Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
16th Edition
ISBN: 9780077639709
Author: Douglas A. Lind, William G Marchal, Samuel A. Wathen
Publisher: McGraw-Hill Education
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Chapter 17, Problem 28CE
To determine
Find the simple aggregate price index using 2000 as the base period.
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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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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
Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
Ch. 17 - Prob. 1.1SRCh. 17 - Prob. 1.2SRCh. 17 - Prob. 1ECh. 17 - The table below reports the earnings per share of...Ch. 17 - Prob. 3ECh. 17 - Prob. 4ECh. 17 - Prob. 2SRCh. 17 - Prob. 5ECh. 17 - Prob. 6ECh. 17 - Prob. 7E
Ch. 17 - Prob. 8ECh. 17 - Prob. 3SRCh. 17 - Prob. 9ECh. 17 - Prob. 10ECh. 17 - Prob. 4SRCh. 17 - Prob. 11ECh. 17 - Prob. 5SRCh. 17 - Prob. 6SRCh. 17 - Prob. 7SRCh. 17 - Prob. 13ECh. 17 - Prob. 14ECh. 17 - Prob. 15ECh. 17 - Prob. 16ECh. 17 - Prob. 17CECh. 17 - Prob. 18CECh. 17 - Prob. 19CECh. 17 - Prob. 20CECh. 17 - Prob. 21CECh. 17 - Prob. 22CECh. 17 - Prob. 23CECh. 17 - Prob. 24CECh. 17 - Prob. 25CECh. 17 - Prob. 26CECh. 17 - Prob. 27CECh. 17 - Prob. 28CECh. 17 - Prob. 29CECh. 17 - Prob. 30CECh. 17 - Prob. 31CECh. 17 - Prob. 32CECh. 17 - Prob. 33CECh. 17 - Prob. 34CECh. 17 - Prob. 35CECh. 17 - Prob. 36CECh. 17 - Prob. 37CECh. 17 - Prob. 38CECh. 17 - Prob. 39CECh. 17 - Prob. 40CECh. 17 - Prob. 41CECh. 17 - Prob. 42CECh. 17 - Prob. 43CECh. 17 - Prob. 44CECh. 17 - Prob. 45CECh. 17 - Prob. 46CECh. 17 - Prob. 47CECh. 17 - Prob. 48CECh. 17 - Prob. 49CECh. 17 - Prob. 50CECh. 17 - Prob. 51CECh. 17 - Prob. 52CECh. 17 - Prob. 53CECh. 17 - Prob. 54CECh. 17 - Prob. 55CECh. 17 - Prob. 56DE
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