STATISTICS-PRINT COMPANION+ACCESS+CARD
2nd Edition
ISBN: 9781119383802
Author: Lock
Publisher: WILEY
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Chapter A, Problem 23E
a.
To determine
Identify the cases of the study.
Find the
b.
To determine
Find the variables in the given dataset.
Check whether each variable is quantitative or categorical.
c.
To determine
Calculate the mean and standard deviations of tip percentage.
Find the five-number summary.
Find the boundary points that classify an observation as an outlier relative to this dataset.
d.
To determine
Construct a histogram for the variable PctTip and explain about shape of the distribution.
e.
To determine
Construct a two-way table of Credit and Day.
Find the proportion of bills paid with a credit card on Thursday and Friday.
Check whether there is an association between the payment method, and whether it is Thursday or Friday.
f.
To determine
Identify the type of graph that explains the relationship between PctTip and Server.
Construct the appropriate graph.
Identify the server that seems to have the highest percent tips.
g.
To determine
Find the response and explanatory variables.
Construct a
Check whether there are any outliers in the scatterplot.
Identify the relationship between the two variables by ignoring the outliers.
h.
To determine
Calculate the
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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.)
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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- 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?arrow_forwardWe 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? 2arrow_forwardQuestion 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_forward
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