Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Chapter 6.2, Problem 53E
To determine
The area under the standard normal curve that lies to the right of 0.43 and explains the reason.
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Students have asked these similar questions
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
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…
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 6 Solutions
Introductory Statistics (10th Edition)
Ch. 6.1 - What is a density curve?Ch. 6.1 - State the two basic properties of every density...Ch. 6.1 - For a variable with a density curve, what is the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...
Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - A curve has area 0.425 to the left of 4 and area...Ch. 6.1 - A curve has area 0.613 to the left of 65 and area...Ch. 6.1 - Prob. 14ECh. 6.1 - A variable is approximately normally distributed....Ch. 6.1 - Precisely what is meant by the statement that a...Ch. 6.1 - Two normally distributed variables have the same...Ch. 6.1 - Which normal distribution has a wider spread: the...Ch. 6.1 - Consider two normal distributions, one with mean 4...Ch. 6.1 - Prob. 20ECh. 6.1 - True or false: The mean of a normal distribution...Ch. 6.1 - Prob. 22ECh. 6.1 - Sketch the normal distribution with a. = 3 and =...Ch. 6.1 - Prob. 24ECh. 6.1 - For a normally distributed variable, what is the...Ch. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - The area under a particular normal curve between...Ch. 6.1 - A variable has the density curve whose equation is...Ch. 6.1 - A variable has the density curve whose equation is...Ch. 6.1 - Waiting for the Train. A commuter train arrives...Ch. 6.1 - Bacteria on a Petri Dish. A petri dish is a small,...Ch. 6.1 - Fire Loss. The loss, in millions of dollars, due...Ch. 6.1 - Emergency Room Traffic. Desert Samaritan Hospital...Ch. 6.1 - Female College Students. Refer to Example 6.3 on...Ch. 6.1 - Female College Students. Refer to Example 6.3 on...Ch. 6.1 - Giant Tarantulas. One of the larger species of...Ch. 6.1 - Serum Cholesterol Levels. According to the...Ch. 6.1 - New York City 10-km Run. As reported in Runners...Ch. 6.1 - Prob. 40ECh. 6.1 - Ages of Mothers. From the document National Vital...Ch. 6.1 - Prob. 42ECh. 6.1 - Cloudiness in Breslau. In the paper Cloudiness:...Ch. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Chips Ahoy! 1,000 Chips Challenge. Students in an...Ch. 6.1 - Gestation Periods of Humans. Refer to the...Ch. 6.1 - Delaying Adulthood. In the paper, Delayed...Ch. 6.2 - With which normal distribution is the standard...Ch. 6.2 - Without consulting Table II, explain why the area...Ch. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain the areas under the...Ch. 6.2 - Use Table II to obtain each shaded area under the...Ch. 6.2 - Use Table II to obtain each shaded area under the...Ch. 6.2 - In each part, find the area under the standard...Ch. 6.2 - The total area under the following standard normal...Ch. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - Prob. 74ECh. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - Prob. 77ECh. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - Prob. 79ECh. 6.2 - Prob. 80ECh. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - In Exercises 6.716.82, use Table II to obtain the...Ch. 6.2 - Complete the following table.Ch. 6.2 - Prob. 84ECh. 6.2 - Prob. 85ECh. 6.3 - Briefly, for a normally distributed variable, how...Ch. 6.3 - Explain why the percentage of all possible...Ch. 6.3 - Prob. 88ECh. 6.3 - Prob. 89ECh. 6.3 - A variable is normally distributed with mean 68...Ch. 6.3 - A variable is normally distributed with mean 10...Ch. 6.3 - Prob. 92ECh. 6.3 - A variable is normally distributed with mean 6 and...Ch. 6.3 - A variable is normally distributed with mean 68...Ch. 6.3 - A variable is normally distributed with mean 10...Ch. 6.3 - A variable is normally distributed with mean 0 and...Ch. 6.3 - Giant Tarantulas. One of the larger species of...Ch. 6.3 - Serum Cholesterol Levels. According to the...Ch. 6.3 - New York City 10-km Run. As reported in Runners...Ch. 6.3 - Green Sea Urchins. From the paper Effects of...Ch. 6.3 - Arterial Cord pH. Umbilical cord blood analysis...Ch. 6.3 - Elephant Pregnancies. G. Wittemeyer et al. studied...Ch. 6.3 - Gibbon Song Duration. A preliminary