Essentials of Statistics; MathXL Valuepack Access Card (6-months) (5th Edition)
5th Edition
ISBN: 9780133954982
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 2.2, Problem 7BSC
In Exercises 5-10, identify the class width, class midpoints, and class boundaries for the given frequency distribution. The frequency distributions are based on real data from Appendix B.
7.
| Verbal IQ Score of Subject Exposed to Lead |
Frequency |
| 50-59 | 4 |
| 60-69 | 10 |
| 70-79 | 25 |
| 80-69 | 43 |
| 90-99 | 26 |
| 100-109 | 8 |
| 110-119 | 3 |
| 120-129 | 2 |
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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?
Chapter 2 Solutions
Essentials of Statistics; MathXL Valuepack Access Card (6-months) (5th Edition)
Ch. 2.2 - Frequency Distribution Table 2-2 on page 45 is a...Ch. 2.2 - Relative Frequency Distribution After construction...Ch. 2.2 - Do You Believe? In a Harris Interactive survey,...Ch. 2.2 - Analyzing a Frequency Distribution The...Ch. 2.2 - In Exercises 5-10, identify the class width, class...Ch. 2.2 - In Exercises 5-10, identify the class width, class...Ch. 2.2 - In Exercises 5-10, identify the class width, class...Ch. 2.2 - In Exercises 5-10, identify the class width, class...Ch. 2.2 - In Exercises 5-10, identify the class width, class...Ch. 2.2 - In Exercises 5-10, identify the class width, class...
Ch. 2.2 - Normal Distributions. In Exercises 11-14, answer...Ch. 2.2 - Normal Distributions. In Exercises 11-14, answer...Ch. 2.2 - Normal Distributions. In Exercises 11-14, answer...Ch. 2.2 - Normal Distributions. In Exercises 11-14, answer...Ch. 2.2 - Relative Frequencies for Comparisons. In Exercises...Ch. 2.2 - Relative Frequencies for Comparisons. In Exercises...Ch. 2.2 - Cumulative Frequency Distributions. In Exercises...Ch. 2.2 - Cumulative Frequency Distributions. In Exercises...Ch. 2.2 - Analysis of Last Digits Heights of statistics...Ch. 2.2 - Analysis of Last Digits Weights of respondents...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Constructing Frequency Distributions. In Exercises...Ch. 2.2 - Categorical Data. In Exercises 29-32, use the...Ch. 2.2 - Categorical Data. In Exercises 29-32, use the...Ch. 2.2 - Categorical Data. In Exercises 29-32, use the...Ch. 2.2 - Categorical Data. In Exercises 29-32, use the...Ch. 2.2 - Interpreting Effects of Outliers Refer to Data Set...Ch. 2.2 - Number of Classes According to what is known as...Ch. 2.3 - Prob. 1BSCCh. 2.3 - Voluntary Response Sample The histogram in Figure...Ch. 2.3 - Small Data NASA provides these duration times (in...Ch. 2.3 - Normal Distribution When it refers to a normal...Ch. 2.3 - Interpreting a Histogram. In Exercises 5-8, answer...Ch. 2.3 - Interpreting a Histogram. In Exercises 5-8, answer...Ch. 2.3 - Interpreting a Histogram. In Exercises 5-8, answer...Ch. 2.3 - Interpreting a Histogram. In Exercises 5-8, answer...Ch. 2.3 - Analysis of Last Digits Use the frequency...Ch. 2.3 - Analysis of Last Digits Use the frequency...Ch. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Prob. 15BSCCh. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Constructing Histograms. In Exercises 9-18,...Ch. 2.3 - Back-to-Back Relative Frequency Histograms When...Ch. 2.3 - Interpreting a Histogram. In Exercises 5-8, answer...Ch. 2.4 - Bar Chart and Pareto Chart A bar chart and a...Ch. 2.4 - Scatterplot What is a scatterplot? What type of...Ch. 2.4 - SAT Scores Listed below are SAT scores from a...Ch. 2.4 - SAT Scores Given that the data in Exercise 3 were...Ch. 2.4 - Scatterplots. In Exercises 5-8, use the given...Ch. 2.4 - Scatterplots. In Exercises 5-8, use the given...Ch. 2.4 - Scatterplots. In Exercises 5-8, use the given...Ch. 2.4 - Scatterplots. In Exercises 5-8, use the given...Ch. 2.4 - Time-Series Graphs. In Exercises 9 and 10,...Ch. 2.4 - Time-Series Graphs. In Exercises 9 and 10,...Ch. 2.4 - Dotplots. In Exercises II and 12, construct the...Ch. 2.4 - Dotplots. In Exercises 11 and 12, construct the...Ch. 2.4 - Stemplots. In Exercises 13 and 14, construct the...Ch. 2.4 - Stemplots. In Exercises 13 and 14, construct the...Ch. 2.4 - Pareto Charts. In Exercises 15 and 16, construct...Ch. 2.4 - Pareto Charts. In Exercises 15 and 16, construct...Ch. 2.4 - Pie Charts. In Exercises 17 and 18, construct the...Ch. 2.4 - Pie Charts. In Exercises 17 and 18, construct the...Ch. 2.4 - Frequency Polygon. In Exercises 19 and 20,...Ch. 2.4 - Frequency Polygon. In Exercises 19 and 20,...Ch. 2.4 - Deceptive Graphs. In Exercises 21-24, identify the...Ch. 2.4 - Deceptive Graphs. 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