Elementary Statistics
3rd Edition
ISBN: 9781260373561
Author: Navidi, William
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 2, Problem 14RE
a.
To determine
To find:The year in which the death rate from cancer is the highest and the year when it was the lowest.
b.
To determine
To find: Whether the life expectancy has been increasing or decreasing during the years 1930-2010.
c.
To determine
To explain: The reason for the increasing death rates due to cancer during 1930 to 2010.
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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
Elementary Statistics
Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - The following bar graph presents the average...Ch. 2.1 - The most common blood typing system divides human...
Ch. 2.1 - Following is a pie chart that presents the...Ch. 2.1 - Government spending: The following pie chart...Ch. 2.1 - U.S. population: The following side-by-side bar...Ch. 2.1 - Super Bowl: The following side-by-side bar graph...Ch. 2.1 - Smartphone sales: The following frequency...Ch. 2.1 - Popular video games: The following frequency...Ch. 2.1 - More smartphones: Using the data in Exercise 19:...Ch. 2.1 - More video games: Using the data in Exercise 20:...Ch. 2.1 - Hospital admissions: The following frequency...Ch. 2.1 - World population: Following are the populations of...Ch. 2.1 - Ages of video garners: The Nielsen Company...Ch. 2.1 - How secure is your job? In a survey, employed...Ch. 2.1 - Back up your data: In a survey commissioned by the...Ch. 2.1 - Education levels: The following frequency...Ch. 2.1 - Twitter followers: The following frequency...Ch. 2.1 - Music sales: The following frequency distribution...Ch. 2.1 - Keeping up with the Kardashians: The following...Ch. 2.1 - Bought a new car lately? The following table...Ch. 2.1 - Bought a new- truck lately? The following table...Ch. 2.1 - Happy Halloween: The following table presents...Ch. 2.1 - Native languages: The following frequency...Ch. 2.1 - Proportion of females: Following are the...Ch. 2.2 - Prob. 5ECh. 2.2 - In Exercises 5—8, fill in each blank with the...Ch. 2.2 - In Exercises 5—8, fill in each blank with the...Ch. 2.2 - In Exercises 5—8, fill in each blank with the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 17 and 18, classify the histogram as...Ch. 2.2 - In Exercises 17 and 18, classify the histogram as...Ch. 2.2 - Student heights: The following frequency histogram...Ch. 2.2 - Trained rats: Forty rats were trained to run a...Ch. 2.2 - Cholesterol: The following histogram shows the...Ch. 2.2 - Blood pressure: The following histogram shows the...Ch. 2.2 - Olympic athletes: The following frequency...Ch. 2.2 - Hows the weather? The following relative frequency...Ch. 2.2 - Skewed which way? For which of the following data...Ch. 2.2 - Skewed which way? For which of the following data...Ch. 2.2 - Batting average: The following frequency...Ch. 2.2 - Batting average: The following frequency...Ch. 2.2 - Time spent playing video games: A sample of 200...Ch. 2.2 - Murder, she wrote: The following frequency...Ch. 2.2 - BMW prices: The following table presents the...Ch. 2.2 - Geysers: The geyser Old Faithful in Yellowstone...Ch. 2.2 - Hail to the chief: There have been 58 presidential...Ch. 2.2 - Internet radio: The following table presents the...Ch. 2.2 - Brothers and sisters: Thirty students in a...Ch. 2.2 - Cough, cough: The following table presents the...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Frequency polygon: Using the data in Exercise 29:...Ch. 2.2 - Prob. 42ECh. 2.2 - Ogive: Using the data in Exercise 27: Compute the...Ch. 2.2 - Ogive: Using the data in Exercise 28: Compute the...Ch. 2.2 - Ogive: Using the data in Exercise 29: Compute the...Ch. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Frequencies and relative frequencies: The...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - Prob. 7ECh. 2.3 - In Exercises 7—10, determine whether the...Ch. 2.3 - In Exercises 7—10, determine whether the...Ch. 2.3 - In Exercises 7—10, determine whether the...Ch. 2.3 - Construct a stem-and-leaf plot for the following...Ch. 2.3 - Construct a stem-and-leaf plot for the following...Ch. 2.3 - List the data in the following stem-and-leaf plot....Ch. 2.3 - List the data in the following stein-and-leaf...Ch. 2.3 - Construct a dotplot for the data in Exercise 11.Ch. 2.3 - Prob. 16ECh. 2.3 - BMW prices: The following table presents the...Ch. 2.3 - Hows the weather? The following table presents the...Ch. 2.3 - Air pollution: The following table presents...Ch. 2.3 - Technology salaries: The following table presents...Ch. 2.3 - Tennis and golf: Following are the ages of the...Ch. 2.3 - Pass the popcorn: Following are the running times...Ch. 2.3 - More weather: Construct a dotplot for the data in...Ch. 2.3 - Prob. 24ECh. 2.3 - Looking for a job: The following table presents...Ch. 2.3 - Prob. 26ECh. 2.3 - Military spending: The following table presents...Ch. 2.3 - Prob. 28ECh. 2.3 - Dining out: The following time-series plot...Ch. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - More gold: The following time series plot presents...Ch. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Vote: The following time-series plot presents the...Ch. 2.3 - Arctic ice sheet: The following table presents the...Ch. 2.3 - Prob. 37ECh. 2.4 - In Exercises 3 and 4, fill in each blank with the...Ch. 2.4 - In Exercises 3 and 4, fill in each blank with the...Ch. 2.4 - CD sales decline: Sales of CDs have been declining...Ch. 2.4 - Music sales: The following time-series plot and...Ch. 2.4 - Stock market prices: The Dow Jones Industrial...Ch. 2.4 - Save your money: In 2007, U.S. residents saved...Ch. 2.4 - Ill take mine with mustard: The following bar...Ch. 2.4 - Stream or download? The following bar graph...Ch. 2.4 - Female senators: Of the 100 members of the United...Ch. 2.4 - Age at marriage: Data compiled by the U.S. Census...Ch. 2.4 - College degrees: Both of the following time-series...Ch. 2.4 - Food expenditures: Both of the following...Ch. 2.4 - Prob. 15ECh. 2 - Following is the list of letter grades for...Ch. 2 - Prob. 2CQCh. 2 - Construct a frequency bar graph for the data in...Ch. 2 - Prob. 4CQCh. 2 - Prob. 5CQCh. 2 - Prob. 6CQCh. 2 - Prob. 7CQCh. 2 - Prob. 8CQCh. 2 - Prob. 9CQCh. 2 - Prob. 10CQCh. 2 - Following are the prices (in dollars) for a sample...Ch. 2 - Prob. 12CQCh. 2 - Prob. 13CQCh. 2 - Prob. 14CQCh. 2 - Prob. 15CQCh. 2 - Trust your doctor: The General Social Survey...Ch. 2 - Internet browsers: The following relative...Ch. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - House freshmen: Newly elected members of the U.S....Ch. 2 - More freshmen: For the data in Exercise 6:...Ch. 2 - Royalty: Following are the ages at death for all...Ch. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Explain why the frequency bar graph and the...Ch. 2 - Prob. 2WAICh. 2 - Prob. 3WAICh. 2 - Prob. 4WAICh. 2 - Prob. 5WAICh. 2 - In the chapter introduction, we presented gas...Ch. 2 - In the chapter introduction, we presented gas...Ch. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 4CSCh. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 6CSCh. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 8CSCh. 2 - In the chapter introduction, we presented gas...
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