Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305445963
Author: PECK
Publisher: Cengage
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Chapter 10.1, Problem 2E
For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why:
- a. H0: μ = 15, Ha: μ = 15
- b. H0: p = 0.4, Ha: p > 0.6
- c. H0: μ = 123, Ha: μ < 123
- d. H0: μ = 123, Ha: μ = 125
- e. H0:
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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 10 Solutions
Introduction to Statistics and Data Analysis
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