Statistics: The Art and Science of Learning From Data, Books a la Carte Edition (4th Edition)
4th Edition
ISBN: 9780133860825
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Textbook Question
Chapter 2.1, Problem 5PB
Discrete/continuous
- a. Explain the difference between a discrete variable and a continuous variable.
- b. Give an example of each type.
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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 2 Solutions
Statistics: The Art and Science of Learning From Data, Books a la Carte Edition (4th Edition)
Ch. 2.1 - Categorical/quantitative difference a. Explain the...Ch. 2.1 - U.S. married-couple households According to a...Ch. 2.1 - Identify the variable type Identify each of the...Ch. 2.1 - Categorical or quantitative? Identify each of the...Ch. 2.1 - Discrete/continuous a. Explain the difference...Ch. 2.1 - Discrete or continuous? Identify each of the...Ch. 2.1 - Discrete or continuous 2 Repeat the previous...Ch. 2.1 - Prob. 8PBCh. 2.1 - Fatal Shark Attacks Few of the shark attacks...Ch. 2.2 - Generating Electricity In 2012 in the United...
Ch. 2.2 - What do alligators eat? The bar chart is from a...Ch. 2.2 - Prob. 12PBCh. 2.2 - Prob. 13PBCh. 2.2 - Prob. 14PBCh. 2.2 - Sugar dot plot For the breakfast cereal data given...Ch. 2.2 - Prob. 16PBCh. 2.2 - Graphing exam scores A teacher shows her class the...Ch. 2.2 - Fertility rates The fertility rate for a nation is...Ch. 2.2 - Split Stems The figure below shows the...Ch. 2.2 - Histogram for sugar For the breakfast cereal data,...Ch. 2.2 - Prob. 21PBCh. 2.2 - Prob. 22PBCh. 2.2 - Prob. 23PBCh. 2.2 - Prob. 24PBCh. 2.2 - Prob. 25PBCh. 2.2 - Prob. 26PBCh. 2.2 - Prob. 27PBCh. 2.2 - Warming in Newnan, Georgia? Access the Newnan, GA...Ch. 2.3 - Median versus mean For each of the following...Ch. 2.3 - Prob. 30PBCh. 2.3 - Prob. 31PBCh. 2.3 - Resistance to an outlier Consider the following...Ch. 2.3 - Income and health insurance According to the U.S....Ch. 2.3 - Prob. 34PBCh. 2.3 - Prob. 35PBCh. 2.3 - Prob. 36PBCh. 2.3 - Public transportationcenter The owner of a company...Ch. 2.3 - Prob. 38PBCh. 2.3 - Prob. 39PBCh. 2.3 - European fertility The European fertility rates...Ch. 2.3 - Sex partners A recent General Social Survey asked...Ch. 2.3 - Prob. 43PBCh. 2.3 - Prob. 44PBCh. 2.3 - Prob. 45PBCh. 2.4 - Sick leave A company decides to investigate the...Ch. 2.4 - Prob. 47PBCh. 2.4 - Prob. 48PBCh. 2.4 - Prob. 49PBCh. 2.4 - Exam standard deviation For an exam given to a...Ch. 2.4 - Heights For the sample heights of Georgia college...Ch. 2.4 - Histograms and standard deviation The figure shows...Ch. 2.4 - Female strength The High School Female Athletes...Ch. 2.4 - Female body weight The College Athletes data file...Ch. 2.4 - Shape of cigarette taxes A recent summary for the...Ch. 2.4 - Empirical rule and skewed, highly discrete...Ch. 2.4 - How much TV? The 2012 General Social Survey asked,...Ch. 2.4 - How many friends? A recent General Social Survey...Ch. 2.4 - Judging skew using x and s If the largest...Ch. 2.4 - Youth unemployment in the EU The Youth...Ch. 2.4 - Create data with a given standard deviation Use...Ch. 2.5 - Vacation days National Geographic Traveler...Ch. 2.5 - Youth unemployment In recent years, many European...Ch. 2.5 - Female strength The High School Female Athletes...Ch. 2.5 - Female body weight The College Athletes data file...Ch. 2.5 - Ways to measure variability The standard...Ch. 2.5 - Variability of cigarette taxes Heres the...Ch. 2.5 - Prob. 68PBCh. 2.5 - Infant mortality Africa The Human Development...Ch. 2.5 - Prob. 70PBCh. 2.5 - Computer use During a recent semester at the...Ch. 2.5 - Central Park temperature distribution revisited...Ch. 2.5 - Box plot for exam The scores on an exam have mean...Ch. 2.5 - Public transportation Exercise 2.37 described a...Ch. 2.5 - Prob. 75PBCh. 2.5 - Prob. 76PBCh. 2.5 - Prob. 77PBCh. 2.5 - Prob. 78PBCh. 2.5 - Prob. 79PBCh. 2.5 - Prob. 80PBCh. 2.5 - Prob. 81PBCh. 2.5 - Prob. 82PBCh. 2.6 - Great pay (on the average) The six full-time...Ch. 2.6 - Prob. 84PBCh. 2.6 - Prob. 85PBCh. 2.6 - Terrorism and war in Iraq In 2004, a college...Ch. 2.6 - Prob. 87PBCh. 2.6 - Prob. 88PBCh. 2 - Categorical or quantitative? Identify each of the...Ch. 2 - Continuous or discrete? Which of the following...Ch. 2 - Prob. 92CPCh. 2 - Cool in China A recent survey8 asked 1200...Ch. 2 - Prob. 94CPCh. 2 - Prob. 95CPCh. 2 - Prob. 96CPCh. 2 - Prob. 97CPCh. 2 - Prob. 98CPCh. 2 - Prob. 99CPCh. 2 - Prob. 100CPCh. 2 - Prob. 101CPCh. 2 - Prob. 103CPCh. 2 - Household net worth A study reported that in 2007...Ch. 2 - Prob. 105CPCh. 2 - Prob. 106CPCh. 2 - Prob. 107CPCh. 2 - Central Park monthly temperatures The MINITAB...Ch. 2 - Prob. 109CPCh. 2 - Female heights According to a recent report from...Ch. 2 - Energy and water consumption In parts a and b,...Ch. 2 - Prob. 112CPCh. 2 - More hurricane damage Refer to the previous...Ch. 2 - Prob. 114CPCh. 2 - Prob. 115CPCh. 2 - Prob. 116CPCh. 2 - Prob. 117CPCh. 2 - Temperatures in Central Park Access the Central...Ch. 2 - Teachers salaries According to Statistical...Ch. 2 - Prob. 120CPCh. 2 - What box plot do you expect? 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The mean, median, and mode can...Ch. 2 - Bad statistic A teacher summarizes grades on an...Ch. 2 - True or false: Soccer According to a story in the...Ch. 2 - Mean for grouped data Refer to the calculation of...Ch. 2 - Prob. 142CPCh. 2 - Range and standard deviation approximation Use the...Ch. 2 - Range the least resistant Weve seen that measures...Ch. 2 - Using MAD to measure variability The standard...Ch. 2 - Prob. 146CPCh. 2 - Create own data For the Mean Versus Median web...
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