Essentials Of Statistics For Business & Economics
9th Edition
ISBN: 9780357045435
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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Chapter 5.7, Problem 55E
a.
To determine
Compute the
b.
To determine
Compute the probability that both of the cards are aces.
c.
To determine
Compute the probability that both of the cards have a point value of 10.
d.
To determine
Compute the probability that a player is dealt blackjack using the answers in part (a), (b) and (c).
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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 5 Solutions
Essentials Of Statistics For Business & Economics
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 - 3. 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 - 7. The probability distribution for the random...Ch. 5.2 - 8. The following data were collected by counting...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 - New Cable Subscribers. Spectrum provides cable...Ch. 5.2 - A psychologist determined that the number of...Ch. 5.2 - 14. 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 - Golf Scores. During the summer of 2018, Coldstream...Ch. 5.3 - 18. The American Housing Survey reported the...Ch. 5.3 - New Tax Accounting Clients. New legislation passed...Ch. 5.3 - The probability distribution for damage claims...Ch. 5.3 - The following probability distributions of job...Ch. 5.3 - 22. The demand for a product of Carolina...Ch. 5.3 - 23. In Gallup’s Annual Consumption Habits Poll,...Ch. 5.3 - 24. The J. R. Ryland Computer Company is...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 - 32. Consider a binomial experiment with n = 10 and...Ch. 5.5 - 33. Consider a binomial experiment with n = 20 and...Ch. 5.5 - 34. For its Music 360 survey, Nielsen Co. asked...Ch. 5.5 - The Center for Medicare and Medical Services...Ch. 5.5 - 36. When a new machine is functioning properly,...Ch. 5.5 - Americans Saving for Retirement. According to a...Ch. 5.5 - Military radar and missile detection systems are...Ch. 5.5 - Market-share-analysis company Net Applications...Ch. 5.5 - 42. A Gallup Poll showed that 30% of Americans are...Ch. 5.5 - Tracked Emails. According to a 2017 Wired magazine...Ch. 5.6 - 44. Consider a Poisson distribution with μ =...Ch. 5.6 - 45. Consider a Poisson distribution with a mean of...Ch. 5.6 - 46. Phone calls arrive at the rate of 48 per hour...Ch. 5.6 - 911 Calls. Emergency 911 calls to a small...Ch. 5.6 - Motor Vehicle Accidents in New York City. In a...Ch. 5.6 - Airline passengers arrive randomly and...Ch. 5.6 - According to the National Oceanic and Atmospheric...Ch. 5.6 - Emails Received. According to a 2017 survey...Ch. 5.7 - Suppose N = 10 and r = 3. Compute the...Ch. 5.7 - 53. Suppose N = 15 and r = 4. What is the...Ch. 5.7 - Online Holiday Shopping. More and more shoppers...Ch. 5.7 - Prob. 55ECh. 5.7 - 56. Axline Computers manufactures personal...Ch. 5.7 - The Zagat Restaurant Survey provides food, decor,...Ch. 5.7 - Prob. 58ECh. 5 - 59. The U.S. Coast Guard (USCG) provides a wide...Ch. 5 - 60. The Car Repair Ratings website provides...Ch. 5 - 61. The budgeting process for a midwestern college...Ch. 5 - 62. A bookstore at the Hartsfield-Jackson Airport...Ch. 5 - The Knowles/Armitage (KA) group at Merrill Lynch...Ch. 5 - 64. The Pew Research Center surveyed adults who...Ch. 5 - Investing in the Stock Market. According to a 2017...Ch. 5 - Many companies use a quality control technique...Ch. 5 - 67. PBS News Hour reported that 39.4% of Americans...Ch. 5 - 68. Mahoney Custom Home Builders, Inc. of Canyon...Ch. 5 - Arrivals to a Car Wash. Cars arrive at a car wash...Ch. 5 - 70. A new automated production process averages...Ch. 5 - A regional director responsible for business...Ch. 5 - Customer arrivals at a bank are random and...Ch. 5 - 73. A deck of playing cards contains 52 cards,...Ch. 5 - 74. U.S. News & World Report’s ranking of...Ch. 5 - Great Grasslands Grains, Inc. (GGG) manufactures...Ch. 5 - Harriet McNeil, proprietor of McNeil’s Auto Mall,...Ch. 5 - Several years ago, management at Tuglar...
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- 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?arrow_forwardWe 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? 2arrow_forwardQuestion 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_forward
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