Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 10.3, Problem 40AYU
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To perform: Testing of 1 sample t-test.
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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 10 Solutions
Statistics: Informed Decisions Using Data (5th Edition)
Ch. 10.1 - 1. A ___________ is a statement regarding a...Ch. 10.1 - 2. ___________ ___________ is a procedure, based...Ch. 10.1 - 3. The ___________ ________ is a statement of no...Ch. 10.1 - 4. The ___________ ___________ is a statement we...Ch. 10.1 - 5. If we reject the null hypothesis when the...Ch. 10.1 - 6. If we do not reject the null hypothesis when...Ch. 10.1 - 7. The ___________ is the probability of making a...Ch. 10.1 - 8. True or False: Sample evidence can prove a null...Ch. 10.1 - Prob. 9AYUCh. 10.1 - In Problems 9–14, the null and alternative...
Ch. 10.1 - Prob. 11AYUCh. 10.1 - Prob. 12AYUCh. 10.1 - Prob. 13AYUCh. 10.1 - Prob. 14AYUCh. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - Prob. 23AYUCh. 10.1 - Prob. 24AYUCh. 10.1 - Prob. 25AYUCh. 10.1 - Prob. 26AYUCh. 10.1 - Prob. 27AYUCh. 10.1 - Prob. 28AYUCh. 10.1 - Prob. 29AYUCh. 10.1 - Prob. 30AYUCh. 10.1 - Prob. 31AYUCh. 10.1 - Prob. 32AYUCh. 10.1 - In Problems 23–34, state the conclusion based on...Ch. 10.1 - Prob. 34AYUCh. 10.1 - Prob. 35AYUCh. 10.1 - Prob. 36AYUCh. 10.1 - 37. E-Cigs According to the Centers for Disease...Ch. 10.1 - 38. Migraines According to the Centers for Disease...Ch. 10.1 - Prob. 39AYUCh. 10.1 - Prob. 40AYUCh. 10.1 - Prob. 41AYUCh. 10.1 - Prob. 42AYUCh. 10.1 - 43. What happens to the probability of making a...Ch. 10.1 - 44. The following is a quotation from Sir Ronald...Ch. 10.1 - 45. In your own words, explain the difference...Ch. 10.2 - 1. When observed results are unlikely under the...Ch. 10.2 - Prob. 2AYUCh. 10.2 - Prob. 3AYUCh. 10.2 - Prob. 4AYUCh. 10.2 - Prob. 5AYUCh. 10.2 - Prob. 6AYUCh. 10.2 - Prob. 7AYUCh. 10.2 - Prob. 8AYUCh. 10.2 - Prob. 9AYUCh. 10.2 - Prob. 10AYUCh. 10.2 - Prob. 11AYUCh. 10.2 - Prob. 12AYUCh. 10.2 - Prob. 13AYUCh. 10.2 - Prob. 14AYUCh. 10.2 - 15. Cramer Correct Less Than Half the Time? The...Ch. 10.2 - 16. Political Pundits In his book, "The Signal and...Ch. 10.2 - NW 17. Lipitor The drug Lipitor is meant to reduce...Ch. 10.2 - 18. Nexium Nexium is a drug that can be used to...Ch. 10.2 - 19. Fatal Traffic Accidents According to the...Ch. 10.2 - 20. Eating Together In December 2001, 38% of...Ch. 10.2 - NW 21. Taught Enough Math? In 1994, 52% of parents...Ch. 10.2 - 22. Living Alone? In 2000, 58% of females aged 15...Ch. 10.2 - Prob. 23AYUCh. 10.2 - Prob. 24AYUCh. 10.2 - Prob. 25AYUCh. 10.2 - Prob. 26AYUCh. 10.2 - Prob. 27AYUCh. 10.2 - 28. Small-Sample Hypothesis Test In 1997, 4% of...Ch. 10.2 - Prob. 29AYUCh. 10.2 - Prob. 30AYUCh. 10.2 - Prob. 31AYUCh. 10.2 - Prob. 32AYUCh. 10.2 - Prob. 33AYUCh. 10.2 - Prob. 34AYUCh. 10.2 - Prob. 35AYUCh. 10.2 - Prob. 36AYUCh. 10.2 - 37. Simulation: Predicting the Future...Ch. 10.2 - Prob. 38AYUCh. 10.2 - 39. Putting It Together: Naughty or Nice? Yale...Ch. 10.2 - Prob. 40AYUCh. 10.2 - Prob. 41AYUCh. 10.2 - Prob. 42AYUCh. 10.2 - Prob. 43AYUCh. 10.2 - Prob. 44AYUCh. 10.2 - Prob. 45AYUCh. 10.3 - 1. (a) Determine the critical value for a...Ch. 10.3 - Prob. 2AYUCh. 10.3 - Prob. 3AYUCh. 