Statistical Techniques in Business and Economics
18th Edition
ISBN: 9781260579611
Author: Douglas Lind; William Marchal; Samuel Wathen
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 11, Problem 20E
a.
To determine
To Find: The null hypothesis and the alternative hypothesis.
b.
To determine
To Find: The p-value of the hypothesis test.
c.
To determine
To Check: If the null hypothesis is rejected.
d.
To determine
To draw: The conclusion obtained from the hypothesis testing.
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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 11 Solutions
Statistical Techniques in Business and Economics
Ch. 11 - Tom Sevits is the owner of the Appliance Patch....Ch. 11 - Prob. 1ECh. 11 - Prob. 2ECh. 11 - Prob. 3ECh. 11 - As part of a study of corporate employees, the...Ch. 11 - Prob. 5ECh. 11 - Mary Jo Fitzpatrick is the vice president for...Ch. 11 - Prob. 2SRCh. 11 - Prob. 7ECh. 11 - For Exercises 7 and 8: (a) state the decision...
Ch. 11 - Prob. 9ECh. 11 - A recent study compared the time spent together by...Ch. 11 - Ms. Lisa Monnin is the budget director for Nexus...Ch. 11 - The Tampa Bay (Florida) Area Chamber of Commerce...Ch. 11 - It is often useful for companies to know who their...Ch. 11 - For exercises 13 and 14, assume the sample...Ch. 11 - Prob. 14ECh. 11 - Prob. 15ECh. 11 - Suppose you are an expert on the fashion industry...Ch. 11 - Prob. 4SRCh. 11 - Prob. 17ECh. 11 - The null and alternate hypotheses are: H0:d=a0...Ch. 11 - Prob. 19ECh. 11 - Prob. 20ECh. 11 - A recent study focused on the number of times men...Ch. 11 - Clark Heter is an industrial engineer at Lyons...Ch. 11 - Prob. 23CECh. 11 - Prob. 24CECh. 11 - Prob. 25CECh. 11 - Prob. 26CECh. 11 - Prob. 27CECh. 11 - Prob. 28CECh. 11 - Prob. 29CECh. 11 - Prob. 30CECh. 11 - Prob. 31CECh. 11 - Prob. 32CECh. 11 - Prob. 33CECh. 11 - Prob. 34CECh. 11 - Prob. 35CECh. 11 - Prob. 36CECh. 11 - Prob. 37CECh. 11 - Prob. 38CECh. 11 - Prob. 39CECh. 11 - Prob. 40CECh. 11 - Prob. 41CECh. 11 - Prob. 42CECh. 11 - Prob. 43CECh. 11 - Prob. 44CECh. 11 - Prob. 45CECh. 11 - Prob. 46CECh. 11 - Prob. 47DACh. 11 - Prob. 49DA
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