STATISTICAL TECHNIQUES-ACCESS ONLY
16th Edition
ISBN: 9780077639648
Author: Lind
Publisher: MCG
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Chapter 5, Problem 2.2SR
To determine
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Identify the concept of probability that is applied.
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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 5 Solutions
STATISTICAL TECHNIQUES-ACCESS ONLY
Ch. 5 - Prob. 1SRCh. 5 - One card will be randomly selected from a standard...Ch. 5 - Prob. 2.2SRCh. 5 - Prob. 2.3SRCh. 5 - Some people are in favor of reducing federal taxes...Ch. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - In each of the following cases, indicate whether...Ch. 5 - Prob. 6E
Ch. 5 - Prob. 7ECh. 5 - A sample of 2,000 licensed drivers revealed the...Ch. 5 - Bank of America customers select their own...Ch. 5 - Prob. 3SRCh. 5 - Prob. 4SRCh. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - Prob. 13ECh. 5 - The chair of the board of directors says, There is...Ch. 5 - Suppose the probability you will get an A in this...Ch. 5 - Two coins are tossed. If A is the event two heads...Ch. 5 - Prob. 17ECh. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - The aquarium at Sea Critters Depot contains 140...Ch. 5 - A National Park Service survey of visitors to the...Ch. 5 - From experience, Teton Tire knows the probability...Ch. 5 - The board of directors of Tarbell Industries...Ch. 5 - Refer to Table 51 on page 151 to find the...Ch. 5 - Consumers were surveyed on the relative number of...Ch. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 9SRCh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - The credit department of Lions Department Store in...Ch. 5 - Prob. 38ECh. 5 - Prob. 10.1SRCh. 5 - Prob. 10.2SRCh. 5 - Prob. 11.1SRCh. 5 - Prob. 11.2SRCh. 5 - Prob. 11.3SRCh. 5 - In a lottery game, three numbers are randomly...Ch. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - A telephone number consists of seven digits, the...Ch. 5 - An overnight express company must include five...Ch. 5 - A representative of the Environmental Protection...Ch. 5 - Sam Sneads restaurant in Conway, South Carolina,...Ch. 5 - A company is creating three new divisions and...Ch. 5 - The marketing research department at Pepsico plans...Ch. 5 - The number of times a particular event occurred in...Ch. 5 - The probability that the cause and the cure for...Ch. 5 - Berdines Chicken Factory has several stores in the...Ch. 5 - Prob. 51CECh. 5 - The first card selected from a standard 52-card...Ch. 5 - Prob. 53CECh. 5 - Refer to the following picture. a. What is the...Ch. 5 - Prob. 55CECh. 5 - Assume the likelihood that any flight on Delta...Ch. 5 - Prob. 57CECh. 5 - Prob. 58CECh. 5 - Prob. 59CECh. 5 - Prob. 60CECh. 5 - Prob. 61CECh. 5 - Forty percent of the homes constructed in the...Ch. 5 - Prob. 63CECh. 5 - Prob. 64CECh. 5 - Prob. 65CECh. 5 - Prob. 66CECh. 5 - Prob. 67CECh. 5 - Prob. 68CECh. 5 - Prob. 69CECh. 5 - An investor purchased 100 shares of Fifth Third...Ch. 5 - Flashner Marketing Research Inc. specializes in...Ch. 5 - Prob. 72CECh. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - ABC Auto Insurance classifies drivers as good,...Ch. 5 - Prob. 89CECh. 5 - The probability a D-Link network server is down is...Ch. 5 - Prob. 91CECh. 5 - Prob. 92DECh. 5 - Refer to the Baseball 2012 data, which reports...Ch. 5 - Refer to the data on the school buses in the Buena...
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- 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…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_forward2.2, 13.2-13.3) question: 5 point(s) possible ubmit test The accompanying table contains the data for the amounts (in oz) in cans of a certain soda. The cans are labeled to indicate that the contents are 20 oz of soda. Use the sign test and 0.05 significance level to test the claim that cans of this soda are filled so that the median amount is 20 oz. If the median is not 20 oz, are consumers being cheated? Click the icon to view the data. What are the null and alternative hypotheses? OA. Ho: Medi More Info H₁: Medi OC. Ho: Medi H₁: Medi Volume (in ounces) 20.3 20.1 20.4 Find the test stat 20.1 20.5 20.1 20.1 19.9 20.1 Test statistic = 20.2 20.3 20.3 20.1 20.4 20.5 Find the P-value 19.7 20.2 20.4 20.1 20.2 20.2 P-value= (R 19.9 20.1 20.5 20.4 20.1 20.4 Determine the p 20.1 20.3 20.4 20.2 20.3 20.4 Since the P-valu 19.9 20.2 19.9 Print Done 20 oz 20 oz 20 oz 20 oz ce that the consumers are being cheated.arrow_forward
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