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 7.2, Problem 1LC

A population has a mean of μ = 65 and a standard deviation of σ = 16.

  • a. Describe the distribution of sample means (shape, central tendency, and variability) for samples of size n = 4 selected from this population.
  • b. Describe the distribution of sample means (shape, central tendency, and variability) for samples of size n = 64 selected from this population.
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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
Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…

Chapter 7 Solutions

Essentials of Statistics for the Behavioral Sciences

Ch. 7.5 - A population forms a normal distribution with a...Ch. 7.5 - A population forms a normal shaped distribution...Ch. 7.5 - The SAT scores for the entering freshman class at...Ch. 7.5 - Prob. 4LCCh. 7 - Describe the distribution of sample means (shape,...Ch. 7 - A sample is selected from a population with a mean...Ch. 7 - The distribution of sample means is not always a...Ch. 7 - A population has a standard deviation of = 24. a....Ch. 7 - For a population with a mean of = 70 and a...Ch. 7 - For a population with a standard deviation of =...Ch. 7 - For a population with = 12, how large a sample is...Ch. 7 - For a sample of n = 25 scores, what is the value...Ch. 7 - For a population with a mean of = 80 and a...Ch. 7 - A sample of n = 4 scores has a mean of M = 75....Ch. 7 - A normal distribution has a mean of = 60 and a...Ch. 7 - A random sample is obtained from a normal...Ch. 7 - The population of IQ scores forms a normal...Ch. 7 - The scores on a standardized mathematics test for...Ch. 7 - A normal distribution has a mean of = 54 and...Ch. 7 - A population of scores forms a normal distribution...Ch. 7 - For random samples of size n = 25 selected from a...Ch. 7 - The distribution ages for students at the state...Ch. 7 - At the end of the spring semester, the Dean of...Ch. 7 - Jumbo shrimp are those that require 10 to 15...Ch. 7 - The average age for licensed drivers in the county...Ch. 7 - Callahan (2009) conducted a study to evaluate the...Ch. 7 - Xu and Garcia (2008) conducted a research study...
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