Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Textbook Question
Chapter 10.4, Problem 2JC
We need to survey a random sample of the 300 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below.
- a) Pick every 10th passenger as people board the plane.
- b) From the boarding list, randomly choose 5 people flying first class and 25 of the other passengers.
- c) Randomly generate 30 seat numbers and survey the passengers who sit there.
- d) Randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats.
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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 10 Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 10.2 - Various claims are often made for surveys. Why is...Ch. 10.4 - We need to survey a random sample of the 300...Ch. 10 - Texas AM Administrators at Texas AM University...Ch. 10 - Satisfied workers The managers of a large company...Ch. 10 - AM again The president of the university plans a...Ch. 10 - Satisfied respondents The companys annual report...Ch. 10 - Sampling students A professor teaching a large...Ch. 10 - Sampling satisfaction A company hoping to assess...Ch. 10 - Sampling AM students For each scenario, identify...Ch. 10 - Satisfactory satisfaction samples For each...
Ch. 10 - Survey students What problems do you see with...Ch. 10 - Happy employees The company plans to have the head...Ch. 10 - Student samples The university administration of...Ch. 10 - Surveying employees The company of Exercise 2 is...Ch. 10 - Roper Through their Roper Reports Worldwide, GfK...Ch. 10 - Student center survey For their class project, a...Ch. 10 - Drug tests Major League Baseball tests players to...Ch. 10 - Gallup At its website (www.gallup.com), the Gallup...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - Prob. 20ECh. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - Mistaken poll A local TV station conducted a...Ch. 10 - Another mistaken poll Prior to the mayoral...Ch. 10 - Parent opinion, part 1 In a large city school...Ch. 10 - Parent opinion, part 2 Lets revisit the school...Ch. 10 - Prob. 28ECh. 10 - Prob. 29ECh. 10 - Roller coasters An amusement park has opened a new...Ch. 10 - Playground, act two The survey described in...Ch. 10 - Wording the survey Two members of the PTA...Ch. 10 - Banning ephedra An online poll on a website asked:...Ch. 10 - Survey questions Examine each of the following...Ch. 10 - More survey questions Examine each of the...Ch. 10 - Phone surveys Any time we conduct a survey, we...Ch. 10 - Cell phone survey What about drawing a random...Ch. 10 - Fuel economy Occasionally, when I fill my car with...Ch. 10 - Prob. 40ECh. 10 - Prob. 41ECh. 10 - Quality control Sammys Salsa, a small local...Ch. 10 - A fish story Concerned about reports of discolored...Ch. 10 - Prob. 44ECh. 10 - Prob. 45ECh. 10 - More sampling methods Consider each of these...
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