Intro Stats, Books a la Carte Edition (5th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 14.3, Problem 6JC
To determine

Explain how many of these 100 interval will fail to include in the true mean age.

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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 14 Solutions

Intro Stats, Books a la Carte Edition (5th Edition)

Ch. 14 - More tips The waiter in Exercise 3 usually waits...Ch. 14 - More groceries Suppose the store in Exercise 4 had...Ch. 14 - Prob. 7ECh. 14 - t-models, part II Using the t tables, software, or...Ch. 14 - t-models, part III Describe how the shape, center,...Ch. 14 - Prob. 10ECh. 14 - Prob. 11ECh. 14 - Home sales again In the previous exercise, you...Ch. 14 - Prob. 13ECh. 14 - Salaries A survey finds that a 95% confidence...Ch. 14 - Cattle Livestock are given a special feed...Ch. 14 - Prob. 16ECh. 14 - Prob. 17ECh. 14 - Student survey revisited Chapter 2, Exercise 86...Ch. 14 - Prob. 19ECh. 14 - Prob. 20ECh. 14 - Meal plan After surveying students at Dartmouth...Ch. 14 - Prob. 22ECh. 14 - Prob. 23ECh. 14 - Crawling Data collected by child development...Ch. 14 - Prob. 25ECh. 14 - Credit card charges A credit card company takes a...Ch. 14 - Prob. 27ECh. 14 - Pulse rates In the latest National Health and...Ch. 14 - Prob. 29ECh. 14 - Parking Hoping to lure more shoppers downtown, a...Ch. 14 - Prob. 31ECh. 14 - Prob. 32ECh. 14 - Speed of light In 1882, Michelson measured the...Ch. 14 - Michelson After his first attempt to determine the...Ch. 14 - Prob. 35ECh. 14 - Prob. 36ECh. 14 - Prob. 37ECh. 14 - Hot dogs A nutrition lab tested 40 hot dogs to see...Ch. 14 - Prob. 39ECh. 14 - Prob. 40ECh. 14 - Prob. 41ECh. 14 - Computer lab fees The technology committee has...Ch. 14 - Prob. 43ECh. 14 - CEO compensation The total compensation of the...Ch. 14 - Prob. 45ECh. 14 - CEOs, revisited In Exercise 44, you looked at the...Ch. 14 - GPAs A colleges data about the incoming freshmen...Ch. 14 - Prob. 48ECh. 14 - Lucky spot? A reporter working on a story about...Ch. 14 - Prob. 50ECh. 14 - Pregnancy Assume that the duration of human...Ch. 14 - Rainfall Statistics from Cornells Northeast...Ch. 14 - Prob. 53ECh. 14 - Prob. 54ECh. 14 - Prob. 55ECh. 14 - Doritos Some students checked 6 bags of Doritos...Ch. 14 - Prob. 57ECh. 14 - Prob. 58ECh. 14 - Chips Ahoy! In 1998, as an advertising campaign,...Ch. 14 - Yogurt Consumer Reports tested 11 brands of...Ch. 14 - Prob. 61ECh. 14 - Prob. 62ECh. 14 - Prob. 63ECh. 14 - Wind power Should you generate electricity with...
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