EBK MATLAB: AN INTRODUCTION WITH APPLIC
5th Edition
ISBN: 8220102007642
Author: GILAT
Publisher: YUZU
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Chapter 6, Problem 16P
Write a program that (a) generates a
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
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Strength of the relationship (strong/moderate/weak):
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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.)
Chapter 6 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 6 - Prob. 1PCh. 6 - Given: a = 2, b = 3, c = 5. Evaluate the following...Ch. 6 - Given: v = [4 1 2 3 1 2 5 0] and u = [5 1 0 3 3 2...Ch. 6 - Use the vectors y and u from Problem 3. Use...Ch. 6 - Evaluate the following expressions without using...Ch. 6 - Use loops to create a 3 × 5 matrix in which the...Ch. 6 - A symmetric (5 × 5) Pascal matrix is displayed on...Ch. 6 - The average monthly precipitation (in.) for Boston...Ch. 6 - Write a program in a script file that finds the...Ch. 6 - Fibonacci numbers are the numbers in a sequence in...
Ch. 6 - The reciprocal Fibonacci constant is defined by...Ch. 6 - Write a program in a script file that determines...Ch. 6 - The value of x can be estimated by: n=1n2 Write a...Ch. 6 - The value of p can be estimated from the...Ch. 6 - Write a program that generates a vector with 20...Ch. 6 - Write a program that (a) generates a vector with...Ch. 6 - Write a program that asks the user Lo input a...Ch. 6 - A vector is given by x = [4.5 5 16.12 21.8 10.1 10...Ch. 6 - The Pythagorean theorem states that a2+ b2= c2....Ch. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - A list of30 exam scores is: 31, 70, 92, 5, 47, 88,...Ch. 6 - The Taylor series expansion for cos(x) is:...Ch. 6 - Write a MATLAB program in a script file that finds...Ch. 6 - Prob. 25PCh. 6 - Body mass index (BMI) is a measure of obesity. In...Ch. 6 - Prob. 27PCh. 6 - Write a program that determines the change given...Ch. 6 - The concentration of a drug in the body CPcan be...Ch. 6 - Prob. 30PCh. 6 - Write a program in a script file that converts a...Ch. 6 - In a one-dimensional random walk, the position x...Ch. 6 - The Sierpinski triangle can be implemented in...Ch. 6 - Cam is a mechanical device that transforms rotary...Ch. 6 - The overall grade in a course is determined from...Ch. 6 - Prob. 36P
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- 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?arrow_forwardWe 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? 2arrow_forwardQuestion 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…arrow_forward
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