Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 1.2, Problem 7CS
To determine
To explain: The programs ranked in the table, the reason for done the given manner.
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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 1 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 1.1 - Prob. 1TYCh. 1.1 - Prob. 2TYCh. 1.1 - Prob. 3TYCh. 1.1 - How is a sample related to a population?Ch. 1.1 - Why is a sample used more often than a population?Ch. 1.1 - What is the difference between a parameter and a...Ch. 1.1 - What are the two main branches of statistics?Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...
Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Graphical Analysis In Exercises 2124, use the Venn...Ch. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Distinguishing Between a Parameter and a Statistic...Ch. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.2 - Prob. 1TYCh. 1.2 - Prob. 2TYCh. 1.2 - Prob. 3TYCh. 1.2 - Name each level of measurement for which data can...Ch. 1.2 - Name each level of measurement for which data can...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Classifying Data by Type In Exercises 714,...Ch. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Classifying Data By Level In Exercises 1520,...Ch. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - The items below appear on a physician's intake...Ch. 1.2 - Graphical Analysis In Exercises 2124, determine...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Classifying Data by Type and Level In Exercises...Ch. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 1CSCh. 1.2 - Prob. 2CSCh. 1.2 - Prob. 3CSCh. 1.2 - Prob. 4CSCh. 1.2 - Prob. 5CSCh. 1.2 - Prob. 6CSCh. 1.2 - Prob. 7CSCh. 1.2 - Prob. 8CSCh. 1.3 - Prob. 1TYCh. 1.3 - Prob. 2TYCh. 1.3 - Prob. 3TYCh. 1.3 - Prob. 4TYCh. 1.3 - What is the difference between an observational...Ch. 1.3 - What is the difference between a census and a...Ch. 1.3 - What is the difference between a random sample and...Ch. 1.3 - What is replication in an experiment? Why is...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - Prob. 8ECh. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Random Number Table Use the sixth row of Table 1...Ch. 1.3 - Random Number Table Use the tenth row of Table 1...Ch. 1.3 - Random Numbers In Exercises 17 and 18, use...Ch. 1.3 - Random Numbers In Exercises 17 and 18, use...Ch. 1.3 - Sleep Deprivation A researcher wants to study the...Ch. 1.3 - Using a Simple Random Sample Volunteers for an...Ch. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Prob. 27ECh. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Choosing Between a Census and a Sampling In...Ch. 1.3 - Choosing Between a Census and a Sampling In...Ch. 1.3 - Recognizing a Biased Question In Exercises 3134,...Ch. 1.3 - Recognizing a Biased Question In Exercises 3134,...Ch. 1.3 - Recognizing a Biased Question In Exercises 3134,...Ch. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Natural Experiments Observational studies are...Ch. 1.3 - Open and Closed Questions Two types of survey...Ch. 1.3 - Prob. 40ECh. 1.3 - Prob. 1ACh. 1.3 - In Exercises 14, identify the population and the...Ch. 1 - Prob. 1.1.1RECh. 1 - Prob. 1.1.2RECh. 1 - Prob. 1.1.3RECh. 1 - Prob. 1.1.4RECh. 1 - Prob. 1.1.5RECh. 1 - Prob. 1.1.6RECh. 1 - Which part of the survey described in Exercise 3...Ch. 1 - Prob. 1.1.8RECh. 1 - Prob. 1.1.9RECh. 1 - Prob. 1.1.10RECh. 1 - In Exercises 1114, determine whether the data are...Ch. 1 - In Exercises 1114, determine whether the data are...Ch. 1 - In Exercises 1518, determine the level of...Ch. 1 - In Exercises 1518, determine the level of...Ch. 1 - Prob. 1.2.15RECh. 1 - In Exercises 1518, determine the level of...Ch. 1 - In Exercises 19 and 20, determine whether the...Ch. 1 - Prob. 1.2.18RECh. 1 - Prob. 1.3.19RECh. 1 - Prob. 1.3.20RECh. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Prob. 1.3.25RECh. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - You want to know the favorite spring break...Ch. 1 - A study of the dietary habits of 359,264 Korean...Ch. 1 - Prob. 1.3.29RECh. 1 - Determine whether each number describes a...Ch. 1 - Prob. 1CQCh. 1 - Prob. 2CQCh. 1 - Determine whether the study is an observational...Ch. 1 - An experiment is performed to test the effects of...Ch. 1 - Prob. 5CQCh. 1 - Which technique used in Exercise 7 could lead to a...Ch. 1 - Determine whether you would take a census or use a...Ch. 1 - Determine whether each number describes a...Ch. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Identify the sampling technique used, and discuss...Ch. 1 - Prob. 4CTCh. 1 - Determine whether the survey question is biased....Ch. 1 - Prob. 6CTCh. 1 - Prob. 1RSRDCh. 1 - Prob. 2RSRDCh. 1 - Prob. 3RSRDCh. 1 - The SEC (Securities and Exchange Commission) is...Ch. 1 - A quality control department is testing 25...Ch. 1 - Consider the population of ten digits: 0, 1, 2, 3,...Ch. 1 - Consider the population of 41 whole numbers from 0...Ch. 1 - Use random numbers to simulate rolling a six-sided...Ch. 1 - Prob. 6TCh. 1 - Use random numbers to simulate tossing a coin 100...Ch. 1 - You tossed a coin 100 times and got 77 heads and...Ch. 1 - A political analyst would like to survey a sample...
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