Elementary Statistics Using Excel (6th Edition)
6th Edition
ISBN: 9780134506623
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 7.1, Problem 33BSC
a.
To determine
To find: The
b.
To determine
To find: The sample size.
c.
To determine
To check: Whether the added knowledge in part (b) has much of an effect on the sample size.
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Students have asked these similar questions
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 7 Solutions
Elementary Statistics Using Excel (6th Edition)
Ch. 7.1 - 1. Poll Results in the Media USA Today provided...Ch. 7.1 - 2. Margin of Error For the poll described in...Ch. 7.1 - 3. Notation For the poll described in Exercise 1,...Ch. 7.1 - 4. Confidence Levels Given specific sample data,...Ch. 7.1 - Prob. 5BSCCh. 7.1 - Prob. 6BSCCh. 7.1 - Prob. 7BSCCh. 7.1 - Prob. 8BSCCh. 7.1 - Formats of Confidence Intervals. In Exercises...Ch. 7.1 - Prob. 10BSC
Ch. 7.1 - Prob. 11BSCCh. 7.1 - Prob. 12BSCCh. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Prob. 14BSCCh. 7.1 - Prob. 15BSCCh. 7.1 - Prob. 16BSCCh. 7.1 - Critical Thinking. In Exercises 17–28, use the...Ch. 7.1 - Prob. 18BSCCh. 7.1 - Prob. 19BSCCh. 7.1 - Critical Thinking. In Exercises 17–28, use the...Ch. 7.1 - 21. Touch Therapy When she was 9 years of age,...Ch. 7.1 - Prob. 22BSCCh. 7.1 - Prob. 23BSCCh. 7.1 - Critical Thinking. In Exercises 17–28, use the...Ch. 7.1 - Prob. 25BSCCh. 7.1 - Prob. 26BSCCh. 7.1 - Prob. 27BSCCh. 7.1 - Prob. 28BSCCh. 7.1 - Using Appendix B Data Sets. In Exercises 29 and...Ch. 7.1 - Prob. 30BSCCh. 7.1 - Determining Sample Size. In Exercises 31–38, use...Ch. 7.1 - Determining Sample Size. In Exercises 31–38, use...Ch. 7.1 - Determining Sample Size. In Exercises 31–38, use...Ch. 7.1 - Determining Sample Size. In Exercises 31–38, use...Ch. 7.1 - Prob. 35BSCCh. 7.1 - Prob. 36BSCCh. 7.1 - Prob. 37BSCCh. 7.1 - Prob. 38BSCCh. 7.1 - Prob. 39BBCh. 7.1 - Prob. 40BBCh. 7.1 - Prob. 41BBCh. 7.2 - In Exercises 1–3, refer to the accompanying screen...Ch. 7.2 - Statistical Literacy and Critical Thinking
In...Ch. 7.2 - Prob. 3BSCCh. 7.2 - Prob. 4BSCCh. 7.2 - Prob. 5BSCCh. 7.2 - Prob. 6BSCCh. 7.2 - Prob. 7BSCCh. 7.2 - Prob. 8BSCCh. 7.2 - Prob. 9BSCCh. 7.2 - Prob. 10BSCCh. 7.2 - Prob. 11BSCCh. 7.2 - Prob. 12BSCCh. 7.2 - Prob. 13BSCCh. 7.2 - Prob. 14BSCCh. 7.2 - Prob. 15BSCCh. 7.2 - Confidence Intervals. In Exercises 9–24, construct...Ch. 7.2 - Prob. 17BSCCh. 7.2 - Prob. 18BSCCh. 7.2 - Prob. 19BSCCh. 7.2 - Prob. 20BSCCh. 7.2 - Prob. 21BSCCh. 7.2 - Confidence Intervals. In Exercises 9–24, construct...Ch. 7.2 - Prob. 23BSCCh. 7.2 - Prob. 24BSCCh. 7.2 - Prob. 25BSCCh. 7.2 - In Exercises 25 – 28, use the Appendix B data sets...Ch. 7.2 - In Exercises 25 – 28, use the Appendix B data sets...Ch. 7.2 - Prob. 28BSCCh. 7.2 - Prob. 29BSCCh. 7.2 - Prob. 30BSCCh. 7.2 - Prob. 31BSCCh. 7.2 - Prob. 32BSCCh. 7.2 - Prob. 33BSCCh. 7.2 - Prob. 34BSCCh. 7.2 - Prob. 35BSCCh. 7.2 - Prob. 36BSCCh. 7.2 - Prob. 37BBCh. 7.2 - Prob. 38BBCh. 7.2 - Prob. 39BBCh. 7.3 - Prob. 1BSCCh. 7.3 - Prob. 2BSCCh. 7.3 - Prob. 3BSCCh. 7.3 - 4. Normality Requirement What is different about...Ch. 7.3 - Prob. 5BSCCh. 7.3 - Prob. 6BSCCh. 7.3 - Prob. 7BSCCh. 7.3 - Prob. 8BSCCh. 7.3 - Prob. 9BSCCh. 7.3 - Finding Confidence Intervals. In Exercises 9–16,...Ch. 7.3 - Prob. 11BSCCh. 7.3 - Prob. 12BSCCh. 7.3 - Prob. 13BSCCh. 7.3 - Prob. 14BSCCh. 7.3 - Finding Confidence Intervals. In Exercises 9–16,...Ch. 7.3 - 16. Comparing Waiting Lines
a. The values listed...Ch. 7.3 - Prob. 17BSCCh. 7.3 - Prob. 18BSCCh. 7.3 - Prob. 19BSCCh. 7.3 - Prob. 20BSCCh. 7.3 - Prob. 21BSCCh. 7.3 - Prob. 22BSCCh. 7.3 - Prob. 23BBCh. 7.3 - Prob. 24BBCh. 7.4 - Prob. 1BSCCh. 7.4 - Prob. 2BSCCh. 7.4 - 3. Bootstrap Sample Given the sample data from...Ch. 7.4 - Prob. 4BSCCh. 7.4 - Prob. 5BSCCh. 7.4 - Prob. 6BSCCh. 7.4 - Prob. 7BSCCh. 7.4 - Prob. 8BSCCh. 7.4 - Prob. 9BSCCh. 7.4 - Prob. 10BSCCh. 7.4 - Prob. 11BSCCh. 7.4 - Prob. 12BSCCh. 7.4 - Prob. 17BSCCh. 7.4 - Prob. 18BSCCh. 7.4 - Prob. 19BSCCh. 7.4 - Prob. 20BSCCh. 7.4 - Analysis of Last Digits Weights of respondents...Ch. 7.4 - Analysis of Last Digits Repeat Exercise 21...Ch. 7.4 - Prob. 23BBCh. 7.4 - Prob. 24BBCh. 7 - Prob. 1CQQCh. 7 - Prob. 2CQQCh. 7 - Prob. 3CQQCh. 7 - 4. Loose Change USA Today reported that 40% of...Ch. 7 - 5. Sample Size for Proportion Find the sample size...Ch. 7 - Prob. 6CQQCh. 7 - Prob. 7CQQCh. 7 - Prob. 8CQQCh. 7 - Prob. 9CQQCh. 7 - Prob. 10CQQCh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 1CRECh. 7 - Prob. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 4CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - Prob. 7CRECh. 7 - Prob. 8CRECh. 7 - Prob. 1EPCh. 7 - Prob. 1FDDCh. 7 - Prob. 2FDDCh. 7 - Prob. 3FDDCh. 7 - Prob. 4FDDCh. 7 - Prob. 5FDD
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