Statistics: Informed Decisions Using Data, Books a la Carte Edition plus NEW MyLab Statistics with Pearson eText-- Access Card Package (5th Edition)
5th Edition
ISBN: 9780134136783
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 3.2, Problem 54AYU
To determine
To explain: The reason for a higher standard deviation of the entire class than the standard deviation of males and females considered separately.
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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 3 Solutions
Statistics: Informed Decisions Using Data, Books a la Carte Edition plus NEW MyLab Statistics with Pearson eText-- Access Card Package (5th Edition)
Ch. 3.1 - 1. What does it mean if a statistic is resistant?
Ch. 3.1 - 2. In the 2013 Current Population Survey conducted...Ch. 3.1 - Prob. 3AYUCh. 3.1 - 4. A histogram of a set of data indicates that the...Ch. 3.1 - 5. If a data set contains 10,000 values arranged...Ch. 3.1 - 6. True or False: A data set will always have...Ch. 3.1 - In Problems 7–10, find the population mean or...Ch. 3.1 - Prob. 8AYUCh. 3.1 - In Problems 7–10, find the population mean or...Ch. 3.1 - In Problems 7–10, find the population mean or...
Ch. 3.1 - Prob. 11AYUCh. 3.1 - 12. The median for the given set of six ordered...Ch. 3.1 - 13. Miles per Gallon The following data represent...Ch. 3.1 - 14. Exam Time The following data represent the...Ch. 3.1 - 15. Concrete Mix A certain type of concrete mix is...Ch. 3.1 - 16. Flight Time The following data represent the...Ch. 3.1 - 17. For each of the three histograms shown,...Ch. 3.1 - 18. Match the histograms shown to the summary...Ch. 3.1 - Prob. 19AYUCh. 3.1 - 20. pH in Water The acidity or alkalinity of a...Ch. 3.1 - 21. Pulse Rates The following data represent the...Ch. 3.1 - 22. Travel Time The data on the next page...Ch. 3.1 - 23. Connection Time A histogram of the connection...Ch. 3.1 - 24. Journal Costs A histogram of the annual...Ch. 3.1 - 25. M&Ms The following data represent the weights...Ch. 3.1 - Prob. 26AYUCh. 3.1 - Prob. 27AYUCh. 3.1 - Prob. 28AYUCh. 3.1 - Prob. 29AYUCh. 3.1 - Prob. 30AYUCh. 3.1 - Prob. 31AYUCh. 3.1 - Prob. 32AYUCh. 3.1 - Prob. 33AYUCh. 3.1 - Prob. 34AYUCh. 3.1 - Prob. 35AYUCh. 3.1 - 36. Sullivan Survey Go to...Ch. 3.1 - Prob. 37AYUCh. 3.1 - 38. Linear Transformations Use the five test...Ch. 3.1 - Prob. 39AYUCh. 3.1 - Prob. 40AYUCh. 3.1 - Prob. 41AYUCh. 3.1 - Prob. 42AYUCh. 3.1 - Prob. 43AYUCh. 3.1 - 44. A researcher with the Department of Energy...Ch. 3.1 - Prob. 45AYUCh. 3.1 - 46. You are negotiating a contract for the Players...Ch. 3.1 - Prob. 47AYUCh. 3.1 - Prob. 48AYUCh. 3.2 - 1. The sum of the deviations about the mean always...Ch. 3.2 - 2. The standard deviation is used in conjunction...Ch. 3.2 - 3. True or False: When comparing two populations,...Ch. 3.2 - Prob. 4AYUCh. 3.2 - Prob. 5AYUCh. 3.2 - Prob. 6AYUCh. 