Essentials of Statistics (6th Edition)
6th Edition
ISBN: 9780134685779
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 3.2, Problem 19BSC
In Exercises 5-20, find the
19. California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?
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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
Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro-
priate for pricing options in practice. Give one reason that would substantiate this claim?
Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager
asks you to pick only one of them to invest in based on the model provided. Which one do you
choose and why ?
Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price
at time t of a European put with maturity T and strike price K. Then, the discounted option
price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.)
Question 4. You are considering pricing an American put option using a Black-Scholes model
for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no
more than 2 sentences), explain how you would proceed to price it.
Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the
interest rate…
Chapter 3 Solutions
Essentials of Statistics (6th Edition)
Ch. 3.1 - Average The defunct website IncomeTaxList.com...Ch. 3.1 - Whats Wrong? USA Today published a list consisting...Ch. 3.1 - Measures of Center In what sense are the mean,...Ch. 3.1 - Resistant Measures Here are four of the Verizon...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...
Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - Weighted Mean A student of the author earned...Ch. 3.1 - Weighted Mean A student of the author earned...Ch. 3.1 - Degrees of Freedom Five pulse rates randomly...Ch. 3.1 - Censored Data Data Set 15 Presidents in Appendix B...Ch. 3.1 - Trimmed Mean Because the mean is very sensitive to...Ch. 3.1 - Harmonic Mean The harmonic mean is often used as a...Ch. 3.1 - Geometric Mean The geometric mean is often used in...Ch. 3.1 - Quadratic Mean The quadratic mean (or root mean...Ch. 3.2 - Range Rule of Thumb for Estimating s The 20 brain...Ch. 3.2 - Range Rule of Thumb for Interpreting s The 20...Ch. 3.2 - Variance The 20 subjects used in Data Set 8 IQ and...Ch. 3.2 - Symbols Identify the symbols used for each of the...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - Identifying Significant Values with the Range Rule...Ch. 3.2 - Prob. 34BSCCh. 3.2 - Foot Lengths Based on Data Set 2 Foot and Height...Ch. 3.2 - Identifying Significant Values with the Range Rule...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - The Empirical Rule Based on Data Set 1 Body Data...Ch. 3.2 - The Empirical Rule Based on Data Set 3 Body...Ch. 3.2 - Chebyshevs Theorem Based on Data Set 1 Body Data...Ch. 3.2 - Chebyshevs Theorem Based on Data Set 3 Body...Ch. 3.2 - Why Divide by n 1? Let a population consist of...Ch. 3.2 - Mean Absolute Deviation Use the same population of...Ch. 3.3 - z Scores LeBron James, one of the most successful...Ch. 3.3 - Heights The boxplot shown below results from the...Ch. 3.3 - Boxplot Comparison Refer to the boxplots shown...Ch. 3.3 - z Scores If your score on your next statistics...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3 - Sleep Mean As part of the National Health and...Ch. 3 - Sleep Median What is the median of the sample...Ch. 3 - Sleep Mode What is the mode of the sample values...Ch. 3 - Sleep Variance The standard deviation of the...Ch. 3 - Prob. 5CQQCh. 3 - Sleep z Score A larger sample of 50 sleep times...Ch. 3 - Sleep Q3 For a sample of 80 sleep times,...Ch. 3 - Sleep 5-Number Summary For a sample of 100 sleep...Ch. 3 - Estimating s A large sample of sleep times...Ch. 3 - Sleep Notation Consider a sample of sleep times...Ch. 3 - Old Faithful Geyser Listed below are prediction...Ch. 3 - z Score Using the sample data from Exercise 1,...Ch. 3 - Boxplot Using the same prediction errors listed in...Ch. 3 - ER Codes In an analysis of activities that...Ch. 3 - Comparing Birth Weights The birth weights of a...Ch. 3 - Effects of an Outlier Listed below are platelet...Ch. 3 - Interpreting a Boxplot Shown below is a boxplot of...Ch. 3 - Estimating Standard Deviation Listed below is a...Ch. 3 - Prob. 1CRECh. 3 - Prob. 2CRECh. 3 - Stemplot Use the amounts of arsenic from Exercise...Ch. 3 - Prob. 4CRECh. 3 - Histogram The accompanying histogram depicts...Ch. 3 - Normal Distribution Examine the distribution shown...
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