INTRODUCTION TO STATISTICS & DATA ANALYS
6th Edition
ISBN: 9780357420447
Author: PECK
Publisher: CENGAGE L
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Textbook Question
Chapter 1.4, Problem 15E
For the following numerical variables, state whether each is discrete or continuous.
- a. The length of a 1-year-old rattlesnake
- b. The altitude of a location in California selected randomly by throwing a dart at a map of the state
- c. The distance from the left edge at which a 12-inch plastic ruler snaps when bent sufficiently to break
- d. The price per gallon paid by the next customer to buy gas at a particular station
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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 1 Solutions
INTRODUCTION TO STATISTICS & DATA ANALYS
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