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 16.3, Problem 4JC
To determine

Whether the null hypothesis is rejected that the proportion is 30% at α=0.05

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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 16 Solutions

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

Ch. 16 - True or false Which of the following are true? If...Ch. 16 - False or true Which of the following are true? If...Ch. 16 - P-values Which of the following are true? If...Ch. 16 - Prob. 4ECh. 16 - Prob. 5ECh. 16 - Prob. 6ECh. 16 - Prob. 7ECh. 16 - More critical values For each of the following...Ch. 16 - Prob. 9ECh. 16 - Significant again? A new reading program may...Ch. 16 - SECTION 16.4 11. Errors For each of the following...Ch. 16 - More errors For each of the following situations,...Ch. 16 - CHAPTER EXERCISES 13. P-value A medical researcher...Ch. 16 - Prob. 14ECh. 16 - Alpha A researcher developing scanners to search...Ch. 16 - Prob. 16ECh. 16 - Prob. 17ECh. 16 - Is the Euro fair? Soon after the Euro was...Ch. 16 - Prob. 19ECh. 16 - Prob. 20ECh. 16 - Prob. 21ECh. 16 - Prob. 22ECh. 16 - Prob. 23ECh. 16 - Prob. 24ECh. 16 - Prob. 25ECh. 16 - Prob. 26ECh. 16 - Prob. 27ECh. 16 - Alzheimers Testing for Alzheimers disease can be a...Ch. 16 - Prob. 29ECh. 16 - Quality control Production managers on an assembly...Ch. 16 - Cars, again As in Exercise 29, state regulators...Ch. 16 - Prob. 32ECh. 16 - Equal opportunity? A company is sued for job...Ch. 16 - Stop signs Highway safety engineers test new road...Ch. 16 - Prob. 35ECh. 16 - Ads A company is willing to renew its advertising...Ch. 16 - Prob. 37ECh. 16 - Prob. 38ECh. 16 - Prob. 39ECh. 16 - Catheters During an angiogram, heart problems can...Ch. 16 - Prob. 41ECh. 16 - Prob. 42ECh. 16 - Prob. 43ECh. 16 - Faulty or not? You are in charge of shipping...Ch. 16 - Prob. 45ECh. 16 - Prob. 46ECh. 16 - Prob. 47ECh. 16 - Prob. 48E
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