Student Solutions Manual For Ewen/nelson's Elementary Technical Mathematics, 11th
11th Edition
ISBN: 9781285199276
Author: Dale Ewen
Publisher: Cengage Learning
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Chapter B, Problem 25E
To determine
To calculate: The solution of the inequality
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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
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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…
Chapter B Solutions
Student Solutions Manual For Ewen/nelson's Elementary Technical Mathematics, 11th
Ch. B - Draw a graph for each inequality on the number...Ch. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Solve each inequality and graph its solution on...Ch. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Solve each inequality and graph its solution on...Ch. B - Prob. 46ECh. B - Prob. 47ECh. B - Solve each inequality and graph its solution on...
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- 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…arrow_forwardNo chatgpt pls will upvote Alreadyarrow_forwardFind the LaPla se trnsofrom of a) chi-square Distribution. b) Normal Distribution. C) Gamma Distribution. prove that Binomial (n, 2) Poisson (2) *********************arrow_forward
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