STATS:DATA+MODELS(LL)-W/ACCESS>CUSTOM<
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ISBN: 9780137643219
Author: DeVeaux
Publisher: PEARSON
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Chapter R, Problem 1.19RE
a.
To determine
Describe the distribution.
b.
To determine
Explain the reason for not appropriate to find summary statistics for this distribution.
c.
To determine
Describe the comparative boxplot for the long and short eruptions.
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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 R Solutions
STATS:DATA+MODELS(LL)-W/ACCESS>CUSTOM<
Ch. R - Prob. 1.1RECh. R - R1.2. Prenatal care Results of a 1996 American...Ch. R - R1.3. Singers by parts The boxplots display the...Ch. R - Prob. 1.4RECh. R - Prob. 1.5RECh. R - Prob. 1.6RECh. R - R1.7. State University Public relations staff...Ch. R - R1.8. Shenandoah rain Based on long-term...Ch. R - Prob. 1.9RECh. R - Prob. 1.10RE
Ch. R - Prob. 1.11RECh. R - R1.12. e-Books A study by the Pew Internet &...Ch. R - Prob. 1.13RECh. R - R1.14. Accidents Progressive Insurance asked...Ch. R - Prob. 1.15RECh. R - R1.16. Hard water II The data set from England and...Ch. R - Prob. 1.17RECh. R - R1.18. Old Faithful It is a common belief that...Ch. R - R1.19. Old Faithful? Does the duration of an...Ch. R - R1.20. Teen drivers 2013 The National Highway...Ch. R - Prob. 1.21RECh. R - Women’s Short Track 2018 The times of skaters in...Ch. R - Prob. 1.23RECh. R - R1.24. Sluggers Babe Ruth was the first great...Ch. R - Prob. 1.25RECh. R - R1.26. Music and memory Is it a good idea to...Ch. R - Prob. 1.27RECh. R - R1.28. Birth order Is your birth order related to...Ch. R - Prob. 1.29RECh. R - R1.30. Birth order revisited Consider again the...Ch. R - Prob. 1.31RECh. R - R1.32. Engines, again Horsepower is another...Ch. R - R1.33. Age and party 2011 The Pew Research Center...Ch. R - R1.34. Pay According to the Bureau of Labor...Ch. R - Prob. 1.35RECh. R - R1.36. Bike safety 2015 The Bicycle Helmet Safety...Ch. R - Prob. 1.37RECh. R - Prob. 1.38RECh. R - Prob. 1.41RECh. R - Prob. 1.42RECh. R - R1.43. Student survey investigation The Student...Ch. R - Prob. 1.44RECh. R - Prob. 2.1RECh. R - Prob. 2.2RECh. R - Prob. 2.3RECh. R - Prob. 2.4RECh. R - Prob. 2.5RECh. R - Prob. 2.6RECh. R - Prob. 2.7RECh. R - Prob. 2.8RECh. R - Prob. 2.9RECh. R - Prob. 2.10RECh. R - Prob. 2.11RECh. R - Prob. 2.12RECh. R - Prob. 2.13RECh. R - Prob. 2.14RECh. R - R2.15. Cars, correlations What factor most...Ch. R - R2.16. Cars, associations Look again at the...Ch. R - Prob. 2.17RECh. R - Prob. 2.18RECh. R - Prob. 2.19RECh. R - Prob. 2.20RECh. R - Prob. 2.21RECh. R - Prob. 2.22RECh. R - Prob. 2.23RECh. R - Prob. 