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

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Answer 1

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

(e)

To determine

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

(e)

To determine

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

(e)

To determine

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 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

(e)

To determine

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 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

(e)

To determine

Interpret the conclusion in the context of the application.

Answer 6

Chapter 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

Answer 7

Chapter 8.3, Problem 11P

(a)

To determine

Find the level of significance.

State the null and alternative hypothesis.

Answer 8

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

Answer 9

(b)

To determine

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

Answer 10

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

Answer 11

(c)

To determine

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

Answer 12

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

Answer 13

(d)

To determine

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

Answer 14

(e)

To determine

Interpret the conclusion in the context of the application.

Answer 15

(e)

To determine

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

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

Videos

Find the level of significance.

State the null and alternative hypothesis.

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.

Interpret the conclusion in the context of the application.

Want to see the full answer?

Chapter 8 Solutions

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

Videos

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

Identify the sampling distribution to be used. Identify whether the sample size is sufficiently large or not. Find the value of the sample test statistic. Find the z value.

Find the P-value. Draw the sampling distribution by showing the area corresponding to the P-value.

Check whether the null hypothesis is rejecting or fail to reject. Identify whether the data statistically significant at level 0.01 or not.

Interpret the conclusion in the context of the application.

Want to see the full answer?

Chapter 8 Solutions

Find the level of significance.

State the null and alternative hypothesis.

Identify the sampling distribution to be used.

Identify whether the sample size is sufficiently large or not.

Find the value of the sample test statistic.

Find the z value.

Find the P-value.

Draw the sampling distribution by showing the area corresponding to the P-value.

Check whether the null hypothesis is rejecting or fail to reject.

Identify whether the data statistically significant at level 0.01 or not.