to Table 8. Is constructing a conditional...Ch. 4.4 - Prob. 3AYUCh. 4.4 - Explain the idea behind Simpsons Paradox.Ch. 4.4 - In Problems 5 and 6, a. Construct a frequency...Ch. 4.4 - In Problems 5 and 6, a. Construct a frequency...Ch. 4.4 - Made in America In a recent Harris Poll, a random...Ch. 4.4 - Desirability Traits In a recent Harris Poll, a...Ch. 4.4 - NW Party Affiliation Is there an association...Ch. 4.4 - Prob. 10AYUCh. 4.4 - Health and Happiness The General Social Survey...Ch. 4.4 - Happy in Your Marriage? The General Social Survey...Ch. 4.4 - Prob. 13AYUCh. 4.4 - Treating Kidney Stones Researchers conducted a...Ch. 4.4 - Sullivan Survey II Go to...Ch. 4 - Basketball Spreads In sports betting, Las Vegas...Ch. 4 - Fat and Calories in Cheeseburgers A nutritionist...Ch. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - a. Draw a scatter diagram treating x as the...Ch. 4 - Use the results from Problems 2 and 4 to compute...Ch. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - New versus Used Car Satisfaction Are you more...Ch. 4 - Unemployment Rates Recessions are an economic...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 1CTCh. 4 - Use the data from Problem 1. a. Find the...Ch. 4 - Use the results from Problems 1 and 2 to compute...Ch. 4 - The following data represent the speed of a car...Ch. 4 - Prob. 5CTCh. 4 - Prob. 6CTCh. 4 - Consider the following contingency table, which...Ch. 4 - What would you say about a set of quantitative...Ch. 4 - If the slope of a least-squares regression line is...Ch. 4 - What does it mean if a linear correlation...
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