A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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Chapter 6, Problem 23E

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A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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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 6, Problem 23E

To determine

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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Answer 3

Question

Chapter 6, Problem 23E

To determine

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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Answer 4

Question

Chapter 6, Problem 23E

To determine

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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Answer 5

Chapter 6, Problem 23E

To determine

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

Answer 6

Chapter 6, Problem 23E

To determine

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

Answer 7

Chapter 6, Problem 23E

To determine

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 6 - Prob. 6.1P Ch. 6 - Prob. 6.2P Ch. 6 - Prob. 6.3P Ch. 6 - Prob. 6.4P Ch. 6 - Prob. 6.5P Ch. 6 - Prob. 6.6P Ch. 6 - Prob. 6.7P Ch. 6 - Prob. 1E Ch. 6 - Prob. 2E Ch. 6 - Prob. 3E

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

Solution Summary: The author explains how the function func2 has a persistent variable count and returns the value instead of printing it.

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A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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Chapter 6 Solutions

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

Solution Summary: The author explains how the function func2 has a persistent variable count and returns the value instead of printing it.

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To write: A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.

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Chapter 6 Solutions

To write:

A modification in the function func2 that has a persistent variable count and instead of having the function print the value of count, the value should be returned.