2.24RECh. R - Prob. 2.25RECh. R - Prob. 2.26RECh. R - Prob. 2.27RECh. R - Prob. 2.28RECh. R - Prob. 2.29RECh. R - Prob. 2.30RECh. R - Prob. 2.31RECh. R - Prob. 2.32RECh. R - Prob. 2.33RECh. R - Prob. 2.34RECh. R - Prob. 2.35RECh. R - Prob. 2.36RECh. R - Prob. 2.37RECh. R - Prob. 2.38RECh. R - Prob. 2.39RECh. R - Prob. 2.40RECh. R - Prob. 2.41RECh. R - Prob. 2.42RECh. R - Prob. 2.43RECh. R - Prob. 2.44RECh. R - Prob. 2.45RECh. R - Prob. 2.46RECh. R - Prob. 2.47RECh. R - Prob. 2.48RECh. R - Prob. 2.49RECh. R - Prob. 2.50RECh. R - Prob. 2.51RECh. R - Prob. 2.52RECh. R - Prob. 3.1RECh. R - Prob. 3.2RECh. R - Prob. 3.3RECh. R - Prob. 3.4RECh. R - Prob. 3.5RECh. R - Prob. 3.6RECh. R - Prob. 3.7RECh. R - Prob. 3.8RECh. R - Prob. 3.9RECh. R - R3.1–R3.18. What design? Analyze the design of...Ch. R - Prob. 3.11RECh. R - Prob. 3.12RECh. R - Prob. 3.13RECh. R - Prob. 3.14RECh. R - Prob. 3.15RECh. R - Prob. 3.16RECh. R - R3.1–R3.18. What design? Analyze the design of...Ch. R - R3.1–R3.18. What design? Analyze the design of...Ch. R - Prob. 3.19RECh. R - Prob. 3.20RECh. R - R3.21. Alternate day fasting A paper published in...Ch. R - Prob. 3.22RECh. R - Prob. 3.23RECh. R - R3.24. Tips, take 2 In another experiment to see...Ch. R - Prob. 3.25RECh. R - Prob. 3.26RECh. R - Prob. 3.27RECh. R - R3.29. Homecoming A college statistics class...Ch. R - Prob. 3.29RECh. R - R3.31. Smoking and Alzheimer’s Medical studies...Ch. R - R3.32. Antacids A researcher wants to compare the...Ch. R - Prob. 3.32RECh. R - Prob. 3.33RECh. R - Prob. 3.34RECh. R - Prob. 3.35RECh. R - Prob. 3.36RECh. R - Prob. 3.37RECh. R - Prob. 3.38RECh. R - R3.39. Acupuncture Research reported in 2008...Ch. R - R3.40. Fuel efficiency Wayne Collier designed an...Ch. R - Prob. 3.41RECh. R - R3.42. Internet speed Carsten, Matt, and Rainer...Ch. R - Prob. 4.1RECh. R - Prob. 4.2RECh. R - Prob. 4.3RECh. R - Bipolar Psychiatrists estimate that about 1 in 100...Ch. R - A game To play a game, you must pay $5 for each...Ch. R - Prob. 4.6RECh. R - Prob. 4.7RECh. R - Prob. 4.8RECh. R - Prob. 4.9RECh. R - Prob. 4.10RECh. R - Prob. 4.11RECh. R - Prob. 4.12RECh. R - Prob. 4.13RECh. R - Prob. 4.14RECh. R - Prob. 4.15RECh. R - R4.17. Stocks Since the stock market began in...Ch. R - Multiple choice A multiple choice test has 50...Ch. R - Prob. 4.18RECh. R - Prob. 4.19RECh. R - Prob. 4.20RECh. R - Prob. 4.21RECh. R - Prob. 4.22RECh. R - Prob. 4.23RECh. R - Prob. 4.24RECh. R - Prob. 4.25RECh. R - Meals A college student on a seven-day meal plan...Ch. R - Prob. 4.27RECh. R - Picking melons Two stores sell watermelons. At the...Ch. R - Prob. 4.29RECh. R - Prob. 4.30RECh. R - Prob. 4.31RECh. R - Prob. 4.32RECh. R - Prob. 4.33RECh. R - Prob. 4.34RECh. R - Prob. 4.35RECh. R - Prob. 4.36RECh. R - Prob. 4.37RECh. R - Prob. 4.38RECh. R - Prob. 4.39RECh. R - Prob. 4.40RECh. R - Prob. 4.41RECh. R - Prob. 4.42RECh. R - Prob. 4.43RECh. R - Prob. 4.44RECh. R - Prob. 5.1RECh. R - Prob. 5.2RECh. R - Prob. 5.3RECh. R - R4.10. Hamsters How large are hamster litters?...Ch. R - Prob. 5.5RECh. R - R4.13. Fake news In a survey of 1002 U.S. adults...Ch. R - Prob. 5.7RECh. R - Prob. 5.8RECh. R - Prob. 5.9RECh. R - Prob. 5.10RECh. R - Prob. 5.11RECh. R - Prob. 5.12RECh. R - Prob. 5.13RECh. R - Prob. 5.14RECh. R - Prob. 5.15RECh. R - R4.27. Language Neurological research has shown...Ch. R - Prob. 5.17RECh. R - Prob. 5.18RECh. R - Prob. 5.19RECh. R - Prob. 5.20RECh. R - Prob. 5.21RECh. R - Prob. 5.22RECh. R - Prob. 5.23RECh. R - Prob. 5.24RECh. R - Prob. 5.25RECh. R - Prob. 5.26RECh. R - Prob. 5.27RECh. R - Prob. 5.28RECh. R - Prob. 5.29RECh. R - Prob. 5.30RECh. R - Prob. 5.31RECh. R - Prob. 5.32RECh. R - Prob. 5.33RECh. R - Prob. 5.34RECh. R - Prob. 5.35RECh. R - Prob. 5.36RECh. R - Prob. 5.37RECh. R - Prob. 5.38RECh. R - Prob. 5.39RECh. R - Prob. 5.40RECh. R - Prob. 6.1RECh. R - Prob. 6.2RECh. R - Prob. 6.3RECh. R - Prob. 6.4RECh. R - Prob. 6.5RECh. R - Prob. 6.6RECh. R - R5.7. Eclampsia deaths Refer again to the research...Ch. R - Prob. 6.8RECh. R - Prob. 6.9RECh. R - Prob. 6.10RECh. R - Prob. 6.11RECh. R - Prob. 6.12RECh. R - Prob. 6.13RECh. R - Prob. 6.14RECh. R - Prob. 6.15RECh. R - Prob. 6.17RECh. R - Prob. 6.18RECh. R - Prob. 6.19RECh. R - Prob. 6.20RECh. R - Prob. 6.21RECh. R - Prob. 6.23RECh. R - Prob. 6.25RECh. R - Prob. 6.28RECh. R - Prob. 6.29RECh. R - Prob. 6.30RECh. R - Prob. 6.31RECh. R - Prob. 6.32RECh. R - Prob. 6.33RECh. R - Prob. 6.34RECh. R - Prob. 6.35RECh. R - Prob. 6.36RECh. R - Prob. 6.37RECh. R - R5.38. Age and party 2016 The Pew Research Center...Ch. R - Prob. 6.39RECh. R - Prob. 6.40RECh. R - Prob. 6.41RECh. R - Prob. 6.42RECh. R - Prob. 6.43RECh. R - Prob. 6.44RECh. R - Prob. 6.45RECh. R - Prob. 6.46RECh. R - Prob. 6.47RECh. R - Prob. 6.48RECh. R - Prob. 6.49RECh. R - R5.50. Cramming Students in two basic Spanish...Ch. R - Prob. 6.51RECh. R - Prob. 6.52RECh. R - Prob. 7.3RECh. R - Prob. 7.4RECh. R - Prob. 7.5RECh. R - Prob. 7.6RECh. R - Prob. 7.7RECh. R - Prob. 7.8RECh. R - Prob. 7.9RECh. R - Prob. 7.10RECh. R - Prob. 7.11RECh. R - Nuclear plants Here are data on 32 light water...Ch. R - Prob. 7.13RECh. R - Prob. 7.15RECh. R - Prob. 7.16RECh. R - Prob. 7.17RECh. R - Prob. 7.18RECh. R - Prob. 7.19RECh. R - Prob. 7.20RECh. R - Prob. 7.21RECh. R - Prob. 7.23RECh. R - Prob. 7.24RECh. R - Prob. 7.25RECh. R - Prob. 7.27RECh. R - Prob. 7.28RECh. R - Prob. 7.29RE
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