The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 9.2, Problem 8MS
Will tomorrow be different? At the beginning of this section’s Mindscapes, data were given on the cost of home Internet access in 2009. If similar data were collected in 2020, do you think that the distribution of the data would be much different? Why or why not? (Hint Do you think there will be differences in the use and cost of Internet acccss in 2020?)
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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?
The Course Name Real Analysis please Solve questions by Real Analysis
Chapter 9 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 9.1 - Embarrassing data. Suppose you asked 100 students...Ch. 9.1 - Hugging both parents (S). You ask 150 students to...Ch. 9.1 - Short test. To save time grading, a professor asks...Ch. 9.1 - Computer polls. Suppose dot-corn entrepreneurs...Ch. 9.1 - Voluntary grade inflation. The dean felt that a...Ch. 9.1 - Pornography (ExH). Suppose you asked 100 students...Ch. 9.1 - Cartoons. Suppose 380 students out of 1000 still...Ch. 9.1 - Bias beef (H). Suppose you have an assignment to...Ch. 9.1 - Drug data (ExH). You ask 250 students to answer...Ch. 9.1 - Kissing. You ask 180 students to answer the...
Ch. 9.1 - Cheating (S). Suppose 60 students out of 200...Ch. 9.1 - Dental hygiene. Suppose you want to know how often...Ch. 9.1 - More homework. In a recent survey of random...Ch. 9.1 - PBS. In the old days, the Nielsen ratings of...Ch. 9.1 - 9:00 AM versus 9:00 PM (H). You take a survey of...Ch. 9.1 - Internet askew. Find ads or articles on the Web...Ch. 9.1 - Sleazy survey (H). The mayor of a city seeks to...Ch. 9.1 - Bread winners? You want to know in what percentage...Ch. 9.1 - Beemer babies (H). You want to estimate what...Ch. 9.1 - Coffee, tea, or milk? Youre considering whether to...Ch. 9.1 - The dog pound. Otis the puppy grew approximately...Ch. 9.1 - Hows that again? An ambitious politician in your...Ch. 9.1 - Smells like team spirit. A losing basketball team...Ch. 9.1 - Stack me timbers. Every October, students from the...Ch. 9.1 - Risky business (H). In a psychology class, the...Ch. 9.1 - Risky II. The psychology instructor from the...Ch. 9.2 - Internet costs. Make a histogram of the data on...Ch. 9.2 - Internet costs—summaries (S). Find the mean and...Ch. 9.2 - Internet costs-more summaries. Compute the...Ch. 9.2 - How variable. Remember that the standard deviation...Ch. 9.2 - Pie or no pie. Below are two graphical...Ch. 9.2 - Stats on steroids. Harry Bonds and Mark McGwire...Ch. 9.2 - Whos the best—short summary. For the home-run...Ch. 9.2 - Will tomorrow be different? At the beginning of...Ch. 9.2 - How different are they? (S) The following...Ch. 9.2 - Whats normal? The histograms of three data sets...Ch. 9.2 - Check the bounce (ExH). Until 1992, members of...Ch. 9.2 - College data. Using the student survey data given...Ch. 9.2 - News data. Find some data in a recent newspaper or...Ch. 9.2 - Which half? Half of the people in the United...Ch. 9.2 - Grades. A student received the following quiz...Ch. 9.2 - Raising scores (ExH). A student received the...Ch. 9.2 - Mean and median (S). Give an example of a data set...Ch. 9.2 - Median and mean. Give an example of a data set...Ch. 9.2 - Some taxing statistics (H). Politicians love to...Ch. 9.2 - Whoops. Find an example in a recent newspaper or...Ch. 9.2 - Further whoops (H). A survey of 100 recent college...Ch. 9.2 - Is this normal? Suppose the data in the previous...Ch. 9.2 - Average the grades. In a math class of 23 men and...Ch. 9.2 - Taxes(ExH). Find an effective graphical...Ch. 9.2 - Kids in the hall. You have three cousins with mean...Ch. 9.2 - Testing the data. A math instructor reports the...Ch. 9.2 - One mean mean. Suppose an instructor reports exam...Ch. 9.2 - Home sweet home. For a political science project,...Ch. 9.2 - No back up (H). You have 120 pieces of data. They...Ch. 9.3 - I.D. please. Identify the Distributions below as...Ch. 9.3 - Deviating from the norm (H). The following three...Ch. 9.3 - Match quest. The following three data sets are...Ch. 9.3 - Doubt the dice. You have four different dice and...Ch. 9.3 - More matching. A class was quizzed on two...Ch. 9.3 - Gas guzzling. In the One-Die Random Gas Station...Ch. 9.3 - Dr Die. Suppose you doctor a standard six-sided...Ch. 9.3 - Dr. Mean (S). What is the mean roll you would...Ch. 9.3 - A podiatrist in the making. Suppose you ask the...Ch. 9.3 - Beanie babies (S). All freshmen entering...Ch. 9.3 - Retiring standards (ExH). A classmate describes a...Ch. 9.3 - Unseasonable weather. The average high temperature...Ch. 