To express: The fact in the form of an if-then statement about R , S and elements of A .

Question

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Answer 1

Question

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

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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?

Answer 2

Question

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

Answer 6

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

Answer 7

Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about R, S and elements of A .

Answer 8

Expert Solution & Answer

Explanation of Solution

Given: The given fact is R⊆S .

For the two relation R and S on set A and R⊆S , then all the elements in relation R also present in S .

∀x, y∈A, (x, y)∈R

Then,

(x, y)∈S

The above fact in if-then format is written as,

For elements a,b∈A if aRb then aSb .

Therefore, the fact in if-then form is written as, “For elements a,b∈A if aRb then aSb .”

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Ch. 3.14 - Write the following relations on the set 1,2,3,4,5...Ch. 3.14 - Prob. 14.2E Ch. 3.14 - Prob. 14.3E Ch. 3.14 - For each of the following relations on the set of...Ch. 3.14 - Prob. 14.5E Ch. 3.14 - Prob. 14.6E Ch. 3.14 - Prob. 14.7E Ch. 3.14 - Prob. 14.8E Ch. 3.14 - Prob. 14.9E Ch. 3.14 - Prob. 14.10E

To express: The fact in the form of an if-then statement about R , S and elements of A .

Concept explainers

To express: The fact in the form of an if-then statement about R, S and elements of A .

Explanation of Solution

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Chapter 3 Solutions