behavioral...Ch. 6.3 - Friendship Motivation. In the article Assessing...Ch. 6.3 - Brain Weights. In 1905, R. Pearl published the...Ch. 6.3 - Children Watching TV. The A. C. Nielsen Company...Ch. 6.3 - Heights of Female Students. Refer to Example 6.3...Ch. 6.3 - Womens Shoes. Research reveals that foot length of...Ch. 6.3 - College-Math Success. Researchers S. Lesik and M....Ch. 6.3 - Tipping. In the article Are Christian/Religious...Ch. 6.3 - Booted Eagles. The rare booted eagle of western...Ch. 6.3 - Emergency Room Traffic. Desert Samaritan Hospital...Ch. 6.3 - Let 0 1. For a normally distributed variable,...Ch. 6.3 - Express the quartiles, Q1, Q2, and Q3, of a...Ch. 6.3 - Express the kth percentile, Pk , of a normally...Ch. 6.4 - Under what circumstances is using a normal...Ch. 6.4 - Explain why assessing the normality of a variable...Ch. 6.4 - Explain in detail what a normal probability plot...Ch. 6.4 - How is a normal probability plot used to detect...Ch. 6.4 - Explain how to obtain normal scores from Table III...Ch. 6.4 - In each of Exercises 6.1216.126, we have provided...Ch. 6.4 - In each of Exercises 6.1216.126, we have provided...Ch. 6.4 - In each of Exercises 6.1216.126, we have provided...Ch. 6.4 - In each of Exercises 6.1216.126, we have provided...Ch. 6.4 - In each of Exercises 6.1216.126, we have provided...Ch. 6.4 - Prob. 126ECh. 6.4 - In Exercises 6.1276.130, a. use Table III in...Ch. 6.4 - Prob. 128ECh. 6.4 - In Exercises 6.1276.130, a. use Table III in...Ch. 6.4 - In Exercises 6.1276.130, a. use Table III in...Ch. 6.4 - Prob. 131ECh. 6.4 - In Exercises 6.1316.134, a. obtain a normal...Ch. 6.4 - Prob. 133ECh. 6.4 - Prob. 134ECh. 6.4 - Body Temperature. A study by researchers at the...Ch. 6.4 - Vegetarians and Omnivores. Philosophical and...Ch. 6.4 - Prob. 137ECh. 6.4 - Finger Length of Criminals. In 1902, W. R....Ch. 6.4 - Prob. 139ECh. 6.4 - Emergency Room Traffic. Desert Samaritan Hospital...Ch. 6.5 - Why should you sometimes use normal-curve areas to...Ch. 6.5 - The rule of thumb for using the normal...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - Prob. 157ECh. 6.5 - Prob. 158ECh. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - In Exercises 6.1436.160, X denotes a binomial...Ch. 6.5 - TrueFalse Exams. Refer to Example 6.20 on page...Ch. 6.5 - Prob. 162ECh. 6.5 - TrueFalse Exams. If, in Example 6.20, the...Ch. 6.5 - TrueFalse Exams. If, in Example 6.20, the...Ch. 6.5 - Applying the Concepts and Skills In Exercises...Ch. 6.5 - In Exercises 6.1656.172, apply Procedure 6.3 on...Ch. 6.5 - In Exercises 6.1656.172, apply Procedure 6.3 on...Ch. 6.5 - In Exercises 6.1656.172, apply Procedure 6.3 on...Ch. 6.5 - In Exercises 6.1656.172, apply Procedure 6.3 on...Ch. 6.5 - In Exercises 6.1656.172, apply Procedure 6.3 on...Ch. 6.5 - In Exercises 6.1656.172, apply Procedure 6.3 on...Ch. 6.5 - Prob. 172ECh. 6.5 - Roulette. An American roulette wheel consists of...Ch. 6.5 - Flashlight Battery Lifetimes. A brand of...Ch. 6.5 - Prob. 175ECh. 6 - What is a density curve, and why are such curves...Ch. 6 - In each of Problems 24, assume that the variable...Ch. 6 - In each of Problems 24, assume that the variable...Ch. 6 - In each of Problems 24, assume that the variable...Ch. 6 - Prob. 5RPCh. 6 - State two of the main reasons for studying the...Ch. 6 - Prob. 7RPCh. 6 - Answer true or false to each statement. Give...Ch. 6 - Explain the relationship between percentages for a...Ch. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 12RPCh. 6 - What key fact permits you to determine percentages...Ch. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 16RPCh. 6 - State the empirical rule for variables.Ch. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - For the standard normal curve, find the z-score(s)...Ch. 6 - Dispensing Coffee. A coffee machine is supposed to...Ch. 6 - Forearm Length. In 1903, K. Pearson and A. Lee...Ch. 6 - Birth Weights. The WONDER database, maintained by...Ch. 6 - Lower Limb Surgery. The study Intrathecal...Ch. 6 - Verbal GRE Scores. The Graduate Record Examination...Ch. 6 - Verbal GRE Scores. Refer to Problem 28, and fill...Ch. 6 - Prob. 30RPCh. 6 - Prob. 31RPCh. 6 - Diarrhea Vaccine. Acute rotavirus diarrhea is the...Ch. 6 - FOCUSING ON DATA ANALYSIS UWEC UNDERGRADUATES...Ch. 6 - CASE STUDY DISCUSSION CHEST SIZES OF SCOTTISH...
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