APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Chapter 2.6, Problem 27SE
To determine
Explain the difference in student responses to the two given questions.
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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 2 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
Ch. 2.1 - What type of data (categorical, discrete...Ch. 2.1 - What type of data (categorical, discrete...Ch. 2.1 - What type of data (categorical, discrete...Ch. 2.1 - (a) Give three original examples of discrete data,...Ch. 2.1 - Which type of data (cross-sectional or time...Ch. 2.1 - Which type of data (cross-sectional or time...Ch. 2.1 - Prob. 7SECh. 2.1 - Give an original example of a time series variable...Ch. 2.2 - Which measurement level (nominal, ordinal,...Ch. 2.2 - Which measurement level (nominal, ordinal,...
Ch. 2.2 - Which measurement level (nominal, ordinal,...Ch. 2.2 - Prob. 12SECh. 2.2 - Prob. 13SECh. 2.2 - (a) Would the measurement level for the data...Ch. 2.3 - Would you use a sample or a census to measure each...Ch. 2.3 - Would you use a sample or a census to measure each...Ch. 2.3 - The target population is all stocks in the SP 500...Ch. 2.4 - The target population is all students in your...Ch. 2.4 - Suppose you want to know the ages of moviegoers...Ch. 2.4 - Suppose you want to study the number of e-mail...Ch. 2.4 - In Excel, type a list containing names for 10 of...Ch. 2.6 - What sources of error might you encounter if you...Ch. 2.6 - What kind of survey (mail, telephone, interview,...Ch. 2.6 - What kind of survey (mail, telephone, interview,...Ch. 2.6 - Prob. 27SECh. 2.6 - What problems are evident in the wording of these...Ch. 2 - Define (a) data, (b) data set (c) observation, and...Ch. 2 - How do business data differ from scientific...Ch. 2 - Distinguish (a) univariate, bivariate, and...Ch. 2 - Define the four measurement levels and give an...Ch. 2 - Prob. 5CRCh. 2 - (a) List three reasons why a census might be...Ch. 2 - Prob. 7CRCh. 2 - (a) List four methods of random sampling. (b) List...Ch. 2 - List five (a) steps in a survey, (b) issues in...Ch. 2 - Prob. 10CRCh. 2 - Prob. 29CECh. 2 - Prob. 30CECh. 2 - Prob. 31CECh. 2 - Which measurement level (nominal, ordinal,...Ch. 2 - Below are five questions from a survey of MBA...Ch. 2 - Below are five questions from a survey of MBA...Ch. 2 - Below are five questions from a survey of MBA...Ch. 2 - Prob. 36CECh. 2 - Identify the following data as either time series...Ch. 2 - Would you use a sample or a census to measure each...Ch. 2 - Would you use a sample or census to measure each...Ch. 2 - Is each of the following a parameter or a...Ch. 2 - Prob. 41CECh. 2 - Prob. 42CECh. 2 - Prob. 43CECh. 2 - Prob. 44CECh. 2 - The IRS estimates that the average taxpayer spent...Ch. 2 - The General Accounting Office conducted random...Ch. 2 - Arsenic (a naturally occurring, poisonous metal)...Ch. 2 - Prob. 48CECh. 2 - Would you expect Noodles Company to use a sample...Ch. 2 - A financial magazine publishes an annual list of...Ch. 2 - Examine each of the following statistics. Which...Ch. 2 - The National Claims History (NCH) contains records...Ch. 2 - Prior to starting a recycling program, a city...Ch. 2 - A university wanted to survey alumni about their...Ch. 2 - The U.S. Fisheries and Wildlife Service requires...Ch. 2 - Prob. 56CECh. 2 - Households can sign up for a telemarketing no-call...Ch. 2 - What level of measurement (nominal, ordinal,...Ch. 2 - Insurance companies are rated by several rating...Ch. 2 - A tabletop survey by a restaurant asked the...Ch. 2 - Give two original examples of (a) discrete data...Ch. 2 - Prob. 64CECh. 2 - Below are 64 names of employees at NilCo. Colors...Ch. 2 - From the display below, pick five cards (without...Ch. 2 - You can test Excels algorithm for selecting random...
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