Find the slope and intercept of the blue horizontal line. Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y ’s. Check whether the line appear to fit the data well. Explain how does the SSE compare to the sum of the areas of the yellow boxes.

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Answer 1

Question

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

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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

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Answer 6

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

Answer 7

Chapter 11.3, Problem 2E

a.

To determine

Find the slope and intercept of the blue horizontal line.

Find the sum of squares of the vertical deviations between the points on the horizontal line and the observed values of the y’s.

Check whether the line appear to fit the data well.

Explain how does the SSE compare to the sum of the areas of the yellow boxes.

Answer 8

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

Answer 9

b.

To determine

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

Answer 10

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

Answer 11

c.

To determine

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

Answer 12

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Answer 13

d.

To determine

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2E Ch. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5E Ch. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7E Ch. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9E Ch. 11.3 - Suppose that we have postulated the model...

Solution Summary: The author explains how to obtain slope, intercept, and sum of squares values using Applet: Select Example 11.1 under Fitting a line using least square.

Concept explainers

Videos

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.

Want to see the full answer?

Chapter 11 Solutions

Solution Summary: The author explains how to obtain slope, intercept, and sum of squares values using Applet: Select Example 11.1 under Fitting a line using least square.

Concept explainers

Videos

Drag the horizontal line to make the slope of the line negative. Explain the lengths of vertical red lines. Check whether SSE increases or decreases. Check whether the line with negative slope appear to fit the data well.

Drag the horizontal line to make the slope is near 0.8. Check whether SSE increases or decreases when the slope is closer to 0.7. Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

Drag the horizontal line until the data fits visually well. Find the slope and intercept of the line. Obtain the value of SSE. Compare the SSE associated with visually fitted model and best model. Compare the slope and intercept associated with visually fitted model and best model.

Want to see the full answer?

Chapter 11 Solutions

Drag the horizontal line to make the slope of the line negative.

Explain the lengths of vertical red lines.

Check whether SSE increases or decreases.

Check whether the line with negative slope appear to fit the data well.

Drag the horizontal line to make the slope is near 0.8.

Check whether SSE increases or decreases when the slope is closer to 0.7.

Find the coordinates of the pivot point consistent with the result obtained in Exercise 11.1.

Drag the horizontal line until the data fits visually well.

Find the slope and intercept of the line.

Obtain the value of SSE.

Compare the SSE associated with visually fitted model and best model.

Compare the slope and intercept associated with visually fitted model and best model.