EP ELEMENTARY STAT.USING EXC.-MYSTATLAB
7th Edition
ISBN: 9780136961888
Author: Triola
Publisher: PEARSON CO
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Chapter 5, Problem 1FDD
(a)
To determine
To calculate: The number of individuals with the experience of facing the problem at least one time within the past five years among the
(b)
To determine
If
(c)
To determine
The conclusion about the claim that less than 50% of adult internet users faced the problem within the past five years.
(d)
To determine
If
(e)
To determine
If
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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 5 Solutions
EP ELEMENTARY STAT.USING EXC.-MYSTATLAB
Ch. 5.1 - Prob. 1BSCCh. 5.1 - 2. Discrete or Continuous? Is the random variable...Ch. 5.1 - 3. Probability Distribution For the accompanying...Ch. 5.1 - Prob. 4BSCCh. 5.1 - Prob. 5BSCCh. 5.1 - Prob. 6BSCCh. 5.1 - Prob. 7BSCCh. 5.1 - Prob. 8BSCCh. 5.1 - Prob. 9BSCCh. 5.1 - Prob. 10BSC
Ch. 5.1 - Prob. 11BSCCh. 5.1 - Prob. 12BSCCh. 5.1 - Prob. 13BSCCh. 5.1 - Prob. 14BSCCh. 5.1 - Prob. 15BSCCh. 5.1 - Prob. 16BSCCh. 5.1 - Prob. 17BSCCh. 5.1 - Prob. 18BSCCh. 5.1 - Prob. 19BSCCh. 5.1 - Prob. 20BSCCh. 5.1 - Prob. 21BSCCh. 5.1 - Prob. 22BSCCh. 5.1 - Prob. 23BSCCh. 5.1 - Prob. 24BSCCh. 5.1 - Prob. 25BSCCh. 5.1 - Prob. 26BSCCh. 5.1 - Prob. 27BSCCh. 5.1 - Prob. 28BSCCh. 5.1 - Prob. 29BBCh. 5.1 - Prob. 30BBCh. 5.1 - Prob. 31BBCh. 5.1 - Prob. 32BBCh. 5.2 - Prob. 1BSCCh. 5.2 - Prob. 2BSCCh. 5.2 - Prob. 3BSCCh. 5.2 - Prob. 4BSCCh. 5.2 - Prob. 5BSCCh. 5.2 - Prob. 6BSCCh. 5.2 - Prob. 7BSCCh. 5.2 - Prob. 8BSCCh. 5.2 - Prob. 9BSCCh. 5.2 - Prob. 10BSCCh. 5.2 - Prob. 11BSCCh. 5.2 - Prob. 12BSCCh. 5.2 - Prob. 13BSCCh. 5.2 - Prob. 14BSCCh. 5.2 - Prob. 15BSCCh. 5.2 - Prob. 16BSCCh. 5.2 - Prob. 17BSCCh. 5.2 - Prob. 18BSCCh. 5.2 - Prob. 19BSCCh. 5.2 - Prob. 20BSCCh. 5.2 - Prob. 21BSCCh. 5.2 - Prob. 22BSCCh. 5.2 - Prob. 23BSCCh. 5.2 - Prob. 24BSCCh. 5.2 - 25. Whitus v. Georgia In the classic legal case of...Ch. 5.2 - Prob. 26BSCCh. 5.2 - Prob. 27BSCCh. 5.2 - Prob. 28BSCCh. 5.2 - Prob. 29BSCCh. 5.2 - Prob. 30BSCCh. 5.2 - Prob. 31BSCCh. 5.2 - Prob. 32BSCCh. 5.2 - Prob. 33BSCCh. 5.2 - Prob. 34BSCCh. 5.2 - Prob. 35BSCCh. 5.2 - Prob. 36BSCCh. 5.2 - Prob. 38BSCCh. 5.2 - Prob. 39BSCCh. 5.2 - Prob. 40BSCCh. 5.2 - Prob. 41BBCh. 5.2 - Prob. 42BBCh. 5.2 - Prob. 43BBCh. 5.3 - Prob. 1BSCCh. 5.3 - Prob. 2BSCCh. 5.3 - Prob. 3BSCCh. 5.3 - Prob. 4BSCCh. 5.3 - Prob. 5BSCCh. 5.3 - Prob. 6BSCCh. 5.3 - Prob. 7BSCCh. 5.3 - Prob. 8BSCCh. 5.3 - Prob. 9BSCCh. 5.3 - Prob. 10BSCCh. 5.3 - 11. Radioactive Decay Radioactive atoms are...Ch. 5.3 - 12. Deaths from Horse Kicks A classical example of...Ch. 5.3 - 13. World War II Bombs In Exercise 1“Notation” we...Ch. 5.3 - Prob. 14BSCCh. 5.3 - Prob. 17BBCh. 5 - Prob. 1CQQCh. 5 - Prob. 2CQQCh. 5 - Prob. 3CQQCh. 5 - Prob. 4CQQCh. 5 - Prob. 5CQQCh. 5 - Prob. 6CQQCh. 5 - Prob. 7CQQCh. 5 - Prob. 8CQQCh. 5 - Prob. 9CQQCh. 5 - Prob. 10CQQCh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - 1. Planets The planets of the solar system have...Ch. 5 - Prob. 2CRECh. 5 - Prob. 3CRECh. 5 - Prob. 4CRECh. 5 - Prob. 5CRECh. 5 - Prob. 6CRECh. 5 - Prob. 7CRECh. 5 - Prob. 8CRECh. 5 - Prob. 1EPCh. 5 - Prob. 1FDD
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