9.3 - Are you normal? Which of the following data sets...Ch. 9.3 - Warming Up? (H) Suppose we measure the temperature...Ch. 9.3 - Possibly uniform. Which of the following data sets...Ch. 9.3 - Under the normally spreading chestnut tree. A...Ch. 9.3 - Abnormal. Give two example of data sets from your...Ch. 9.3 - Heavry petting. You adopt a kitten from the animal...Ch. 9.3 - Less than normal. Here are some distributions that...Ch. 9.3 - Gas guzzling (ExH). Consider the Two-Dice Random...Ch. 9.3 - The 68-95-99.7rule. Referring back to a discussion...Ch. 9.3 - Heads up. The marching band is getting new...Ch. 9.3 - Knees up. Building on the previous Mindscape,...Ch. 9.3 - Mother Brown (H). The most popular pizza place...Ch. 9.3 - Scoring some Zs. Refer to the formula for the...Ch. 9.3 - 2Catchin some Zs. You happen to know the z-score...Ch. 9.4 - Sophomore survey. You want to survey all students...Ch. 9.4 - IntenaI confidence. Which of the following best...Ch. 9.4 - Voting bodies. Calculate the percentage of the...Ch. 9.4 - Play the percentages. If n=100, what is the value...Ch. 9.4 - Play the percentages backwards (S). If 1n=0.05...Ch. 9.4 - Election up for grabs. In the upcoming election...Ch. 9.4 - U.S. samples (S). Suppose you can be quite...Ch. 9.4 - Bigger confidence? Suppose a pollster reports that...Ch. 9.4 - Overlapping confidence. Suppose two surveys are...Ch. 9.4 - Does size matter? (ExH) You want to gather data...Ch. 9.4 - More voting bodies (H). You want to gather data...Ch. 9.4 - National poll. Suppose you do polling in each of...Ch. 9.4 - Dizzy Lincoln. The text describes a penny-spinning...Ch. 9.4 - Hire a consultant. A consulting firm analyzed...Ch. 9.4 - House of cards. Your friend hands you a deck of 52...Ch. 9.4 - A fish story (ExH). You are a biologist sampling...Ch. 9.4 - Political gamble. The mayor of a small city has...Ch. 9.4 - The power of placebo. A study of pain relief...Ch. 9.4 - Marge Innoverra. You test 100 light bulbs randomly...Ch. 9.4 - How many math students does it take …(S). How...Ch. 9.4 - … to screw in a lightbulb? How many light bulbs...Ch. 9.4 - Snack sample (H). A survey asking students whether...Ch. 9.4 - Stop the study (ExH). A 2006 NIH study of...Ch. 9.4 - The sniff test. In 2004 the British Medical...Ch. 9.4 - Roving report. In 2006 there was a scandal...Ch. 9.4 - Polling roundup (H). A polling organization wants...Ch. 9.4 - Rodent roundup. Your psychology class is planning...Ch. 9.4 - Even more confident. Mindscape 27 gives a more...Ch. 9.4 - ESP. Your psychology class does some experiments...Ch. 9.4 - Trying trials. Your roommate is supervising an...Ch. 9.5 - Mendels snapdragons. Another of Mendels...Ch. 9.5 - Telephone/soda twins. Suppose your school has 1000...Ch. 9.5 - Correlation comparison. Below are three...Ch. 9.5 - Percent practice. Convert the fractions below to...Ch. 9.5 - Family dinner. Recent studies have reported on the...Ch. 9.5 - More Mendel (S). Given Mendels snapdragon...Ch. 9.5 - Oedipus red. Given Mendels work described in...Ch. 9.5 - Oedipus white. Given Mende1 work described in...Ch. 9.5 - Prob. 9MSCh. 9.5 - Astrology. An experiment is done to test the value...Ch. 9.5 - Stressful diet. One hundred young women were given...Ch. 9.5 - Abstinence evidence? President George W. Bush...Ch. 9.5 - Matching correlations. Below are some scatterplots...Ch. 9.5 - Fast data (H). If you plot the wining Olympic mens...Ch. 9.5 - College town. You go to school in a college town....Ch. 9.5 - Car count (S). You wonder how many cars there are...Ch. 9.5 - For Mindscapes 19-22, say whether or not each is...Ch. 9.5 - For Mindscapes 19-22, say whether or not each is...Ch. 9.5 - For Mindscapes 19-22, say whether or not each is...Ch. 9.5 - For Mindscapes 19-22, say whether or not each is...Ch. 9.5 - Mendel genealogy (H). We return once again to...Ch. 9.5 - Martian genetics. A certain alien species has...Ch. 9.5 - More Martians. Given the scenario from the...Ch. 9.5 - Politics as usual. During the presidential...Ch. 9.5 - Going postal. Your company will sign a contract...Ch. 9.5 - Fast paradox (ExH). The correlation between year...Ch. 9.5 - Up and down. In the past year, the grade point...Ch. 9.5 - Modified Mendel. We again return to Mendel...Ch. 9.5 - Going extinct. A paleontologist has gathered data...Ch. 9.5 - Diners delight. There are five dining halls on...Ch. 9.5 - The candy man. Your math instructor brings a...Ch. 9.5 - The candy jars. Your math instructor brings two...Ch. 9.5 - Correlated chorus (H). The chorus has data on the...Ch. 9.5 - Correlated Britney. The Britney S. Fan Club has...
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