Business Analytics
3rd Edition
ISBN: 9780135231678
Author: Evans, James R. (james Robert)
Publisher: PEARSON EDUCATION (COLLEGE)
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Textbook Question
Chapter 4, Problem 2.5CYU
What does an ogive display?
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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 4 Solutions
Business Analytics
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Ch. 4 - Prob. 3.1CYUCh. 4 - Prob. 3.2CYUCh. 4 - Prob. 3.3CYUCh. 4 - What is a cross-tabulation?Ch. 4 - Prob. 4.2CYUCh. 4 - Explain the difference between a population and a...Ch. 4 - List and explain the common measures of location...Ch. 4 - Prob. 5.3CYUCh. 4 - Prob. 5.4CYUCh. 4 - Prob. 5.5CYUCh. 4 - Prob. 5.6CYUCh. 4 - Prob. 5.7CYUCh. 4 - Prob. 5.8CYUCh. 4 - Prob. 6.1CYUCh. 4 - Use Excel to find the mean and variance for the...Ch. 4 - Prob. 7.1CYUCh. 4 - Prob. 7.2CYUCh. 4 - Prob. 8.1CYUCh. 4 - Prob. 8.2CYUCh. 4 - Prob. 9.1CYUCh. 4 - Prob. 9.2CYUCh. 4 - Prob. 9.3CYUCh. 4 - What rules are typically used to identify...Ch. 4 - Prob. 10.2CYUCh. 4 - Summarize statistical tools that are typically...Ch. 4 - Prob. 11.2CYUCh. 4 - What are the principles of statistical thinking?Ch. 4 - Prob. 12.2CYUCh. 4 - Prob. 12.3CYUCh. 4 - A survey handed out to individuals at a major...Ch. 4 - Prob. 1.2PECh. 4 - Identify each of the variables in the Excel file...Ch. 4 - Prob. 1.4PECh. 4 - Prob. 1.5PECh. 4 - Prob. 1.6PECh. 4 - Prob. 1.7PECh. 4 - Prob. 1.8PECh. 4 - Prob. 1.9PECh. 4 - Prob. 1.10PECh. 4 - Prob. 1.11PECh. 4 - Prob. 1.12PECh. 4 - Use a PivotTable to construct a frequency...Ch. 4 - Prob. 1.14PECh. 4 - Prob. 1.15PECh. 4 - Prob. 1.16PECh. 4 - Prob. 1.17PECh. 4 - Prob. 1.18PECh. 4 - Prob. 1.19PECh. 4 - Prob. 1.20PECh. 4 - Use a PivotTable to construct a cross-tabulation...Ch. 4 - Use PivotTables to construct cross-tabulations for...Ch. 4 - Prob. 1.23PECh. 4 - Prob. 1.24PECh. 4 - Prob. 1.25PECh. 4 - Compute the mean, median, midrange, and mode for...Ch. 4 - Considering the data in the Excel file Home Market...Ch. 4 - Considering the data in the Excel file Home Market...Ch. 4 - In the Excel file Facebook Survey, find the range,...Ch. 4 - Prob. 1.30PECh. 4 - For the Excel file Tablet Computer Sales, find the...Ch. 4 - The Excel file Atlanta Airline Data provides...Ch. 4 - Prob. 1.33PECh. 4 - Prob. 1.34PECh. 4 - Apply the Descriptive Statistics tool for subsets...Ch. 4 - Use the Descriptive Statistics tool to summarize...Ch. 4 - Prob. 1.38PECh. 4 - The Data worksheet in the Excel file Airport...Ch. 4 - Prob. 1.40PECh. 4 - Prob. 1.41PECh. 4 - Prob. 1.42PECh. 4 - Prob. 1.43PECh. 4 - Prob. 1.44PECh. 4 - Prob. 1.45PECh. 4 - Prob. 1.46PECh. 4 - Prob. 1.47PECh. 4 - Prob. 1.48PECh. 4 - Prob. 1.49PECh. 4 - Prob. 1.50PECh. 4 - Prob. 1.51PECh. 4 - Prob. 1.52PECh. 4 - Prob. 1.53PECh. 4 - In the Excel file Debt and Retirement Savings, use...Ch. 4 - Prob. 1.55PECh. 4 - Prob. 1.56PECh. 4 - Prob. 1.57PECh. 4 - Prob. 1.58PECh. 4 - Prob. 1.59PECh. 4 - In the Excel file Weddings, determine the...Ch. 4 - Prob. 1.61PECh. 4 - The Excel file Beverage Sales lists a sample of...Ch. 4 - For the Presidents Inn Guest Database, find the...Ch. 4 - Prob. 1.64PECh. 4 - For the Excel file Credit Risk Data, compute the...Ch. 4 - Compute the z-scores for the data in the Excel...Ch. 4 - Prob. 1.67PECh. 4 - In the Excel file Weddings, find the mean, median,...Ch. 4 - Use the following approaches to analyze the survey...Ch. 4 - Prob. 1.70PECh. 4 - A producer of computer-aided design software for...Ch. 4 - Prob. 1.72PECh. 4 - Prob. 1.73PECh. 4 - A Midwest pharmaceutical company manufactures...Ch. 4 - Find the mean and variance of a deck of 52 cards,...Ch. 4 - Elizabeth Burke has received several questions...
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