Elementary Statistics Using the TI-83/84 Plus Calculator, Books a la Carte Edition (4th Edition)
4th Edition
ISBN: 9780321953902
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 3.2, Problem 1BSC
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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 3 Solutions
Elementary Statistics Using the TI-83/84 Plus Calculator, Books a la Carte Edition (4th Edition)
Ch. 3.2 - Prob. 1BSCCh. 3.2 - 2. Average The web site IncomeTaxList.com lists...Ch. 3.2 - Prob. 3BSCCh. 3.2 - Measures of Center In what sense are the mean,...Ch. 3.2 - Prob. 5BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...
Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - In Exercises 2124, find the mean and median for...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - Prob. 25BSCCh. 3.2 - Prob. 26BSCCh. 3.2 - Prob. 27BSCCh. 3.2 - Prob. 28BSCCh. 3.2 - Prob. 29BSCCh. 3.2 - Prob. 30BSCCh. 3.2 - Prob. 31BSCCh. 3.2 - Prob. 32BSCCh. 3.2 - 33. Degrees of Freedom Carbon monoxide is measured...Ch. 3.2 - Prob. 34BBCh. 3.2 - Prob. 35BBCh. 3.2 - Prob. 36BBCh. 3.2 - Prob. 37BBCh. 3.2 - Prob. 38BBCh. 3.2 - Prob. 39BBCh. 3.3 - Prob. 1BSCCh. 3.3 - 2. Correct Statements? Which of the following...Ch. 3.3 - 3. Variation and Variance In statistics, how do...Ch. 3.3 - 4. Symbols Identify the symbols used for each of...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - Large Data Sets from Appendix B. In Exercises...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - In Exercises 5–20, find the range, variance, and...Ch. 3.3 - Prob. 21BSCCh. 3.3 - In Exercises 2124, find the coefficient of...Ch. 3.3 - Prob. 23BSCCh. 3.3 - Prob. 24BSCCh. 3.3 - Prob. 25BSCCh. 3.3 - Prob. 26BSCCh. 3.3 - Prob. 27BSCCh. 3.3 - Prob. 28BSCCh. 3.3 - Prob. 29BSCCh. 3.3 - Prob. 30BSCCh. 3.3 - Prob. 31BSCCh. 3.3 - Prob. 32BSCCh. 3.3 - Prob. 33BSCCh. 3.3 - Identifying Unusual Values with the Range Rule of...Ch. 3.3 - Identifying Unusual Values with the Range Rule of...Ch. 3.3 - Identifying Unusual Values with the Range Rule of...Ch. 3.3 - Prob. 37BSCCh. 3.3 - Prob. 38BSCCh. 3.3 - Prob. 39BSCCh. 3.3 - Prob. 40BSCCh. 3.3 - Prob. 41BSCCh. 3.3 - Prob. 42BSCCh. 3.3 - Prob. 43BSCCh. 3.3 - Chebyshevs Theorem Based on Data Set 3 Body...Ch. 3.3 - Prob. 45BBCh. 3.3 - Prob. 46BBCh. 3.4 - Prob. 1BSCCh. 3.4 - z Scores If your score on your next statistics...Ch. 3.4 - 3. Boxplots Shown below is a STATDISK-generated...Ch. 3.4 - 4. Measures of Location The values of P50, Q2 and...Ch. 3.4 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.4 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.4 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.4 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.4 - Usual and Unusual Values. In Exercises 9-12,...Ch. 3.4 - Usual and Unusual Values. In Exercises 9-12,...Ch. 3.4 - Usual and Unusual Values. In Exercises 9-12,...Ch. 3.4 - Usual and Unusual Values. In Exercises 9-12,...Ch. 3.4 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.4 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.4 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.4 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.4 - Prob. 17BSCCh. 3.4 - Prob. 18BSCCh. 3.4 - Prob. 19BSCCh. 3.4 - Prob. 20BSCCh. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - In Exercises 21-28, use the same list of 24 sorted...Ch. 3.4 - Boxplots. In Exercises 29–32, use the given data...Ch. 3.4 - Boxplots. In Exercises 29–32, use the given data...Ch. 3.4 - Boxplots. In Exercises 29–32, use the given data...Ch. 3.4 - Boxplots. In Exercises 29–32, use the given data...Ch. 3.4 - Prob. 33BSCCh. 3.4 - Prob. 34BSCCh. 3.4 - Prob. 35BSCCh. 3.4 - Prob. 36BSCCh. 3.4 - Prob. 37BBCh. 3.4 - Prob. 38BBCh. 3 - Prob. 1CQQCh. 3 - Prob. 2CQQCh. 3 - Prob. 3CQQCh. 3 - Prob. 4CQQCh. 3 - Prob. 5CQQCh. 3 - Prob. 6CQQCh. 3 - Prob. 7CQQCh. 3 - Prob. 8CQQCh. 3 - Prob. 9CQQCh. 3 - Prob. 10CQQCh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 1CRECh. 3 - Prob. 2CRECh. 3 - Prob. 3CRECh. 3 - Prob. 5CRECh. 3 - Prob. 6CRECh. 3 - 7. Sampling Shortly after the World Trade Center...Ch. 3 - Prob. 8CRE
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