Understanding Basic Statistics
8th Edition
ISBN: 9781337672320
Author: BRASE
Publisher: Cengage
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Chapter 4.2, Problem 23P
Expand Your Knowledge: Logarithmic Transformations, Exponential Growth Model Letx = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa.
| x | 2 | 3 | 5 | 8 | 10 |
| y | 2 | 3 | 12 | 125 | 630 |
(a) Draw a
(b) Now consider a transformation
(c) Use a calculator with regression keys to find the linear regression equation for the data pairs (x, y'). What is the
(d) The exponential growth model is
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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 4 Solutions
Understanding Basic Statistics
Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Critical Thinking: Linear Correlation Look at the...Ch. 4.1 - Critical Thinking: Linear Correlation Look at the...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...
Ch. 4.1 - Interpretation Trevor conducted a study and found...Ch. 4.1 - Interpretation Do people who spend more time on...Ch. 4.1 - Veterinary Science: Shetland Ponies How much...Ch. 4.1 - Health Insurance:Administrative Cost The following...Ch. 4.1 - Meteorology: Cyclones Can a low barometer reading...Ch. 4.1 - Geology: Earthquakes Is the magnitude of an...Ch. 4.1 - Baseball: Batting Averages and Home Runs In...Ch. 4.1 - University Crime: FBI Report Do larger...Ch. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Expand Your Knowledge: Using a Table to Test The...Ch. 4.1 - Expand Your Knowledge: Sample Size and...Ch. 4.1 - Prob. 23PCh. 4.2 - Statistical Literacy In the least-squares line...Ch. 4.2 - Statistical Literacy In the least squares line...Ch. 4.2 - Critical Thinking When we use a least-squares line...Ch. 4.2 - Critical Thinking If two variables have a negative...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Economics: Entry-Level Jobs An economist is...Ch. 4.2 - Ranching: Cattle You are the foreman of the Bar-S...Ch. 4.2 - Weight of Car: Miles per Gallon Do heavier cars...Ch. 4.2 - Basketball: Fouls Data for this problem are based...Ch. 4.2 - Auto Accidents: Age Data for this problem are...Ch. 4.2 - Auto Accidents: Age Let x be the age of a licensed...Ch. 4.2 - Incoine: Medicai Care Let x be per capita income...Ch. 4.2 - Violent Crimes: Prisons Does prison really deter...Ch. 4.2 - Education: Violent Crime The following data are...Ch. 4.2 - Research: Patents The following data are based on...Ch. 4.2 - Archaeology: Artifacts Data for this problem are...Ch. 4.2 - Cricket Chirps: Temperature Anyone who has been...Ch. 4.2 - Expand Your Knowledge: Residual Plot The...Ch. 4.2 - Residual Plot: Miles per Gallon Consider the data...Ch. 4.2 - Expand Your knowledge: Logarithmic...Ch. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4.2 - Prob. 24PCh. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4 - Terminology Consider the equation of a...Ch. 4 - Terminology Consider the values of the sample...Ch. 4 - Terminology Suppose we have a set of ordered pairs...Ch. 4 - Terminology Consider the following terms in a...Ch. 4 - Statistical Literacy Suppose the scatter diagram...Ch. 4 - Critical Thinking Suppose you and a friend each...Ch. 4 - Statistical Literacy When using the least-squares...Ch. 4 - StatisticalLiteracy Suppose that for x = 3. the...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - Prob. 1UTACh. 4 - Prob. 2UTACh. 4 - Prob. 3UTACh. 4 - Prob. 4UTACh. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...
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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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- A special interest group reports a tiny margin of error (plus or minus 0.04 percent) for its online survey based on 50,000 responses. Is the margin of error legitimate? (Assume that the group’s math is correct.)arrow_forwardSuppose that 73 percent of a sample of 1,000 U.S. college students drive a used car as opposed to a new car or no car at all. Find an 80 percent confidence interval for the percentage of all U.S. college students who drive a used car.What sample size would cut this margin of error in half?arrow_forwardYou want to compare the average number of tines on the antlers of male deer in two nearby metro parks. A sample of 30 deer from the first park shows an average of 5 tines with a population standard deviation of 3. A sample of 35 deer from the second park shows an average of 6 tines with a population standard deviation of 3.2. Find a 95 percent confidence interval for the difference in average number of tines for all male deer in the two metro parks (second park minus first park).Do the parks’ deer populations differ in average size of deer antlers?arrow_forward
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