ELEMENTARY STATISTICS PKG. F13
13th Edition
ISBN: 9781269373333
Author: Triola
Publisher: PEARSON C
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Chapter 13.6, Problem 14BSC
Appendix B Data Sets. In Exercises 13–16, use the data in Appendix B to test for rank
14. Ages of Best Actresses and Best Actors Repeat Exercise 8 using all of the paired ages from Data Set 14 “Oscar Winner Age” in Appendix B.
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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 13 Solutions
ELEMENTARY STATISTICS PKG. F13
Ch. 13.2 - Prob. 1BSCCh. 13.2 - Prob. 2BSCCh. 13.2 - Contradicting H1 An important step in conducting...Ch. 13.2 - Efficiency of the Sign Test Refer to Table 13-2 on...Ch. 13.2 - Matched Pairs. In Exercises 58, use the sign test...Ch. 13.2 - Matched Pairs. In Exercises 58, use the sign test...Ch. 13.2 - Matched Pairs. In Exercises 58, use the sign test...Ch. 13.2 - Matched Pairs. In Exercises 58, use the sign test...Ch. 13.2 - Nominal Data. In Exercises 912, use the sign test...Ch. 13.2 - Nominal Data. In Exercises 912, use the sign test...
Ch. 13.2 - Nominal Data. In Exercises 912, use the sign test...Ch. 13.2 - Nominal Data. In Exercises 912, use the sign test...Ch. 13.2 - Appendix B Data Sets. In Exercises 1316, refer to...Ch. 13.2 - Appendix B Data Sets. In Exercises 1316, refer to...Ch. 13.2 - Appendix B Data Sets. In Exercises 1316, refer to...Ch. 13.2 - Appendix B Data Sets. In Exercises 1316, refer to...Ch. 13.2 - Procedures for Handling Ties In the sign lest...Ch. 13.2 - Finding Critical Values Table A-7 lists critical...Ch. 13.3 - Wilcoxon Signed-Ranks Test for Body Temperatures...Ch. 13.3 - Prob. 2BSCCh. 13.3 - Prob. 3BSCCh. 13.3 - Prob. 4BSCCh. 13.3 - Using the Wilcoxon Signed-Ranks Test. In Exercises...Ch. 13.3 - Using the Wilcoxon Signed-Ranks Test. In Exercises...Ch. 13.3 - Using the Wilcoxon Signed-Ranks Test. In Exercises...Ch. 13.3 - Using the Wilcoxon Signed-Ranks Test. In Exercises...Ch. 13.3 - Prob. 9BSCCh. 13.3 - Prob. 10BSCCh. 13.3 - Prob. 11BSCCh. 13.3 - Prob. 12BSCCh. 13.3 - Rank Sums Exercise 12 uses Data Set 23 Old...Ch. 13.4 - Prob. 1BSCCh. 13.4 - Rank Sum After ranking the combined list of...Ch. 13.4 - Prob. 3BSCCh. 13.4 - Prob. 4BSCCh. 13.4 - Wilcoxon Rank-Sum Test. In Exercises 58, use the...Ch. 13.4 - Wilcoxon Rank-Sum Test. In Exercises 58, use the...Ch. 13.4 - Wilcoxon Rank-Sum Test. In Exercises 58, use the...Ch. 13.4 - Wilcoxon Rank-Sum Test. In Exercises 58, use the...Ch. 13.4 - Prob. 9BSCCh. 13.4 - Appendix B Data Sets. In Exercises 912, refer to...Ch. 13.4 - Appendix B Data Sets. In Exercises 912, refer to...Ch. 13.4 - Appendix B Data Sets. In Exercises 912, refer to...Ch. 13.4 - Prob. 13BBCh. 13.4 - Finding Critical Values Assume that we have two...Ch. 13.5 - Prob. 1BSCCh. 13.5 - Requirements Assume that we want to use the data...Ch. 13.5 - Notation For the data given in Exercise 1,...Ch. 13.5 - Efficiency Refer to Table 13-2 on page 600 and...Ch. 13.5 - Prob. 5BSCCh. 13.5 - Prob. 6BSCCh. 13.5 - Prob. 7BSCCh. 13.5 - Prob. 8BSCCh. 13.5 - Appendix B Data Sets. In Exercises 912, use the...Ch. 13.5 - Prob. 10BSCCh. 13.5 - Appendix B Data Sets. In Exercises 912, use the...Ch. 13.5 - Appendix B Data Sets. In Exercises 912, use the...Ch. 13.5 - Correcting the H Test Statistic for Ties In using...Ch. 13.6 - Regression If the methods of this section are used...Ch. 13.6 - Level of Measurement Which of the levels of...Ch. 13.6 - Notation What do r, rs , and ps denote? Why is the...Ch. 13.6 - Prob. 4BSCCh. 13.6 - In Exercises 5 and 6, use the scatterplot to find...Ch. 13.6 - In Exercises 5 and 6, use the scatterplot to find...Ch. 13.6 - Testing for Rank Correlation. In Exercises 712,...Ch. 13.6 - Prob. 8BSCCh. 13.6 - Testing for Rank Correlation. In Exercises 712,...Ch. 13.6 - Testing for Rank Correlation. In Exercises 712,...Ch. 13.6 - Prob. 11BSCCh. 13.6 - Testing for Rank Correlation. In Exercises 712,...Ch. 13.6 - Prob. 13BSCCh. 13.6 - Appendix B Data Sets. In Exercises 1316, use the...Ch. 13.6 - Appendix B Data Sets. In Exercises 1316, use the...Ch. 13.6 - Prob. 16BSCCh. 13.6 - Prob. 17BBCh. 13.7 - In Exercises 14, use the following sequence of...Ch. 13.7 - Prob. 2BSCCh. 13.7 - Prob. 3BSCCh. 13.7 - Prob. 4BSCCh. 13.7 - Using the Runs Test for Randomness. In Exercises...Ch. 13.7 - Prob. 6BSCCh. 13.7 - Prob. 7BSCCh. 13.7 - Using the Runs Test for Randomness. In Exercises...Ch. 13.7 - Prob. 9BSCCh. 13.7 - Prob. 10BSCCh. 13.7 - Runs Test with Large Samples. In Exercises 912,...Ch. 13.7 - Prob. 12BSCCh. 13 - Prob. 1CQQCh. 13 - Prob. 2CQQCh. 13 - Prob. 3CQQCh. 13 - Prob. 4CQQCh. 13 - Prob. 5CQQCh. 13 - Prob. 6CQQCh. 13 - Prob. 7CQQCh. 13 - Prob. 8CQQCh. 13 - Prob. 9CQQCh. 13 - Which Test? Three different judges give the same...Ch. 13 - Prob. 1RECh. 13 - Using Nonparametric Tests. In Exercises 110, use a...Ch. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Using Nonparametric Tests. In Exercises 110, use a...Ch. 13 - Prob. 8RECh. 13 - Using Nonparametric Tests. In Exercises 1-10, use...Ch. 13 - Prob. 10RECh. 13 - Prob. 1CRECh. 13 - Prob. 2CRECh. 13 - In Exercises 13, use the data listed below. The...Ch. 13 - Prob. 4CRECh. 13 - Prob. 5CRECh. 13 - Prob. 6CRECh. 13 - Prob. 7CRECh. 13 - Prob. 8CRECh. 13 - Fear of Heights Among readers of a USA Today...Ch. 13 - Cell Phones and Crashes: Analyzing Newspaper...Ch. 13 - Prob. 1TPCh. 13 - Prob. 1FDD
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