The claim; and to state H 0 and H 1

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Answer 1

Question

Chapter 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

b.

To determine

To find: The critical value.

c.

To determine

To find: The test statistic.

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

e.

To determine

To interpret: The decision in the context of the original claim.

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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 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

b.

To determine

To find: The critical value.

c.

To determine

To find: The test statistic.

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

e.

To determine

To interpret: The decision in the context of the original claim.

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Answer 3

Question

Chapter 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

b.

To determine

To find: The critical value.

c.

To determine

To find: The test statistic.

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

e.

To determine

To interpret: The decision in the context of the original claim.

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Answer 4

Question

Chapter 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

b.

To determine

To find: The critical value.

c.

To determine

To find: The test statistic.

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

e.

To determine

To interpret: The decision in the context of the original claim.

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Answer 5

Chapter 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

b.

To determine

To find: The critical value.

c.

To determine

To find: The test statistic.

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

e.

To determine

To interpret: The decision in the context of the original claim.

Answer 6

Chapter 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

Answer 7

Chapter 11.1, Problem 20E

a.

To determine

To identify: The claim; and to state H0 and H1

Answer 8

b.

To determine

To find: The critical value.

Answer 9

b.

To determine

To find: The critical value.

Answer 10

c.

To determine

To find: The test statistic.

Answer 11

c.

To determine

To find: The test statistic.

Answer 12

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

Answer 13

d.

To determine

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

Answer 14

e.

To determine

To interpret: The decision in the context of the original claim.

Answer 15

e.

To determine

To interpret: The decision in the context of the original claim.

Answer 16

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Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

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The claim; and to state H 0 and H 1

Solution Summary: entailment

Concept explainers

Videos

To identify: The claim; and to state H0 and H1

To find: The critical value.

To find: The test statistic.

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .

To interpret: The decision in the context of the original claim.

Want to see the full answer?

Chapter 11 Solutions

The claim; and to state H 0 and H 1

Solution Summary: entailment

Concept explainers

Videos

To identify: The claim; and to state H0 and H1

To find: The critical value.

To find: The test statistic.

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance α=0.05 .

To interpret: The decision in the context of the original claim.

Want to see the full answer?

Chapter 11 Solutions

To decide: Whether to reject or fail to reject the null hypothesis at a level of significance

α=0.05 .