An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Chapter 4.18, Problem 1E
Indicate which interpretation of the
- a. A casino in New Jersey posts a probability of .02 that the Dallas Cowboys will win Super Bowl L.
- b. A purchaser of a single ticket in the Texas Powerball has a probability of 1/175,223,510 of winning the big payout.
- c. The quality control engineer of a large pharmaceutical firm conducts an intensive process reliability study. Based on the findings of the study, the engineer claims that the probability that a bottle of a newly produced drug will have a shelf life greater than 2 years is .952.
- d. The probability that the control computer on a nuclear power plant and its backup will both fail is .00001.
- e. The state meteorologist of Michigan reports that there is a 70/30 chance that the rainfall during the months of June through August in 2014 will be below normal; that is, there is a .70 probability of the rainfall being below normal and a .30 probability of the rainfall being above normal.
- f. A miniature tablet that is small enough to be worn as a watch is in beta testing. In a preliminary report, the company states that more than 55% the 500 testers found the device to be easier to use than a full-sized tablet. The probability of this happening is .011 provided there is no difference in ease of use of the two devices.
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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 4 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 4.18 - Indicate which interpretation of the probability...Ch. 4.18 - If you are having a stroke, it is critical that...Ch. 4.18 - In reporting highway safety, the National Highway...Ch. 4.18 - In a cable TV program concerning the risk of...Ch. 4.18 - The gaming commission in its annual examination of...Ch. 4.18 - The state vehicle inspection bureau provided the...Ch. 4.18 - The Texas Lottery has a game, Daily 4, in which a...Ch. 4.18 - A die is rolled two times. Provide a list of the...Ch. 4.18 - Refer to Exercise 4.10. Assume that the die is a...Ch. 4.18 - Refer to Exercise 4.11. a. Describe the event that...
Ch. 4.18 - Refer to Exercise 4.11. a. Are events A and B...Ch. 4.18 - A credit union takes a sample of four mortgages...Ch. 4.18 - A nuclear power plant has double redundancy on the...Ch. 4.18 - The population distribution in the United States...Ch. 4.18 - The makers of the candy MMs report that their...Ch. 4.18 - Refer to Exercise 4.11. Compute the following...Ch. 4.18 - Prob. 19ECh. 4.18 - Prob. 20ECh. 4.18 - Refer to Exercise 4.16. Let W be the event that...Ch. 4.18 - Is it possible for events A and B to be both...Ch. 4.18 - A survey of 1,000 U.S. government employees who...Ch. 4.18 - Refer to Exercise 4.23. Define the following...Ch. 4.18 - Prob. 25ECh. 4.18 - A large corporation has spent considerable time...Ch. 4.18 - The utility company in a large metropolitan area...Ch. 4.18 - Prob. 28ECh. 4.18 - Of a finance companys loans, 1% are defaulted (not...Ch. 4.18 - Refer to Exercise 4.29. Show that the posterior...Ch. 4.18 - Prob. 31ECh. 4.18 - In Example 4.4, compute the probability that the...Ch. 4.18 - Prob. 33ECh. 4.18 - In a January 15, 1998, article, the New England...Ch. 4.18 - Prob. 35ECh. 4.18 - Classify each of the following random variables as...Ch. 4.18 - Prob. 37ECh. 4.18 - Texting while driving is a very dangerous...Ch. 4.18 - Prob. 39ECh. 4.18 - The numbers of cars failing an emissions test on...Ch. 4.18 - A traditional call center has a simple mission:...Ch. 4.18 - A biologist randomly selects 10 portions of water,...Ch. 4.18 - Examine the accompanying newspaper clipping. Does...Ch. 4.18 - A survey is conducted to estimate the percentage...Ch. 4.18 - In an attempt to decrease drunk driving, police...Ch. 4.18 - The quality control department examines all the...Ch. 4.18 - Prob. 47ECh. 4.18 - The CFO of a hospital is concerned about the risk...Ch. 4.18 - Suppose the random variable y has a Poisson...Ch. 4.18 - Customers arrive at a grocery store checkout at a...Ch. 4.18 - A firm is considering using the Internet to...Ch. 4.18 - Prob. 52ECh. 4.18 - Prob. 53ECh. 4.18 - Prob. 54ECh. 4.18 - Prob. 55ECh. 4.18 - Prob. 56ECh. 4.18 - Prob. 57ECh. 4.18 - Prob. 58ECh. 4.18 - Prob. 59ECh. 4.18 - Prob. 60ECh. 4.18 - In Exercises 4.57 through 4.63, let z be a random...Ch. 4.18 - Prob. 62ECh. 4.18 - Prob. 63ECh. 4.18 - Prob. 64ECh. 4.18 - Let y be a random variable having a normal...Ch. 4.18 - Suppose that y is a random variable having a...Ch. 4.18 - Suppose that z is a random variable having a...Ch. 4.18 - Prob. 68ECh. 4.18 - Records maintained by the office of budget in a...Ch. 4.18 - The College Boards, which are administered each...Ch. 4.18 - Monthly sales figures for a particular food...Ch. 4.18 - Refer to Exercise 4.70. An honor society wishes to...Ch. 4.18 - Prob. 73ECh. 4.18 - Prob. 74ECh. 4.18 - A psychologist is interested in studying women who...Ch. 4.18 - Prob. 76ECh. 4.18 - A random sample of 16 measurements is drawn from a...Ch. 4.18 - Prob. 78ECh. 4.18 - Psychomotor retardation scores for a particular...Ch. 4.18 - Federal resources have been tentatively approved...Ch. 4.18 - Refer to Exercise 4.80. What size facility should...Ch. 4.18 - Based on the 1990 census, the number of hours per...Ch. 4.18 - The level of a particular pollutant, nitrogen...Ch. 4.18 - Refer to Exercise 4.83. A company has a fleet of...Ch. 4.18 - The baggage limit for an airplane is set at 100...Ch. 4.18 - A patient visits her doctor with concerns about...Ch. 4.18 - Critical key-entry errors in the data processing...Ch. 4.18 - Prob. 88ECh. 4.18 - Let y be a binomial random variable with n = 10...Ch. 4.18 - Prob. 90ECh. 4.18 - A marketing research firm advises a new client...Ch. 4.18 - Prob. 92ECh. 4.18 - Suppose a population consists of the 10...Ch. 4.18 - The fracture toughness in concrete specimens is a...Ch. 4.18 - One way to audit expense accounts for a large...Ch. 4.18 - The breaking strengths for 1-foot-square samples...Ch. 4.18 - Refer to Exercise 4.96. Suppose that a new...Ch. 4.18 - Refer to Exercise 4.97. Suppose that the mean...Ch. 4.18 - Prob. 99SECh. 4.18 - Prob. 100SECh. 4.18 - Experts consider high serum cholesterol levels to...Ch. 4.18 - Prob. 102SECh. 4.18 - Prob. 103SECh. 4.18 - Prob. 104SECh. 4.18 - Prob. 105SECh. 4.18 - Prob. 106SECh. 4.18 - Refer to Exercise 4.106. Plot the sampling...Ch. 4.18 - Random samples of size 5, 20, and 80 are drawn...Ch. 4.18 - Prob. 109SECh. 4.18 - Suppose the probability that a major earthquake...Ch. 4.18 - Prob. 111SECh. 4.18 - Airlines overbook (sell more tickets than there...Ch. 4.18 - Prob. 113SECh. 4.18 - As part of a study to determine factors that may...
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