EP ELEMENTARY STAT.USING EXC.-MYSTATLAB
7th Edition
ISBN: 9780136961888
Author: Triola
Publisher: PEARSON CO
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Chapter 4, Problem 2RE
To determine
To find: The
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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 4 Solutions
EP ELEMENTARY STAT.USING EXC.-MYSTATLAB
Ch. 4.1 - Prob. 1BSCCh. 4.1 - 2. Probability Rewrite the following statement so...Ch. 4.1 - Prob. 3BSCCh. 4.1 - Prob. 4BSCCh. 4.1 - 5. Identifying Probability Values Which of the...Ch. 4.1 - 6. Penicillin “Who discovered penicillin: Sean...Ch. 4.1 - Prob. 7BSCCh. 4.1 - Prob. 8BSCCh. 4.1 - Prob. 9BSCCh. 4.1 - Prob. 10BSC
Ch. 4.1 - Prob. 11BSCCh. 4.1 - Prob. 12BSCCh. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - 14. SAT Test When making a random guess for an...Ch. 4.1 - Prob. 15BSCCh. 4.1 - Prob. 16BSCCh. 4.1 - 17. Randomness When using a computer to randomly...Ch. 4.1 - Prob. 18BSCCh. 4.1 - Prob. 19BSCCh. 4.1 - Prob. 20BSCCh. 4.1 - Prob. 21BSCCh. 4.1 - Prob. 22BSCCh. 4.1 - Prob. 23BSCCh. 4.1 - Prob. 24BSCCh. 4.1 - Prob. 25BSCCh. 4.1 - Prob. 26BSCCh. 4.1 - Prob. 27BSCCh. 4.1 - Prob. 28BSCCh. 4.1 - Prob. 29BSCCh. 4.1 - Prob. 30BSCCh. 4.1 - Prob. 31BSCCh. 4.1 - Prob. 32BSCCh. 4.1 - Prob. 33BSCCh. 4.1 - Prob. 34BSCCh. 4.1 - Prob. 35BSCCh. 4.1 - Prob. 36BSCCh. 4.1 - Prob. 37BSCCh. 4.1 - Prob. 38BSCCh. 4.1 - Prob. 39BSCCh. 4.1 - Prob. 40BSCCh. 4.1 - Prob. 41BBCh. 4.1 - Prob. 42BBCh. 4.1 - Prob. 43BBCh. 4.1 - Prob. 44BBCh. 4.2 - Prob. 1BSCCh. 4.2 - 2. Notation When randomly selecting adults, let M...Ch. 4.2 - Prob. 3BSCCh. 4.2 - Prob. 4BSCCh. 4.2 - Prob. 5BSCCh. 4.2 - Prob. 6BSCCh. 4.2 - Prob. 7BSCCh. 4.2 - Prob. 8BSCCh. 4.2 - Prob. 9BSCCh. 4.2 - Prob. 10BSCCh. 4.2 - Prob. 11BSCCh. 4.2 - Prob. 12BSCCh. 4.2 - Prob. 13BSCCh. 4.2 - Prob. 14BSCCh. 4.2 - Prob. 15BSCCh. 4.2 - Prob. 16BSCCh. 4.2 - Prob. 17BSCCh. 4.2 - Prob. 18BSCCh. 4.2 - Prob. 19BSCCh. 4.2 - Prob. 20BSCCh. 4.2 - Prob. 21BSCCh. 4.2 - Prob. 22BSCCh. 4.2 - Prob. 23BSCCh. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - Prob. 25BSCCh. 4.2 - Prob. 26BSCCh. 4.2 - Prob. 27BSCCh. 4.2 - Prob. 28BSCCh. 4.2 - Prob. 29BSCCh. 4.2 - Prob. 30BSCCh. 4.2 - Prob. 31BBCh. 4.2 - 32. Same Birthdays If 25 people are randomly...Ch. 4.2 - Prob. 33BBCh. 4.2 - Prob. 34BBCh. 4.3 - Prob. 1BSCCh. 