Pearson eText for Basic Business Statistics -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137400119
Author: MARK BERENSON, David Levine
Publisher: PEARSON+
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Chapter 8, Problem 52PS
Why is it true that for a given
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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.)
Chapter 8 Solutions
Pearson eText for Basic Business Statistics -- Instant Access (Pearson+)
Ch. 8 - If X=85, =8,andn=64, construct a 95 confidence...Ch. 8 - If X=125,=24,andn=36, construct a 99 confidence...Ch. 8 - Why is it not possible in Example 8.1 on page 280...Ch. 8 - Is it true in Example 8.1 on page 280 that you do...Ch. 8 - A market researcher selects a simple random sample...Ch. 8 - Suppose that you are going to collect a set of...Ch. 8 - Consider the confidence interval estimate...Ch. 8 - You are working as an assistant to the dean of...Ch. 8 - A bottled water distributor wants to estimate the...Ch. 8 - The operations manager at a light emitting diode...
Ch. 8 - If X=75,S=24,andn=36, and assuming that the...Ch. 8 - Determine the critical value of t in each of the...Ch. 8 - Assuming that the populations is normally...Ch. 8 - Assuming that the population is normally...Ch. 8 - A marketing researcher wants to estimate the mean...Ch. 8 - A survey of nonprofit organizations showed that...Ch. 8 - The U.S. Department of Transportation requires...Ch. 8 - The file FastFood contains the amount that a...Ch. 8 - The file AirportRating contains the rating of...Ch. 8 - The annual NFL Super Bowl is the most widely...Ch. 8 - Is there a difference in the yields of different...Ch. 8 - One of the major measures of the quality of...Ch. 8 - A manufacturing company produces electric...Ch. 8 - The file MobileCommerce contains mobile commerce...Ch. 8 - One operation of a mill is cut pieces of steel...Ch. 8 - Ifn=200andX=50, Construct a 95 confidence interval...Ch. 8 - ifn=400andX=25, Construct a 99 confidence interval...Ch. 8 - A cellphone provider has the business objective of...Ch. 8 - In a survey of 1,003 adults concerning complaints...Ch. 8 - What do you value most when shopping in a retail...Ch. 8 - In a survey of 823 human resource professionals...Ch. 8 - A Pew Research Center survey of 4,787 adults found...Ch. 8 - What business, economic, policy and environmental...Ch. 8 - If you want to be 95 confident of estimating the...Ch. 8 - If you want to be 99 confident of estimating of...Ch. 8 - If you want to be 99 confident of estimating the...Ch. 8 - If you want to be 95 confident of estimating the...Ch. 8 - A survey is planned to determine the mean annual...Ch. 8 - If the manager of a bottled water distributor...Ch. 8 - If a light bulb manufacturing company wants to...Ch. 8 - If the inspection division of a county weights and...Ch. 8 - An advertising media analyst wants to estimate the...Ch. 8 - An advertising media analyst wants to estimate the...Ch. 8 - A growing niche in the restaurant business is...Ch. 8 - What does brand loyalty mean to consumers?...Ch. 8 - A Federal Reserve Bank of Atlanta report looks at...Ch. 8 - In a study of 443 nonprofits nationwide, 130...Ch. 8 - Cybersecurity is a critical business issue that...Ch. 8 - Personal data is the new currency of the digital...Ch. 8 - Why can you never really have 100 confidence of...Ch. 8 - When should you use the t distribution to develop...Ch. 8 - Why is it true that for a given sample size, n an...Ch. 8 - Why is the sample size needed to determine the...Ch. 8 - GlobalWablndex study noted the percentage of...Ch. 8 - How do smartphone owners use their smartphones...Ch. 8 - A market researcher for a consumer electronics...Ch. 8 - An information technology (IT) provider of cloud...Ch. 8 - The human resource (HR) director of a large...Ch. 8 - A national association devoted to HR and workplace...Ch. 8 - The financial impact of IT system downtime is a...Ch. 8 - The branch manager of an outlet (Store 1) of a...Ch. 8 - Scarlett and Heather, the owners of an upscale...Ch. 8 - The manufacturer of Ice Melt claims that its...Ch. 8 - Claims fraud (illegitimate claims) and buildup...Ch. 8 - A quality characteristic of interest for a...Ch. 8 - Call centers today play an important role in...Ch. 8 - The manufacturer of Boston and Vermont asphalt...Ch. 8 - The manufacturer of Boston and Vermont asphalt...Ch. 8 - Referring to the results in Problem 8.66...
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