Elementary Statistics 2nd Edition
2nd Edition
ISBN: 9781259724275
Author: William Navidi, Barry Monk
Publisher: McGraw-Hill Education
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Chapter 15.2, Problem 16E
To determine
To find:Whether the
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Question 2. An American option on a stock has payoff given by F = f(St) when it is exercised
at time t. We know that the function f is convex. A person claims that because of convexity,
it is optimal to exercise at expiration T. Do you agree with them?
Question 4. We consider a CRR model with So == 5 and up and down factors u = 1.03 and
d = 0.96. We consider the interest rate r = 4% (over one period). Is this a suitable CRR
model? (Explain your answer.)
Question 3. We want to price a put option with strike price K and expiration T. Two financial
advisors estimate the parameters with two different statistical methods: they obtain the same
return rate μ, the same volatility σ, but the first advisor has interest r₁ and the second advisor
has interest rate r2 (r1>r2). They both use a CRR model with the same number of periods to
price the option. Which advisor will get the larger price? (Explain your answer.)
Chapter 15 Solutions
Elementary Statistics 2nd Edition
Ch. 15.1 - In Exercises 3 and 4, fill in each blank with the...Ch. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.1 - In Exercises 5 and 6, determine whether the...Ch. 15.1 - Prob. 7ECh. 15.1 - Prob. 8ECh. 15.1 - Prob. 9ECh. 15.1 - Prob. 10ECh. 15.1 - Weight loss: A weight loss company claims that the...Ch. 15.1 - At the movies: A sample of 12 movies released in a...
Ch. 15.1 - Prob. 13ECh. 15.1 - Prob. 14ECh. 15.1 - Prob. 15ECh. 15.1 - Prob. 16ECh. 15.1 - Scam alert: The rates of fraud complaints (per...Ch. 15.1 - Prob. 18ECh. 15.1 - Prob. 19ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5ECh. 15.2 - Prob. 6ECh. 15.2 - Prob. 7ECh. 15.2 - Prob. 8ECh. 15.2 - Prob. 9ECh. 15.2 - In Exercises 7-10, compute s,s, and the value of...Ch. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Recovery times: A new postsurgical treatment was...Ch. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.3 - Prob. 7ECh. 15.3 - Prob. 8ECh. 15.3 - Prob. 9ECh. 15.3 - Prob. 10ECh. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Prob. 16ECh. 15.3 - Exercise 17 demonstrates that the results of the...Ch. 15 - Prob. 1CQCh. 15 - Prob. 2CQCh. 15 - Prob. 3CQCh. 15 - Prob. 4CQCh. 15 - Prob. 5CQCh. 15 - Prob. 6CQCh. 15 - Prob. 7CQCh. 15 - Prob. 8CQCh. 15 - In Exercises 8-10, use the signed-rank test to...Ch. 15 - Prob. 10CQCh. 15 - Prob. 1RECh. 15 - Prob. 2RECh. 15 - Prob. 3RECh. 15 - Prob. 4RECh. 15 - Prob. 5RECh. 15 - Prob. 6RECh. 15 - Prob. 7RECh. 15 - Prob. 8RECh. 15 - Prob. 9RECh. 15 - Prob. 10RECh. 15 - Prob. 1WAICh. 15 - Prob. 2WAICh. 15 - Prob. 3WAICh. 15 - Prob. 1CSCh. 15 - Prob. 2CSCh. 15 - Microorganisms play a crucial role in wastewater...Ch. 15 - Prob. 4CS
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- Question 5. We consider a put option with strike price K and expiration T. This option is priced using a 1-period CRR model. We consider r > 0, and σ > 0 very large. What is the approximate price of the option? In other words, what is the limit of the price of the option as σ∞. (Briefly justify your answer.)arrow_forwardQuestion 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.arrow_forwardSeveral 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.arrow_forward
- 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 Soarrow_forwardIn 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…arrow_forwardIn 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_forward
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