Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Textbook Question
Chapter 3, Problem 122BITH
Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled.
122. Suppose that you randomly draw two cards, one at a time, without replacement. G1 = first card is green
G2 = second card is green
a. Draw a tree diagram of the situation.
b. Find P(G1AND G2).
c. Find P(at least one green).
d. Find P(G2|G1). e. Are G2 and G1 independent
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Question 6. You collect daily data for the stock of a company Z over the past 4 months (i.e. 80
days) and calculate the log-returns (yk)/(-1. You want to build a CRR model for the evolution
of the stock. The expected value and standard deviation of the log-returns are y = 0.06 and
Sy 0.1. The money market interest rate is r = 0.04. Determine the risk-neutral probability of
the model.
Several markets (Japan, Switzerland) introduced negative interest rates on their money market.
In this problem, we will consider an annual interest rate r < 0. We consider a stock modeled
by an N-period CRR model where each period is 1 year (At = 1) and the up and down factors
are u and d.
(a) We consider an American put option with strike price K and expiration T. Prove that if
<0, the optimal strategy is to wait until expiration T to exercise.
We consider an N-period CRR model where each period is 1 year (At = 1), the up factor is
u = 0.1, the down factor is d = e−0.3 and r = 0. We remind you that in the CRR model, the
stock price at time tn is modeled (under P) by
Sta
=
So exp (μtn + σ√AtZn),
where (Zn) is a simple symmetric random walk.
(a) Find the parameters μ and σ for the CRR model described above.
(b) Find P
Ste
So
55/50
€ > 1).
StN
(c) Find lim P
804-N
(d) Determine q. (You can use e- 1 x.)
Ste
(e) Find Q
So
(f) Find lim Q
004-N
StN
So
Chapter 3 Solutions
Introductory Statistics
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