Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Chapter 8, Problem 8.14TI
Suppose an Internet marketing company wants to determine the cunent percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion Is within five percentage points of the ue population proportion of customers who click on ads on their smartphones?
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Several markets (Japan, Switzerland) introduced negative interest rates on their money market.
In this problem, we will consider an annual interest rate r < 0. We consider a stock modeled
by an N-period CRR model where each period is 1 year (At = 1) and the up and down factors
are u and d.
(a) We consider an American put option with strike price K and expiration T. Prove that if
<0, the optimal strategy is to wait until expiration T to exercise.
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u = 0.1, the down factor is d = e−0.3 and r = 0. We remind you that in the CRR model, the
stock price at time tn is modeled (under P) by
Sta
=
So exp (μtn + σ√AtZn),
where (Zn) is a simple symmetric random walk.
(a) Find the parameters μ and σ for the CRR model described above.
(b) Find P
Ste
So
55/50
€ > 1).
StN
(c) Find lim P
804-N
(d) Determine q. (You can use e- 1 x.)
Ste
(e) Find Q
So
(f) Find lim Q
004-N
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In this problem, we consider a 3-period stock market model with evolution given in Fig. 1 below.
Each period corresponds to one year. The interest rate is r = 0%.
16
22
28
12
16
12
8
4
2
time
Figure 1: Stock evolution for Problem 1.
(a) A colleague notices that in the model above, a movement up-down leads to the same value
as a movement down-up. He concludes that the model is a CRR model. Is your colleague
correct? (Explain your answer.)
(b) We consider a European put with strike price K = 10 and expiration T = 3 years. Find
the price of this option at time 0. Provide the replicating portfolio for the first period.
(c) In addition to the call above, we also consider a European call with strike price K = 10
and expiration T = 3 years. Which one has the highest price? (It is not necessary to
provide the price of the call.)
(d) We now assume a yearly interest rate r = 25%. We consider a Bermudan put option with
strike price K = 10. It works like a standard put, but you can exercise it…
Chapter 8 Solutions
Introductory Statistics
Ch. 8 - Suppose we have data from a sample. The sample...Ch. 8 - Suppose average pizza delivery times are normally...Ch. 8 - Table 8.2 shows a different random sampling of 20...Ch. 8 - Refer back to the pizza-delivery Try It exercise....Ch. 8 - Refer back to the pizza-deliver Try It exercise....Ch. 8 - Suppose we know that a confidence interval is...Ch. 8 - The population standard deviation for the height...Ch. 8 - You do a study of hypnotherapy to determine how...Ch. 8 - A random sample of statistics students were asked...Ch. 8 - Suppose 250 randomly selected people are surveyed...
Ch. 8 - A student polls his school to see If students In...Ch. 8 - Out of a random sample of 65 freshmen at State...Ch. 8 - The Berkman Center Study referenced in Example...Ch. 8 - Suppose an Internet marketing company wants to...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use (he following information to answer the next...Ch. 8 - Use (he following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - 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Use the following information answer the next six...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use (he following information o answer the next...Ch. 8 - Use the following information o answer the next...Ch. 8 - Use the following information o answer the next...Ch. 8 - 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Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Use the following information to answer the next...Ch. 8 - Among various ethnic groups, the standard...Ch. 8 - Announcements for 8.1 upcoming engineering...Ch. 8 - Suppose that an accounting firm does a study to...Ch. 8 - A sample of 16 small bags of the same brand of...Ch. 8 - A camp director is interested in the mean number...Ch. 8 - What Is meant by the tetm 90% confident when...Ch. 8 - The Federal Election Commission collects...Ch. 8 - The American Community Survey (ACS), part of the...Ch. 8 - The average height of young adult males has a...Ch. 8 - In six packages of The Flintstones Real Fruit...Ch. 8 - A random survey of enrollment at 35 community...Ch. 8 - Suppose that a committee is studying whether or...Ch. 8 - A pharmaceutical company makes tranquilizers. It...Ch. 8 - Suppose that 14 children, who were learning to...Ch. 8 - The Federal Election Commission (FEC) collects...Ch. 8 - Forbes magazine published data on the best small...Ch. 8 - Unoccupied seats on flights cause airlines to lose...Ch. 8 - In a recent sample of 84 used car sales costs, the...Ch. 8 - Six different national brands of chocolate chip...Ch. 8 - A survey of the mean number of cents off that...Ch. 8 - Use the following information o ansier the next...Ch. 8 - Use the following information o ansier the next...Ch. 8 - Insurance companies are interested In knowing the...Ch. 8 - Suppose that the insurance companies did do a...Ch. 8 - According to a recent survey of 1,200 people. 61%...Ch. 8 - An article regarding interracial dating and...Ch. 8 - Refer to the information In Exercise 8.120. a....Ch. 8 - Stanford University conducted a study of whether...Ch. 8 - A telephone poll of 1,000 adult Americans was...Ch. 8 - Refer to Exercise 8.123. Another question in the...Ch. 8 - Use the following informariton to answer the next...Ch. 8 - Use the following informariton to answer the next...Ch. 8 - Use the following informariton to answer the next...Ch. 8 - Use the following information to answer the next v...Ch. 8 - Use the following information to answer the next v...Ch. 8 - On May 23, 2013, Gallup reported that of the 1,005...Ch. 8 - A national survey of 1000 adults was conducted on...Ch. 8 - Public Policy Polling recently conducted a survey...Ch. 8 - You plan to conduct a survey on your college...Ch. 8 - In a recent Zogby International Poll, nine of .18...
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