4.3 - Prob. 2BSCCh. 4.3 - Prob. 3BSCCh. 4.3 - Prob. 4BSCCh. 4.3 - Prob. 5BSCCh. 4.3 - Prob. 6BSCCh. 4.3 - Prob. 7BSCCh. 4.3 - Prob. 8BSCCh. 4.3 - Prob. 9BSCCh. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Prob. 11BSCCh. 4.3 - Prob. 12BSCCh. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Prob. 14BSCCh. 4.3 - Prob. 15BSCCh. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Prob. 17BSCCh. 4.3 - Prob. 18BSCCh. 4.3 - Prob. 19BSCCh. 4.3 - Prob. 20BSCCh. 4.3 - Prob. 21BSCCh. 4.3 - Prob. 22BSCCh. 4.3 - Prob. 23BSCCh. 4.3 - 24. Composite Water Samples The Fairfield County...Ch. 4.3 - Prob. 25BBCh. 4.3 - Prob. 26BBCh. 4.4 - Prob. 1BSCCh. 4.4 - Prob. 2BSCCh. 4.4 - Prob. 3BSCCh. 4.4 - Prob. 4BSCCh. 4.4 - Prob. 5BSCCh. 4.4 - 6. Social Security Numbers A Social Security...Ch. 4.4 - Prob. 7BSCCh. 4.4 - Prob. 8BSCCh. 4.4 - Prob. 9BSCCh. 4.4 - 10. Radio Station Call Letters If radio station...Ch. 4.4 - Prob. 11BSCCh. 4.4 - Prob. 12BSCCh. 4.4 - Prob. 13BSCCh. 4.4 - Prob. 14BSCCh. 4.4 - Prob. 15BSCCh. 4.4 - Prob. 16BSCCh. 4.4 - Prob. 17BSCCh. 4.4 - Prob. 18BSCCh. 4.4 - 19. ZIP Code If you randomly select five digits,...Ch. 4.4 - Prob. 20BSCCh. 4.4 - Prob. 21BSCCh. 4.4 - Prob. 22BSCCh. 4.4 - Prob. 23BSCCh. 4.4 - Prob. 24BSCCh. 4.4 - Prob. 25BSCCh. 4.4 - Prob. 26BSCCh. 4.4 - Prob. 27BSCCh. 4.4 - Prob. 28BSCCh. 4.4 - Prob. 29BSCCh. 4.4 - Prob. 31BSCCh. 4.4 - Prob. 32BSCCh. 4.4 - Prob. 33BSCCh. 4.4 - Prob. 34BSCCh. 4.4 - Prob. 35BSCCh. 4.4 - Prob. 36BSCCh. 4.4 - Prob. 37BBCh. 4.4 - Prob. 38BBCh. 4.4 - Prob. 39BBCh. 4.5 - Prob. 1BSCCh. 4.5 - Prob. 2BSCCh. 4.5 - Prob. 3BSCCh. 4.5 - Prob. 4BSCCh. 4.5 - Prob. 5BSCCh. 4.5 - Prob. 6BSCCh. 4.5 - Prob. 7BSCCh. 4.5 - Prob. 8BSCCh. 4.5 - Prob. 9BSCCh. 4.5 - Prob. 10BSCCh. 4.5 - Prob. 11BSCCh. 4.5 - Prob. 12BSCCh. 4.5 - Prob. 13BBCh. 4.5 - Prob. 14BBCh. 4.5 - Prob. 15BBCh. 4 - Prob. 1CQQCh. 4 - Prob. 2CQQCh. 4 - Prob. 3CQQCh. 4 - Prob. 4CQQCh. 4 - Prob. 5CQQCh. 4 - Prob. 6CQQCh. 4 - Prob. 7CQQCh. 4 - Prob. 8CQQCh. 4 - Prob. 9CQQCh. 4 - Prob. 10CQQCh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 1FDDCh. 4 - Prob. 2FDDCh. 4 - Prob. 3FDDCh. 4 - Prob. 4FDDCh. 4 - Prob. 5FDDCh. 4 - Prob. 6FDDCh. 4 - Prob. 7FDDCh. 4 - Prob. 8FDDCh. 4 - Prob. 9FDD
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