Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
7th Edition
ISBN: 9781337298353
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
Publisher: South-Western College Pub
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Chapter 14.8, Problem 49E
The DATAfile named CostLiving contains the cost of living indexes and the population densities (number of people per square mile) for 61 cities in the United States. The cost of living index measures the cost of living in a particular city relative to the cost of living in New York City. San Francisco has an index of 112.15, meaning that is 12.15% more expensive to live in San Francisco than New York City. Washington DC has an index of 84.64, which means that the cost to live in Washington DC is only 84.64% of what it costs to live in New York City (Numbeo website, July 13, 2016).
a. Develop the estimated regression equation that can be used to predict the cost of living index for a U.S. city, given the city's population density.
b. Construct a residual plot against the independent variable.
c. Review the residual plot constructed in part (b). Do the assumptions of the error term and model form seem reasonable?
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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 14 Solutions
Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
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