Essentials of Statistics for the Behavioral Sciences
Essentials of Statistics for the Behavioral Sciences
8th Edition
ISBN: 9781133956570
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Chapter 12.2, Problem 1LC

Explain the difference between the testwise alpha level and the experiment wise alpha level.

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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)
Problem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?
We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2

Chapter 12 Solutions

Essentials of Statistics for the Behavioral Sciences

Ch. 12.5 - Prob. 2LCCh. 12.6 - With k = 2 treatments, are post hoc tests...Ch. 12.6 - Prob. 2LCCh. 12.7 - A researcher uses an independent-measures t test...Ch. 12.7 - An ANOVA produces an F-ratio with df = 1, 34....Ch. 12 - Explain why the F-ratio is expected to be near...Ch. 12 - Several factors influence the size of the F-ratio....Ch. 12 - Why should you use ANOVA instead of several t...Ch. 12 - Posttests are done after an ANOVA. a. What is the...Ch. 12 - An independent-measures study comparing four...Ch. 12 - The following data summarize the results from an...Ch. 12 - For the preceding problem you should find that...Ch. 12 - The following data summarize the results from an...Ch. 12 - For the preceding problem you should find that...Ch. 12 - The following data summarize the results from an...Ch. 12 - Prob. 11PCh. 12 - The following values are from an...Ch. 12 - There is some evidence that high school students...Ch. 12 - A researcher reports an F-ratio with df = 2. 27...Ch. 12 - A research report from an independent-measures...Ch. 12 - The following summary table presents the results...Ch. 12 - A pharmaceutical company has developed a drug that...Ch. 12 - A developmental psychologist is examining the...Ch. 12 - The following data were obtained from an...Ch. 12 - The following values summarize the results from an...Ch. 12 - The following data are from an...Ch. 12 - One possible explanation for why some birds...Ch. 12 - There is some research indicating that college...Ch. 12 - New research suggests that watching television,...
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