APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Chapter 17.1, Problem 5SE
Explain the role of statisticians in quality improvement.
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
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Strength of the relationship (strong/moderate/weak):
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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 17 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
Ch. 17.1 - Define (a) productivity, (b) quality control, and...Ch. 17.1 - Explain the relationship between productivity and...Ch. 17.1 - Explain the difference between common cause...Ch. 17.1 - Prob. 4SECh. 17.1 - Explain the role of statisticians in quality...Ch. 17.2 - Prob. 6SECh. 17.2 - Prob. 7SECh. 17.3 - Prob. 8SECh. 17.3 - Prob. 9SECh. 17.3 - Identify three common quality improvement programs...
Ch. 17.3 - Why is the quality improvement process...Ch. 17.3 - Prob. 12SECh. 17.3 - Prob. 13SECh. 17.4 - Prob. 14SECh. 17.4 - Prob. 15SECh. 17.5 - (a) To construct control limits for an x chart,...Ch. 17.5 - Prob. 17SECh. 17.5 - List four rules for detecting abnormal (special...Ch. 17.5 - Set up control limits for an x chart, given x =...Ch. 17.5 - Prob. 20SECh. 17.5 - Prob. 21SECh. 17.5 - To print 8.5 5.5 note pads, a copy shop uses...Ch. 17.6 - Prob. 23SECh. 17.6 - Prob. 24SECh. 17.7 - Prob. 25SECh. 17.7 - Prob. 26SECh. 17.7 - Prob. 27SECh. 17.7 - Prob. 28SECh. 17.9 - Prob. 29SECh. 17.9 - Prob. 30SECh. 17.9 - Prob. 31SECh. 17 - Define (a) quality, (b) process, and (c)...Ch. 17 - Prob. 2CRCh. 17 - Prob. 3CRCh. 17 - Prob. 4CRCh. 17 - Prob. 5CRCh. 17 - Prob. 6CRCh. 17 - (a) Who was W. Edwards Deming and why is he...Ch. 17 - List three influential thinkers other than Deming...Ch. 17 - (a) Briefly explain each acronym: TQM, BPR, SQC,...Ch. 17 - (a) What is shown on the x chart? (b) Name three...Ch. 17 - Prob. 11CRCh. 17 - Prob. 12CRCh. 17 - Prob. 13CRCh. 17 - Prob. 14CRCh. 17 - Prob. 15CRCh. 17 - Briefly explain (a) the overadjustment problem,...Ch. 17 - Prob. 32CECh. 17 - Prob. 33CECh. 17 - Prob. 34CECh. 17 - Define three quality metrics that might be used to...Ch. 17 - Prob. 36CECh. 17 - Prob. 37CECh. 17 - Prob. 38CECh. 17 - Prob. 39CECh. 17 - Use your favorite Internet search engine to look...Ch. 17 - Make a fishbone chart (cause-and-effect diagram)...Ch. 17 - Make a fishbone chart (cause-and-effect diagram)...Ch. 17 - Make a fishbone chart (cause-and-effect diagram)...Ch. 17 - Prob. 44CECh. 17 - In painting an automobile, the thickness of the...Ch. 17 - Prob. 46CECh. 17 - Prob. 47CECh. 17 - Prob. 48CECh. 17 - In painting an automobile at the factory, the...Ch. 17 - Prob. 50CECh. 17 - Prob. 51CECh. 17 - Prob. 52CECh. 17 - Prob. 53CECh. 17 - A Nabisco Fig Newton has a process mean weight of...Ch. 17 - A new type of smoke detector battery is developed....Ch. 17 - Prob. 56CECh. 17 - Prob. 57CECh. 17 - Prob. 58CECh. 17 - Each gum drop in two bags of Sathers Gum Drops was...Ch. 17 - Prob. 60CECh. 17 - Prob. 61CECh. 17 - Prob. 62CECh. 17 - Prob. 63CECh. 17 - Refer to the bolt strength problem 17.47. Assuming...Ch. 17 - Refer to the paint problem 17.49 with =1.00 and ...
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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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