3.2 - In Problems 5–10, by hand, find the population...Ch. 3.2 - Prob. 8AYUCh. 3.2 - Prob. 9AYUCh. 3.2 - Prob. 10AYUCh. 3.2 - 11. Miles per Gallon The following data represent...Ch. 3.2 - 12. Exam Time The following data represent the...Ch. 3.2 - Prob. 13AYUCh. 3.2 - Prob. 14AYUCh. 3.2 - 15. Which histogram depicts a higher standard...Ch. 3.2 - 16. Match the histograms in the next column to the...Ch. 3.2 - 17. Exam Scores The following data represent exam...Ch. 3.2 - 18. pH in Water The acidity or alkalinity of a...Ch. 3.2 - 19. Pulse Rates The data on the following page...Ch. 3.2 - Prob. 20AYUCh. 3.2 - Prob. 21AYUCh. 3.2 - Prob. 22AYUCh. 3.2 - 23. The Empirical Rule The following data...Ch. 3.2 - 24. The Empirical Rule The following data...Ch. 3.2 - 25. Which Car Would You Buy? Suppose that you are...Ch. 3.2 - Prob. 26AYUCh. 3.2 - 27. Rates of Returns of Stocks Stocks may be...Ch. 3.2 - Prob. 28AYUCh. 3.2 - 29. The Empirical Rule The Stanford–Binet...Ch. 3.2 - 30. The Empirical Rule SAT Math scores have a...Ch. 3.2 - 31. The Empirical Rule The weight, in grams, of...Ch. 3.2 - 32. The Empirical Rule The distribution of the...Ch. 3.2 - Prob. 33AYUCh. 3.2 - Prob. 34AYUCh. 3.2 - NW 35. Chebyshev's Inequality In December 2014,...Ch. 3.2 - 36. Chebyshev's Inequality According to the U.S....Ch. 3.2 - Prob. 37AYUCh. 3.2 - Prob. 38AYUCh. 3.2 - 39. Resistance and Sample Size Each of the...Ch. 3.2 - Prob. 40AYUCh. 3.2 - Prob. 41AYUCh. 3.2 - Prob. 42AYUCh. 3.2 - Prob. 43AYUCh. 3.2 - 44. Coefficient of Skewness Karl Pearson developed...Ch. 3.2 - Prob. 45AYUCh. 3.2 - 46. More Spread? The data set on the left...Ch. 3.2 - Prob. 47AYUCh. 3.2 - Prob. 48AYUCh. 3.2 - Prob. 49AYUCh. 3.2 - 50. What is meant by the phrase degrees of freedom...Ch. 3.2 - Prob. 51AYUCh. 3.2 - Prob. 52AYUCh. 3.2 - Prob. 53AYUCh. 3.2 - Prob. 54AYUCh. 3.2 - Prob. 55AYUCh. 3.2 - Prob. 56AYUCh. 3.2 - Prob. 57AYUCh. 3.2 - 58. Draw two histograms with different standard...Ch. 3.2 - 59. Fast Pass In 2000, the Walt Disney Company...Ch. 3.3 - 1. Savings Recently, a random sample of 25–34 year...Ch. 3.3 - 2. Square Footage of Housing The frequency...Ch. 3.3 -
3. Household Winter Temperature Often, frequency...Ch. 3.3 - 4. Living in Poverty (See Problem 3.) The...Ch. 3.3 - 5. Multiple Births The following data represent...Ch. 3.3 - 6. Birth Weight The following frequency...Ch. 3.3 - Prob. 7AYUCh. 3.3 - Prob. 8AYUCh. 3.3 - 9. Grade-Point Average Marissa has just completed...Ch. 3.3 - 10. Computing Class Average In Marissa's calculus...Ch. 3.3 - 11. Mixed Chocolates Michael and Kevin want to buy...Ch. 3.3 - Prob. 12AYUCh. 3.3 - Prob. 13AYUCh. 3.3 - 14. Age of Mother The following data represent the...Ch. 3.3 - Prob. 15AYUCh. 3.3 - Prob. 16AYUCh. 3.3 - Prob. 17AYUCh. 3.3 - Prob. 18AYUCh. 3.4 - 1. The ______ represents the number of standard...Ch. 3.4 - Prob. 2AYUCh. 3.4 - 3. ______ divide data sets into fourths.
