(a) To Explain: The given statement based on the given information.

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Answer 1

Question

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

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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.)

Answer 2

Question

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Expert Solution & Answer

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Answer 3

Question

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Expert Solution & Answer

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Answer 4

Question

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Expert Solution & Answer

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Answer 5

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Answer 6

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

Answer 7

Chapter 2, Problem 55E

To determine

(a)

To Explain:

The given statement based on the given information.

Answer 8

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

Answer 9

To determine

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

Answer 10

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Answer 11

To determine

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - Consider the weighted voting system[q:7,5,3]. Find...Ch. 2 - Consider the weighted voting system...Ch. 2 - A committee has four members (P1,P2,P3,andP4). In...Ch. 2 - A committee has six members...

(a) To Explain: The given statement based on the given information.

Solution Summary: The author explains that P is a dummy if the Banzhaf power index (BPI) for the player is 0.

Concept explainers

Videos

(a)

To Explain:

The given statement based on the given information.

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.

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Chapter 2 Solutions

(a) To Explain: The given statement based on the given information.

Solution Summary: The author explains that P is a dummy if the Banzhaf power index (BPI) for the player is 0.

Concept explainers

Videos

(a) To Explain: The given statement based on the given information.

(b) To Explain: P is a dummy if and only if the Banzhaf power index of P is 0.

(c) To Explain: P is a dummy if and only if the Shapley-Shubik power index of P is 0.

Want to see the full answer?

Chapter 2 Solutions

(a)

To Explain:

The given statement based on the given information.

(b)

To Explain:

P is a dummy if and only if the Banzhaf power index of P is 0.

(c)

To Explain:

P is a dummy if and only if the Shapley-Shubik power index of P is 0.