ELEMENTARY STAT.USING EXCEL-MYSTATLAB
7th Edition
ISBN: 9780136961970
Author: Triola
Publisher: PEARSON
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Chapter 2, Problem 1FDD
To determine
To construct: The frequency distribution and the histogram of the last digits of the weight.
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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 2 Solutions
ELEMENTARY STAT.USING EXCEL-MYSTATLAB
Ch. 2.1 - Prob. 1BSCCh. 2.1 - Prob. 2BSCCh. 2.1 - Prob. 3BSCCh. 2.1 - Prob. 4BSCCh. 2.1 - Prob. 5BSCCh. 2.1 - Prob. 6BSCCh. 2.1 - Prob. 7BSCCh. 2.1 - Prob. 8BSCCh. 2.1 - Prob. 9BSCCh. 2.1 - Prob. 10BSC
Ch. 2.1 - Prob. 11BSCCh. 2.1 - Prob. 12BSCCh. 2.1 - Prob. 13BSCCh. 2.1 - Prob. 14BSCCh. 2.1 - Prob. 15BSCCh. 2.1 - Prob. 16BSCCh. 2.1 - Prob. 17BSCCh. 2.1 - Prob. 18BSCCh. 2.1 - Prob. 19BSCCh. 2.1 - Prob. 20BSCCh. 2.1 - Prob. 21BSCCh. 2.1 - Prob. 22BSCCh. 2.1 - Prob. 23BSCCh. 2.1 - Prob. 24BSCCh. 2.1 - Prob. 25BSCCh. 2.1 - Prob. 26BSCCh. 2.1 - Prob. 27BSCCh. 2.1 - Prob. 28BSCCh. 2.1 - Prob. 29BSCCh. 2.1 - Prob. 30BSCCh. 2.1 - Prob. 31BSCCh. 2.1 - Prob. 32BSCCh. 2.1 - Prob. 33BSCCh. 2.1 - Prob. 34BSCCh. 2.2 - 1. Heights Heights of adult males are normally...Ch. 2.2 - Prob. 2BSCCh. 2.2 - Prob. 3BSCCh. 2.2 - Prob. 4BSCCh. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Prob. 9BSCCh. 2.2 - Prob. 10BSCCh. 2.2 - Prob. 11BSCCh. 2.2 - Prob. 12BSCCh. 2.2 - Prob. 13BSCCh. 2.2 - Prob. 14BSCCh. 2.2 - Prob. 15BSCCh. 2.2 - Prob. 16BSCCh. 2.2 - Prob. 17BSCCh. 2.2 - Prob. 18BSCCh. 2.2 - Prob. 19BBCh. 2.3 - Prob. 1BSCCh. 2.3 - Prob. 2BSCCh. 2.3 - 3. Ethics There are data showing that smoking is...Ch. 2.3 - Prob. 4BSCCh. 2.3 - Pulse Rates Listed below are pulse rates (beats...Ch. 2.3 - Diastolic Blood Pressure Listed below are...Ch. 2.3 - Pulse Rates Refer to the data listed in Exercise...Ch. 2.3 - Diastolic Blood Pressure Refer to the data listed...Ch. 2.3 - Prob. 9BSCCh. 2.3 - Prob. 10BSCCh. 2.3 - Prob. 11BSCCh. 2.3 - Prob. 12BSCCh. 2.3 - Prob. 13BSCCh. 2.3 - Prob. 14BSCCh. 2.3 - Prob. 15BSCCh. 2.3 - Prob. 16BSCCh. 2.3 - Prob. 17BSCCh. 2.3 - Deceptive Graphs. In Exercises 17-20, identify how...Ch. 2.3 - Prob. 19BSCCh. 2.3 - Prob. 20BSCCh. 2.3 - Prob. 21BBCh. 2.3 - Prob. 22BBCh. 2.4 - 1. Linear Correlation In this section we use r to...Ch. 2.4 - Prob. 2BSCCh. 2.4 - Prob. 3BSCCh. 2.4 - Prob. 4BSCCh. 2.4 - Prob. 5BSCCh. 2.4 - Prob. 6BSCCh. 2.4 - Prob. 7BSCCh. 2.4 - Prob. 8BSCCh. 2.4 - Prob. 9BSCCh. 2.4 - Prob. 10BSCCh. 2.4 - Prob. 11BSCCh. 2.4 - Prob. 12BSCCh. 2.4 - Prob. 13BBCh. 2.4 - Prob. 14BBCh. 2.4 - Prob. 15BBCh. 2.4 - Prob. 16BBCh. 2 - Prob. 1CQQCh. 2 - Prob. 2CQQCh. 2 - Prob. 3CQQCh. 2 - Prob. 4CQQCh. 2 - Prob. 5CQQCh. 2 - Prob. 6CQQCh. 2 - Prob. 7CQQCh. 2 - Prob. 8CQQCh. 2 - Prob. 9CQQCh. 2 - Prob. 10CQQCh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 1CRECh. 2 - Prob. 2CRECh. 2 - Prob. 3CRECh. 2 - Prob. 4CRECh. 2 - Prob. 5CRECh. 2 - Prob. 1EPCh. 2 - Prob. 1FDDCh. 2 - Prob. 2FDDCh. 2 - Prob. 3FDDCh. 2 - Prob. 4FDD
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