Elementary Statistics Using the TI-83/84 Plus Calculator
4th Edition
ISBN: 9780558737030
Author: Triola
Publisher: PEARSON
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Chapter 1.2, Problem 16BSC
To determine
Whether the result has the statistical and practical significance or not.
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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 1 Solutions
Elementary Statistics Using the TI-83/84 Plus Calculator
Ch. 1.2 - Statistical Significance Versus Practical...Ch. 1.2 - Prob. 2BSCCh. 1.2 - Prob. 3BSCCh. 1.2 - Prob. 4BSCCh. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Prob. 6BSCCh. 1.2 - Prob. 7BSCCh. 1.2 - Prob. 8BSCCh. 1.2 - Prob. 9BSCCh. 1.2 - Prob. 10BSC
Ch. 1.2 - Prob. 11BSCCh. 1.2 - Prob. 12BSCCh. 1.2 - Prob. 13BSCCh. 1.2 - Prob. 14BSCCh. 1.2 - Prob. 15BSCCh. 1.2 - Prob. 16BSCCh. 1.2 - Prob. 17BSCCh. 1.2 - Prob. 18BSCCh. 1.2 - Prob. 19BSCCh. 1.2 - Prob. 20BSCCh. 1.2 - Prob. 21BSCCh. 1.2 - Prob. 22BSCCh. 1.2 - Prob. 23BSCCh. 1.2 - Prob. 24BSCCh. 1.2 - What's Wrong? In Exercises 25-28, identify what is...Ch. 1.2 - Prob. 26BSCCh. 1.2 - What’s Wrong? In Exercises 25-28, identify what is...Ch. 1.2 - Prob. 28BSCCh. 1.2 - Prob. 29BSCCh. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Prob. 31BSCCh. 1.2 - Prob. 32BSCCh. 1.2 - Prob. 33BSCCh. 1.2 - Prob. 34BSCCh. 1.2 - Prob. 35BSCCh. 1.2 - Prob. 36BSCCh. 1.2 - Prob. 37BBCh. 1.2 - Falsifying Data A researcher at the...Ch. 1.2 - Whats Wrong with This Picture? The Newport...Ch. 1.3 - Prob. 1BSCCh. 1.3 - Prob. 2BSCCh. 1.3 - Prob. 3BSCCh. 1.3 - Prob. 4BSCCh. 1.3 - Prob. 5BSCCh. 1.3 - Prob. 6BSCCh. 1.3 - In Exercises 5-12, identify whether the given...Ch. 1.3 - Prob. 8BSCCh. 1.3 - Prob. 9BSCCh. 1.3 - In Exercises 5-12, identify whether the given...Ch. 1.3 - Prob. 11BSCCh. 1.3 - Prob. 12BSCCh. 1.3 - Prob. 13BSCCh. 1.3 - Prob. 14BSCCh. 1.3 - Prob. 15BSCCh. 1.3 - Prob. 16BSCCh. 1.3 - Prob. 17BSCCh. 1.3 - Prob. 18BSCCh. 1.3 - Prob. 19BSCCh. 1.3 - Prob. 20BSCCh. 1.3 - Prob. 21BSCCh. 1.3 - Prob. 22BSCCh. 1.3 - Prob. 23BSCCh. 1.3 - Prob. 24BSCCh. 1.3 - Prob. 25BSCCh. 1.3 - Prob. 26BSCCh. 1.3 - Prob. 27BSCCh. 1.3 - Prob. 28BSCCh. 1.3 - Prob. 29BSCCh. 1.3 - Prob. 30BSCCh. 1.3 - Prob. 31BSCCh. 1.3 - Prob. 32BSCCh. 1.3 - Prob. 33BBCh. 1.3 - Prob. 34BBCh. 1.3 - Prob. 35BBCh. 1.4 - Prob. 1BSCCh. 1.4 - Prob. 2BSCCh. 1.4 - Prob. 3BSCCh. 1.4 - Prob. 4BSCCh. 1.4 - Prob. 5BSCCh. 1.4 - Prob. 6BSCCh. 1.4 - Prob. 7BSCCh. 1.4 - Prob. 8BSCCh. 1.4 - Prob. 9BSCCh. 1.4 - Prob. 10BSCCh. 1.4 - Prob. 11BSCCh. 1.4 - Prob. 12BSCCh. 1.4 - Prob. 13BSCCh. 1.4 - Prob. 14BSCCh. 1.4 - Prob. 15BSCCh. 1.4 - Prob. 16BSCCh. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - Prob. 18BSCCh. 1.4 - Prob. 19BSCCh. 1.4 - Prob. 20BSCCh. 1.4 - Prob. 21BSCCh. 1.4 - Prob. 22BSCCh. 1.4 - Prob. 23BSCCh. 1.4 - Prob. 24BSCCh. 1.4 - Prob. 25BSCCh. 1.4 - Prob. 26BSCCh. 1.4 - Prob. 27BBCh. 1.4 - Prob. 28BBCh. 1.4 - Prob. 29BBCh. 1.4 - Prob. 30BBCh. 1.4 - Prob. 31BBCh. 1.4 - Prob. 32BBCh. 1.4 - In Exercises 33-36, identify which of these...Ch. 1.4 - Prob. 34BBCh. 1.4 - Prob. 35BBCh. 1.4 - Prob. 36BBCh. 1.5 - Equals Key On many calculators, the end of a...Ch. 1.5 - Prob. 2BSCCh. 1.5 - Prob. 3BSCCh. 1.5 - Prob. 4BSCCh. 1.5 - Prob. 5BSCCh. 1.5 - Prob. 6BSCCh. 1.5 - Prob. 7BSCCh. 1.5 - Prob. 8BSCCh. 1.5 - Prob. 9BSCCh. 1.5 - Prob. 10BSCCh. 1.5 - Prob. 11BSCCh. 1.5 - Prob. 12BSCCh. 1.5 - Prob. 13BSCCh. 1.5 - Prob. 14BSCCh. 1.5 - Prob. 15BSCCh. 1.5 - Prob. 16BSCCh. 1.5 - Prob. 17BSCCh. 1.5 - Prob. 18BSCCh. 1.5 - Prob. 19BSCCh. 1.5 - Prob. 20BSCCh. 1.5 - Prob. 21BSCCh. 1.5 - Prob. 22BSCCh. 1.5 - Scientific Notation in Exercises 2124, use the...Ch. 1.5 - Scientific Notation in Exercises 2124, use the...Ch. 1.5 - Prob. 26BBCh. 1 - Prob. 1CQQCh. 1 - Prob. 2CQQCh. 1 - Prob. 3CQQCh. 1 - Prob. 4CQQCh. 1 - Prob. 5CQQCh. 1 - Prob. 6CQQCh. 1 - Prob. 7CQQCh. 1 - Prob. 8CQQCh. 1 - Prob. 9CQQCh. 1 - 10. Statistical Significance and Practical...Ch. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - 9. Marijuana Survey Identify the type of sampling...Ch. 1 - Prob. 10RECh. 1 - Prob. 1CRECh. 1 - Prob. 2CRECh. 1 - Prob. 3CRECh. 1 - Prob. 4CRECh. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - Prob. 6CRECh. 1 - Prob. 7CRECh. 1 - Prob. 8CRECh. 1 - Prob. 9CRECh. 1 - Prob. 10CRECh. 1 - Prob. 11CRECh. 1 - Prob. 12CRECh. 1 - Prob. 1TPCPCh. 1 - Prob. 1FDDCh. 1 - Prob. 2FDD
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