Ch. 3.4 - 4. The ______ ________ is the range of the middle...Ch. 3.4 - 5. Birth Weights Babies born after a gestation...Ch. 3.4 - 6. Birth Weights Babies born after a gestation...Ch. 3.4 - Prob. 7AYUCh. 3.4 - Prob. 8AYUCh. 3.4 - Prob. 9AYUCh. 3.4 - 10. Batting Champions The highest batting average...Ch. 3.4 - 11. Swim Ryan Murphy, nephew of the author, swims...Ch. 3.4 - 12. Triathlon Roberto finishes a triathlon...Ch. 3.4 - 13. School Admissions A highly selective boarding...Ch. 3.4 - Prob. 14AYUCh. 3.4 - Prob. 15AYUCh. 3.4 - 16. You Explain It! Percentiles Explain the...Ch. 3.4 - 17. You Explain It! Quartiles Violent crimes...Ch. 3.4 - 18. You Explain It! Quartiles One variable that is...Ch. 3.4 - Prob. 19AYUCh. 3.4 - 20. Ogives and Percentiles The following graph is...Ch. 3.4 - 21. SMART Car The following data represent the...Ch. 3.4 - 22. Hemoglobin in Cats The following data...Ch. 3.4 - Prob. 23AYUCh. 3.4 - Prob. 24AYUCh. 3.4 - 25. Fraud Detection As part of its "Customers...Ch. 3.4 - 26. Stolen Credit Card A credit card company has a...Ch. 3.4 - 27. Student Survey of Income A survey of 50...Ch. 3.4 - Prob. 28AYUCh. 3.4 - Prob. 29AYUCh. 3.4 - Prob. 30AYUCh. 3.4 - Prob. 31AYUCh. 3.4 - 32. Write a paragraph that explains the meaning of...Ch. 3.4 - Prob. 33AYUCh. 3.4 - Prob. 34AYUCh. 3.4 - Prob. 35AYUCh. 3.4 - Prob. 36AYUCh. 3.4 - Prob. 37AYUCh. 3.4 - Prob. 38AYUCh. 3.4 - Prob. 39AYUCh. 3.5 - 1. What does the five-number summary consist of?
Ch. 3.5 - 2. In a boxplot, if the median is to the left of...Ch. 3.5 - Prob. 3AYUCh. 3.5 - In Problems 3 and 4, (a) identify the shape of the...Ch. 3.5 - Prob. 5AYUCh. 3.5 - 6. Use the side-by-side boxplots shown to answer...Ch. 3.5 - 7. Exam Scores After giving a statistics exam,...Ch. 3.5 - 8. Speed Reading Jessica enrolled in a course that...Ch. 3.5 - 9. Age at Inauguration The following data...Ch. 3.5 - Prob. 10AYUCh. 3.5 - 11. Age of Mother at Birth The data below...Ch. 3.5 - Prob. 12AYUCh. 3.5 - 13. M&Ms In Problem 25 from Section 3.1, we drew a...Ch. 3.5 - Prob. 14AYUCh. 3.5 - Prob. 15AYUCh. 3.5 - 16. Chips per Cookie Do store-brand chocolate chip...Ch. 3.5 - 17. Putting It Together: Earthquakes Go to...Ch. 3.5 - 18. Putting It Together: Paternal Smoking It is...Ch. 3.5 - Prob. 19AYUCh. 3.5 - Prob. 20AYUCh. 3.5 - 21. Explain how to determine the shape of a...Ch. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - 5. Chebyshev's Inequality and the Empirical Rule...Ch. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - 10. Presidential Inaugural Addresses Ever wonder...Ch. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - 4. (a) Determine the standard deviation of the...Ch. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - 1. Generate a data set consisting of the length of...Ch. 3 - Prob. 2CSCh. 3 - Prob. 3CSCh. 3 - 4. What other information would be useful to...
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