INTRODUCTION TO STATISTICS & DATA ANALYS
6th Edition
ISBN: 9780357420447
Author: PECK
Publisher: CENGAGE L
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Chapter 13.1, Problem 2E
Consider the variables and population regression line given in the previous exercise.
- a. What is the
mean value of gas usage for houses with 2100 sq. ft. of space? - b. What is the average change in usage associated with a 1 sq. ft. increase in size?
- c. What is the average change in usage associated with a 100 sq. ft. increase in size?
- d. Should the model be used to predict mean usage for a 500 sq. ft. house? Why or why not? (Hint: See the discussion following Example 13.2.)
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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 13 Solutions
INTRODUCTION TO STATISTICS & DATA ANALYS
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