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 17.4, Problem 17E
Consider the following time series data.
- a. Construct a time series plot. What type of pattern exists in the data?
- b. Develop the linear trend equation for this time series.
- c. What is the forecast for t = 6?
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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
Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 17.2 - Consider the following time series data. Week 1 2...Ch. 17.2 - Refer to the time series data in exercise 1. Using...Ch. 17.2 - Exercises 1 and 2 used different forecasting...Ch. 17.2 - Consider the following time series data. Month 1 2...Ch. 17.3 - Consider the following time series data. Week 1 2...Ch. 17.3 - Consider the following time series data. Month 1 2...Ch. 17.3 - Refer to the gasoline sales time series data in...Ch. 17.3 - Refer again to the gasoline sales time series data...Ch. 17.3 - With the gasoline time series data from Table...Ch. 17.3 - With a smoothing constant of = .2, equation...
Ch. 17.3 - For the Hawkins Company, the monthly percentages...Ch. 17.3 - Corporate triple-A bond interest rates for 12...Ch. 17.3 - The values of Alabama building contracts (in ...Ch. 17.3 - The following time series shows the sales of a...Ch. 17.3 - Ten weeks of data on the Commodity Futures Index...Ch. 17.3 - The U.S. Census Bureau tracks the median price for...Ch. 17.4 - Consider the following time series data. a....Ch. 17.4 - Prob. 18ECh. 17.4 - Consider the following time series. a. Construct a...Ch. 17.4 - Prob. 20ECh. 17.4 - Prob. 21ECh. 17.4 - Prob. 22ECh. 17.4 - The president of a small manufacturing firm is...Ch. 17.4 - FRED (Federal Reserve Economic Data), a database...Ch. 17.4 - Automobile unit sales at B. J. Scott Motors, Inc.,...Ch. 17.4 - Giovanni Food Products produces and sells frozen...Ch. 17.4 - Prob. 27ECh. 17.5 - Consider the following time series. a. Construct a...Ch. 17.5 - Consider the following time series data. a....Ch. 17.5 - The quarterly sales data (number of copies sold)...Ch. 17.5 - Air pollution control specialists in southern...Ch. 17.5 - South Shore Construction builds permanent docks...Ch. 17.5 - Prob. 33ECh. 17.5 - Three years of monthly lawn-maintenance expenses...Ch. 17.6 - Consider the following time series data. a....Ch. 17.6 - Refer to exercise 35. a. Deseasonalize the time...Ch. 17.6 - The quarterly sales data (number of copies sold)...Ch. 17.6 - Three years of monthly lawn-maintenance expenses...Ch. 17.6 - Air pollution control specialists in southern...Ch. 17.6 - Electric power consumption is measured in...Ch. 17 - The weekly demand (in cases) for a particular...Ch. 17 - The following table reports the percentage of...Ch. 17 - United Dairies. Inc., supplies milk to several...Ch. 17 - Prob. 44SECh. 17 - Prob. 45SECh. 17 - The Mayfair Department Store in Davenport, Iowa,...Ch. 17 - Canton Supplies, Inc., is a service firm that...Ch. 17 - The Costello Music Company has been in business...Ch. 17 - Consider the Costello Music Company problem in...Ch. 17 - Refer to the Costello Music Company problem in...Ch. 17 - Refer to the Costello Music Company time series in...Ch. 17 - Hudson Marine has been an authorized dealer for CD...Ch. 17 - Refer to the Hudson Marine problem in exercise 52....Ch. 17 - Refer to the Hudson Marine problem in exercise 53....Ch. 17 - Refer to the Hudson Marine data in exercise 53. a....Ch. 17 - Forecasting Food and Beverage Sales The Vintage...Ch. 17 - Forecasting Lost Sales The Carlson Department...
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