Statistics for Business & Economics, Revised (MindTap Course List)
12th Edition
ISBN: 9781285846323
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: South-Western College Pub
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Textbook Question
Chapter 5.6, Problem 44E
Consider a Poisson distribution with μ = 3.
- a. write the appropriate Poisson
probability function . - b. Compute f(2).
- c. Compute f(1).
- d. Compute P(x ≥ 2).
Expert Solution & Answer
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Students have asked these similar questions
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?
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
Chapter 5 Solutions
Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 5.1 - Consider the experiment of tossing a coin twice....Ch. 5.1 - Consider the experiment of a worker assembling a...Ch. 5.1 - Three students scheduled interviews for summer...Ch. 5.1 - In January the U.S. unemployment rate dropped to...Ch. 5.1 - To perform a certain type of blood analysis, lab...Ch. 5.1 - Listed is a series of experiments and associated...Ch. 5.2 - The probability distribution for the random...Ch. 5.2 - The following data were collected by counting the...Ch. 5.2 - For unemployed persons in the United States, the...Ch. 5.2 - The percent frequency distributions of job...
Ch. 5.2 - A technician services mailing machines at...Ch. 5.2 - The two largest cable providers are Comcast Cable...Ch. 5.2 - A psychologist determined that the number of...Ch. 5.2 - The following table is a partial probability...Ch. 5.3 - The following table provides a probability...Ch. 5.3 - The following table provides a probability...Ch. 5.3 - The number of students taking the SAT has risen to...Ch. 5.3 - The American Housing Survey reported the following...Ch. 5.3 - The National Basketball Association (NBA) records...Ch. 5.3 - The probability distribution for damage claims...Ch. 5.3 - The following probability distributions of job...Ch. 5.3 - The demand for a product of Carolina Industries...Ch. 5.3 - Prob. 23ECh. 5.3 - The J. R. Ryland Computer Company is considering a...Ch. 5.4 - Given below is a bivariate distribution for the...Ch. 5.4 - A person is interested in constructing a...Ch. 5.4 - The Chamber of Commerce in a Canadian city has...Ch. 5.4 - PortaCom has developed a design for a high-quality...Ch. 5.4 - J.P. Morgan Asset Management publishes information...Ch. 5.4 - In addition to the information in exercise 29 on...Ch. 5.5 - Consider a binomial experiment with two trials and...Ch. 5.5 - Consider a binomial experiment with n = 10 and p =...Ch. 5.5 - Consider a binomial experiment with n = 20 and p =...Ch. 5.5 - A Harris Interactive survey for InterContinental...Ch. 5.5 - In San Francisco, 30% of workers take public...Ch. 5.5 - When a new machine is functioning properly, only...Ch. 5.5 - A Randstad/Harris interactive survey reported that...Ch. 5.5 - Military radar and missile detection systems are...Ch. 5.5 - Twelve of the top 20 finishers in the 2009 PGA...Ch. 5.5 - The Census Bureaus Current Population Survey shows...Ch. 5.5 - A university found that 20% of its students...Ch. 5.5 - According to a survey conducted by TD Ameritrade,...Ch. 5.5 - Twenty-three percent of automobiles are not...Ch. 5.6 - Consider a Poisson distribution with = 3. a....Ch. 5.6 - Consider a Poisson distribution with a mean of two...Ch. 5.6 - Phone calls arrive at the rate of 48 per hour at...Ch. 5.6 - During the period of time that a local university...Ch. 5.6 - More than 50 million guests stay at bed and...Ch. 5.6 - Airline passengers arrive randomly and...Ch. 5.6 - An average of 15 aircraft accidents occur each...Ch. 5.6 - The National Safety Council (NSC) estimates that...Ch. 5.7 - Suppose N = 10 and r = 3. Compute the...Ch. 5.7 - Suppose N = 15 and r = 4. What is the probability...Ch. 5.7 - In a survey conducted by the Gallup Organization,...Ch. 5.7 - Blackjack, or twenty-one as it is frequently...Ch. 5.7 - Axline Computers manufactures personal computers...Ch. 5.7 - The Zagat Restaurant Survey provides food, decor,...Ch. 5.7 - The Troubled Asset Relief Program (TARP), passed...Ch. 5 - The Barrons Big Money Poll asked 131 investment...Ch. 5 - The American Association of Individual Investors...Ch. 5 - The budgeting process for a midwestern college...Ch. 5 - A bookstore at the Hartsfield-Jackson Airport in...Ch. 5 - The Knowles/Armitage (KA) group at Merrill Lynch...Ch. 5 - A survey showed that the average commuter spends...Ch. 5 - A political action group is planning to interview...Ch. 5 - Many companies use a quality control technique...Ch. 5 - The unemployment rate in the state of Arizona is...Ch. 5 - A poll conducted by Zogby International showed...Ch. 5 - Cars arrive at a car wash randomly and...Ch. 5 - A new automated production process averages 1.5...Ch. 5 - A regional director responsible for business...Ch. 5 - Customer arrivals at a bank are random and...Ch. 5 - A deck of playing cards contains 52 cards, four of...Ch. 5 - U.S. News World Reports ranking of Americas best...
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- 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…arrow_forwardIn 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.)arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward
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