The Essentials of Statistics: A Tool for Social Research
The Essentials of Statistics: A Tool for Social Research
4th Edition
ISBN: 9781305802698
Author: Joseph F. Healey
Publisher: Cengage Learning US
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Chapter 6, Problem 6.18P

You are the automotive specialist for the monthly magazine Consumer Beware. Part of your job is to investigate the claims made by automakers in their TV commercials. You are particularly suspicious of a new economy car that the automaker claims will get 78 miles per gallon. After checking the mileage figures for a random sample of 125 owners of this car, you find an average miles per gallon of 75.5, with a standard deviation of 3.7. At the 99% level, do your results tend to confirm or refute the manufacturer’s claims?

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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.)

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