Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 14.4, Problem 9AYU
(a)
To determine
The least-squares regression equation.
(b)
To determine
To test: The provided hypothesis.
(c)
To determine
To construct: The
(d)
To determine
The least-squares regression equation.
(e)
To determine
To test: The provided hypotheses.
(f)
To determine
The conclusion from the above test.
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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 14 Solutions
Statistics: Informed Decisions Using Data (5th Edition)
Ch. 14.1 - 1. Suppose a least-squares regression line is...Ch. 14.1 - 2. True or False: In a least-squares regression,...Ch. 14.1 - 3. In the least-squares regression model, yi =...Ch. 14.1 - 4. If H0: β1 = 0 is not rejected, what is the best...Ch. 14.1 - In Problems 5–10, use the results of Problems...Ch. 14.1 - In Problems 5–10, use the results of Problems...Ch. 14.1 - In Problems 5–10, use the results of Problems...Ch. 14.1 - In Problems 5–10, use the results of Problems...Ch. 14.1 - In Problems 5–10, use the results of Problems...Ch. 14.1 - In Problems 5–10, use the results of Problems...
Ch. 14.1 - 11. An Unhealthy Commute The following data...Ch. 14.1 - 12. Credit Scores An economist wants to determine...Ch. 14.1 - Prob. 13AYUCh. 14.1 - 14. Hurricanes The following data represent the...Ch. 14.1 - 15. Concrete As concrete cures, it gains...Ch. 14.1 - Prob. 16AYUCh. 14.1 - 17. Invest in Education Go to...Ch. 14.1 - 18. American Black Bears In 1969, Dr. Michael R....Ch. 14.1 - 19. CEO Performance (Refer to Problem 31 in...Ch. 14.1 - 20. Bear Markets (Refer to Problem 32, Section...Ch. 14.1 - 21. Age versus HDL Cholesterol A doctor wanted to...Ch. 14.1 - 22. The U.S. Population The following data...Ch. 14.1 - Prob. 23AYUCh. 14.1 - 24. The output shown was obtained from...Ch. 14.1 - 25. Influential Observations Zillow.com is a site...Ch. 14.1 - 26. Why is it important to perform graphical as...Ch. 14.1 - 27. What do the y-coordinates on the least-squares...Ch. 14.1 - 28. Why is it desirable to have the explanatory...Ch. 14.1 - 29. Why don't we conduct inference on the linear...Ch. 14.2 - 1. Intervals constructed about the predicted value...Ch. 14.2 - 2. Intervals constructed about the predicted value...Ch. 14.2 - In Problems 3–6, use the results of Problems 5–8...Ch. 14.2 - In Problems 3–6, use the results of Problems 5–8...Ch. 14.2 - Prob. 5AYUCh. 14.2 - Prob. 6AYUCh. 14.2 - Prob. 7AYUCh. 14.2 - Prob. 8AYUCh. 14.2 - Prob. 9AYUCh. 14.2 - Prob. 10AYUCh. 14.2 - Prob. 11AYUCh. 14.2 - Prob. 12AYUCh. 14.2 - Prob. 13AYUCh. 14.2 - Prob. 14AYUCh. 14.2 - Prob. 15AYUCh. 14.2 - Prob. 16AYUCh. 14.2 - 17. Putting It Together: Predicting Intelligence...Ch. 14.3 - Prob. 1AYUCh. 14.3 - Prob. 2AYUCh. 14.3 - Prob. 3AYUCh. 14.3 - Prob. 4AYUCh. 14.3 - Prob. 5AYUCh. 14.3 - Prob. 6AYUCh. 14.3 - Prob. 7AYUCh. 14.3 - Prob. 8AYUCh. 14.3 - Prob. 9AYUCh. 14.3 - Prob. 10AYUCh. 14.3 - 11. For the data...Ch. 14.3 - 12. For the data...Ch. 14.3 - Prob. 13AYUCh. 14.3 - Prob. 14AYUCh. 14.3 - Prob. 15AYUCh. 14.3 - Prob. 16AYUCh. 14.3 - Prob. 17AYUCh. 14.3 - Prob. 18AYUCh. 14.3 - Prob. 19AYUCh. 14.3 - Prob. 20AYUCh. 14.3 - Prob. 21AYUCh. 14.3 - Prob. 22AYUCh. 14.3 - Prob. 23AYUCh. 14.3 - Prob. 24AYUCh. 14.4 - Prob. 1AYUCh. 14.4 - Prob. 2AYUCh. 14.4 - Prob. 3AYUCh. 14.4 - Prob. 4AYUCh. 14.4 - Prob. 5AYUCh. 14.4 - Prob. 6AYUCh. 14.4 - Prob. 7AYUCh. 14.4 - Prob. 8AYUCh. 14.4 - Prob. 9AYUCh. 14.4 - Prob. 10AYUCh. 14.4 - Prob. 11AYUCh. 14.5 - Prob. 1AYUCh. 14.5 - Prob. 2AYUCh. 14.5 - Prob. 3AYUCh. 14.5 - Prob. 4AYUCh. 14.5 - Prob. 5AYUCh. 14.5 - Prob. 6AYUCh. 14.5 - Prob. 7AYUCh. 14.6 - Prob. 1AYUCh. 14.6 - Prob. 2AYUCh. 14.6 - 3. Housing Prices A realtor wanted to find a...Ch. 14.6 - Prob. 4AYUCh. 14.6 - Prob. 5AYUCh. 14.6 - Prob. 6AYUCh. 14.6 - Prob. 7AYUCh. 14.6 - Prob. 8AYUCh. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 1CTCh. 14 - Prob. 2CTCh. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - Prob. 5CTCh. 14 - 6. A nutritionist wants to develop a model that...Ch. 14 - During the early 2000s, the United States...
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