Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)
12th Edition
ISBN: 9780135998304
Author: Margaret L. Lial, Tom Hungerford, John P. Holcomb, Bernadette Mullins
Publisher: PEARSON
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Question
Chapter 11.1, Problem 5E
(a)
To determine
To calculate: The value of indicated limit
(b)
To determine
To calculate: The value of indicated limit
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Students have asked these similar questions
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
In this problem, we consider a 3-period stock market model with evolution given in Fig. 1 below.
Each period corresponds to one year. The interest rate is r = 0%.
16
22
28
12
16
12
8
4
2
time
Figure 1: Stock evolution for Problem 1.
(a) A colleague notices that in the model above, a movement up-down leads to the same value
as a movement down-up. He concludes that the model is a CRR model. Is your colleague
correct? (Explain your answer.)
(b) We consider a European put with strike price K = 10 and expiration T = 3 years. Find
the price of this option at time 0. Provide the replicating portfolio for the first period.
(c) In addition to the call above, we also consider a European call with strike price K = 10
and expiration T = 3 years. Which one has the highest price? (It is not necessary to
provide the price of the call.)
(d) We now assume a yearly interest rate r = 25%. We consider a Bermudan put option with
strike price K = 10. It works like a standard put, but you can exercise it…
In this problem, we consider a 2-period stock market model with evolution given in Fig. 1 below.
Each period corresponds to one year (At = 1). The yearly interest rate is r = 1/3 = 33%. This
model is a CRR model.
25
15
9
10
6
4
time
Figure 1: Stock evolution for Problem 1.
(a) Find the values of up and down factors u and d, and the risk-neutral probability q.
(b) We consider a European put with strike price K
the price of this option at time 0.
==
16 and expiration T = 2 years. Find
(c) Provide the number of shares of stock that the replicating portfolio contains at each pos-
sible position.
(d) You find this option available on the market for $2. What do you do? (Short answer.)
(e) We consider an American put with strike price K
= 16 and expiration T
=
2 years. Find
the price of this option at time 0 and describe the optimal exercising strategy.
(f) We consider an American call with strike price K ○ = 16 and expiration T = 2 years. Find
the price of this option at time 0 and describe…
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