STATISTICS-PRINT COMPANION+ACCESS+CARD
2nd Edition
ISBN: 9781119383802
Author: Lock
Publisher: WILEY
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Chapter A, Problem 67RE
a.
To determine
Find the number of patients received the drug and number of patients received a placebo.
b.
To determine
Find the percent of all patients in the study had less than 50% blockage within 6 months of the angioplasty.
c.
To determine
Find the percent were on rosiglitazone of the patients with greater than 50% blockage.
d.
To determine
Find the percent of the patients given a placebo had less than 50% blockage.
e.
To determine
Find the relevant percentages to make the given comparison and explain the results.
f.
To determine
Check whether the rosiglitazone is appear to be effective.
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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 A Solutions
STATISTICS-PRINT COMPANION+ACCESS+CARD
Ch. A - Prob. 1ECh. A - Prob. 2ECh. A - Prob. 3ECh. A - Prob. 4ECh. A - Prob. 5ECh. A - Prob. 6ECh. A - Prob. 7ECh. A - Prob. 8ECh. A - Prob. 9ECh. A - Prob. 10E
Ch. A - Prob. 11ECh. A - WHICH GRAPH AND STATISTIC?
For the each of the...Ch. A - Prob. 13ECh. A - Prob. 14ECh. A - Prob. 15ECh. A - Prob. 16ECh. A - Prob. 17ECh. A - Penguin Tags May Do Harm In Data 1.3 on page 10,...Ch. A - Prob. 19ECh. A - Prob. 20ECh. A - Prob. 21ECh. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - Student Survey: Sample or Population? The results...Ch. A - Intensive Care Unit Admissions Data 2.3 on page 69...Ch. A - Prob. 27RECh. A - Prob. 28RECh. A - Prob. 29RECh. A - Prob. 30RECh. A - Prob. 31RECh. A - Prob. 32RECh. A - Prob. 33RECh. A - Prob. 34RECh. A - Prob. 35RECh. A - Prob. 36RECh. A - Prob. 37RECh. A - Prob. 38RECh. A - Prob. 39RECh. A - Prob. 40RECh. A - Prob. 41RECh. A - Percent of College Graduates by Region of the US...Ch. A - Prob. 43RECh. A - Prob. 44RECh. A - Prob. 45RECh. A - Prob. 46RECh. A - Prob. 47RECh. A - Prob. 48RECh. A - Prob. 49RECh. A - Prob. 50RECh. A - Prob. 51RECh. A - Prob. 52RECh. A - Prob. 53RECh. A - Prob. 54RECh. A - Prob. 55RECh. A - Prob. 56RECh. A - Prob. 57RECh. A - Prob. 58RECh. A - Prob. 59RECh. A - Prob. 60RECh. A - Prob. 61RECh. A - Prob. 62RECh. A - Prob. 63RECh. A - Prob. 64RECh. A - Prob. 65RECh. A - Prob. 66RECh. A - Prob. 67RECh. A - Prob. 68RECh. A - Prob. 69RECh. A - Prob. 70RECh. A - Prob. 71RECh. A - Prob. 72RECh. A - Prob. 73RECh. A - Prob. 74RECh. A - Prob. 75RECh. A - Prob. 76RECh. A - Prob. 77RECh. A - Prob. 78RECh. A - Prob. 79RECh. A - Prob. 80RECh. A - Prob. 81RECh. A - Prob. 82RECh. A - Prob. 83RECh. A - Prob. 84RECh. A - Prob. 85RECh. A - Prob. 86RECh. A - Prob. 87RECh. A - Prob. 88RECh. A - Prob. 89RECh. A - Prob. 90RECh. A - Prob. 91RECh. A - Prob. 92RECh. A - Prob. 93RECh. A - Prob. 94RECh. A - Prob. 95RECh. A - Prob. 96RECh. A - Prob. 97RECh. A - Predicting Percent of College Graduates Using High...Ch. A - Predicting Percent of College Graduates Using...Ch. A - Investigating NBA Statistics The dataset...Ch. A - Investigating the Happy Planet Index In Exercise...
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- Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn 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.)arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward
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