10.3 - 4. To test H0: µ = 40 versus H1: > 40, a simple...Ch. 10.3 - 5. To test H0: μ = 100 versus H1: μ ≠ 100, a...Ch. 10.3 - Prob. 6AYUCh. 10.3 - Prob. 7AYUCh. 10.3 - 8. To test H0: μ = 4.5 versus H1: μ > 4.5, a...Ch. 10.3 - Prob. 9AYUCh. 10.3 - Prob. 10AYUCh. 10.3 - Prob. 11AYUCh. 10.3 - Prob. 12AYUCh. 10.3 - NW 13. Ready for College? The ACT is a college...Ch. 10.3 - 14. SAT Verbal Scores Do students who learned...Ch. 10.3 - 15. Effects of Alcohol on the Brain In a study...Ch. 10.3 - 16. Effects of Plastic Resin Para-nonylphenol is...Ch. 10.3 - 17. Credit Scores A Fair Isaac Corporation (FICO)...Ch. 10.3 - 18. TVaholics According to the American Time Use...Ch. 10.3 - 19. Age of Death-Row Inmates In 2002, the mean age...Ch. 10.3 - 20. Energy Consumption In 2001, the mean household...Ch. 10.3 - Prob. 21AYUCh. 10.3 - Prob. 22AYUCh. 10.3 - Prob. 23AYUCh. 10.3 - Prob. 24AYUCh. 10.3 - Prob. 25AYUCh. 10.3 - Prob. 26AYUCh. 10.3 - Prob. 27AYUCh. 10.3 - Prob. 28AYUCh. 10.3 - Prob. 29AYUCh. 10.3 - Prob. 30AYUCh. 10.3 - 31. Statistical Significance versus Practical...Ch. 10.3 - Prob. 32AYUCh. 10.3 - Prob. 33AYUCh. 10.3 - Prob. 34AYUCh. 10.3 - Prob. 35AYUCh. 10.3 - Prob. 36AYUCh. 10.3 - Prob. 37AYUCh. 10.3 - Prob. 38AYUCh. 10.3 - Prob. 39AYUCh. 10.3 - Prob. 40AYUCh. 10.4 - 1. (a) Determine the critical value for a...Ch. 10.4 - Prob. 2AYUCh. 10.4 - Prob. 3AYUCh. 10.4 - Prob. 4AYUCh. 10.4 - Prob. 5AYUCh. 10.4 - Prob. 6AYUCh. 10.4 - Prob. 7AYUCh. 10.4 - Prob. 8AYUCh. 10.4 - NW 9. Mutual Fund Risk One measure of the risk of...Ch. 10.4 - 10. Filling Machine A machine fills bottles with...Ch. 10.4 - 11. Pump Design The piston diameter of a certain...Ch. 10.4 - 12. Counting Carbs The manufacturer of processed...Ch. 10.4 - Prob. 13AYUCh. 10.4 - Prob. 14AYUCh. 10.4 - Prob. 15AYUCh. 10.4 - Prob. 16AYUCh. 10.4 - Prob. 17AYUCh. 10.4 - Prob. 18AYUCh. 10.5 - 1. A simple random sample of size n = 19 is drawn...Ch. 10.5 - 2. A simple random sample of size n = 200...Ch. 10.5 - Prob. 3AYUCh. 10.5 - Prob. 4AYUCh. 10.5 - Prob. 5AYUCh. 10.5 - Prob. 6AYUCh. 10.5 - Prob. 7AYUCh. 10.5 - 8. A simple random sample of size n = 320 adults...Ch. 10.5 - Prob. 9AYUCh. 10.5 - Prob. 10AYUCh. 10.5 - Prob. 11AYUCh. 10.5 - Prob. 12AYUCh. 10.5 - Prob. 13AYUCh. 10.5 - Prob. 14AYUCh. 10.5 - Prob. 15AYUCh. 10.5 - Prob. 16AYUCh. 10.5 - Prob. 17AYUCh. 10.5 - Prob. 18AYUCh. 10.5 - Prob. 19AYUCh. 10.5 - Prob. 20AYUCh. 10.5 - Prob. 21AYUCh. 10.5 - Prob. 22AYUCh. 10.5 - Prob. 23AYUCh. 10.5 - Prob. 24AYUCh. 10.5 - Prob. 25AYUCh. 10.5 - Prob. 26AYUCh. 10.5 - Prob. 27AYUCh. 10.5 - Prob. 28AYUCh. 10.5 - Prob. 29AYUCh. 10.6 - Prob. 1AYUCh. 10.6 - Prob. 2AYUCh. 10.6 - Prob. 3AYUCh. 10.6 - Prob. 4AYUCh. 10.6 - Prob. 5AYUCh. 10.6 - Prob. 6AYUCh. 10.6 - Prob. 7AYUCh. 10.6 - Prob. 8AYUCh. 10.6 - Prob. 9AYUCh. 10.6 - Prob. 10AYUCh. 10.6 - Prob. 11AYUCh. 10.6 - Prob. 12AYUCh. 10.6 - Prob. 13AYUCh. 10.6 - Prob. 14AYUCh. 10.6 - Prob. 15AYUCh. 10.6 - Prob. 16AYUCh. 10.6 - Prob. 17AYUCh. 10.6 - Prob. 18AYUCh. 10.6 - Prob. 19AYUCh. 10.6 - Prob. 20AYUCh. 10.6 - Prob. 21AYUCh. 10.6 - Prob. 22AYUCh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - 23. Explain the difference between "accepting" and...Ch. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 1CTCh. 10 - Prob. 2CTCh. 10 - Prob. 3CTCh. 10 - Prob. 4CTCh. 10 - Prob. 5CTCh. 10 - Prob. 6CTCh. 10 - Prob. 7CTCh. 10 - Prob. 8CTCh. 10 - Prob. 9CTCh. 10 - Prob. CS
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