Identify the test to be used.

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Answer 1

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Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(c)

To determine

Find the sample test statistic R, the number of runs.

(d)

To determine

Find the lower critical value.

Find the upper critical value.

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

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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

Answer 2

Question

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(c)

To determine

Find the sample test statistic R, the number of runs.

(d)

To determine

Find the lower critical value.

Find the upper critical value.

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(c)

To determine

Find the sample test statistic R, the number of runs.

(d)

To determine

Find the lower critical value.

Find the upper critical value.

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(c)

To determine

Find the sample test statistic R, the number of runs.

(d)

To determine

Find the lower critical value.

Find the upper critical value.

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(c)

To determine

Find the sample test statistic R, the number of runs.

(d)

To determine

Find the lower critical value.

Find the upper critical value.

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Answer 6

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

Answer 7

Chapter 11, Problem 9CRP

(a)

To determine

Identify the test to be used.

Answer 8

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

Answer 9

(b)

To determine

Find the level of significance.

State the null and alternative hypothesis.

Answer 10

(c)

To determine

Find the sample test statistic R, the number of runs.

Answer 11

(c)

To determine

Find the sample test statistic R, the number of runs.

Answer 12

(d)

To determine

Find the lower critical value.

Find the upper critical value.

Answer 13

(d)

To determine

Find the lower critical value.

Find the upper critical value.

Answer 14

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Answer 15

(e)

To determine

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

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Identify the test to be used.

Solution Summary: The author states the null and alternative hypothesis that the sequence of answers to a true-false exam is randomly mixed.

Videos

Identify the test to be used.

Find the level of significance.

State the null and alternative hypothesis.

Find the sample test statistic R, the number of runs.

Find the lower critical value.

Find the upper critical value.

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.

Want to see the full answer?

Chapter 11 Solutions

Identify the test to be used.

Solution Summary: The author states the null and alternative hypothesis that the sequence of answers to a true-false exam is randomly mixed.

Videos

Identify the test to be used.

Find the level of significance. State the null and alternative hypothesis.

Find the sample test statistic R, the number of runs.

Find the lower critical value. Find the upper critical value.

Mention the conclusion of the test. Interpret the conclusion in the context of the application.

Want to see the full answer?

Chapter 11 Solutions

Find the level of significance.

State the null and alternative hypothesis.

Find the lower critical value.

Find the upper critical value.

Mention the conclusion of the test.

Interpret the conclusion in the context of the application.