MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Chapter 4, Problem 12P
An isosceles triangle sign is designed to have a triangular printed area of 600 in.2 (shaded area with a base length of a and height of h in the figure). As shown in the figure, there is a 2-in. gap between the sides of the triangles. Write a MATLAB program that determine the dimensions a and h, such that the overall area of the sign will be as small as possible. In the program define a
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Students have asked these similar questions
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.)
Chapter 4 Solutions
MATLAB: An Introduction with Applications
Ch. 4 - Prob. 1PCh. 4 - The altitude, h, as a function of air pressure can...Ch. 4 - Write a MATLAB program that determines the radius,...Ch. 4 - Radioactive decay can be modeled by the equation...Ch. 4 - A fuel tank is made of a half cylinder (r =14 in.)...Ch. 4 - A 300-lb garage door is being opened by pulling on...Ch. 4 - Write a MATLAB program in a script file that...Ch. 4 - The reduction of the amount of medication in the...Ch. 4 - The value of a saving account, V, after t years is...Ch. 4 - The electricity supply cables of the three houses...
Ch. 4 - Early explorers often estimated altitude by...Ch. 4 - An isosceles triangle sign is designed to have a...Ch. 4 - The angle ? at which a viewer sees the picture on...Ch. 4 - A 12-ft (144-in.) wire is cut into eight pieces...Ch. 4 - A person at point A spots a child in trouble at...Ch. 4 - The maximum stress smax at the edge of a hole...Ch. 4 - The airplane shown is flying at a constant speed...Ch. 4 - The intrinsic electrical conductivity a of a...Ch. 4 - The pressure drop ?p in pascals (Pa) for a fluid...Ch. 4 - The net heat exchange by radiation from plate 1...Ch. 4 - The equation of a circle in a plane with radius R...Ch. 4 - A truss is a structure made of members joined at...Ch. 4 - A truss is a Structure made of members joined at...Ch. 4 - The graph of the function f(x)=ax3+bx2+cx+d passes...Ch. 4 - The graph of the function f(x)=ax4+bx3+cx2+dx+e...Ch. 4 - The surface of many airfoils can be described with...Ch. 4 - During a golf match, a certain number of points...Ch. 4 - The dissolution of copper sulfide in aqueous...Ch. 4 - The heat index HI, calculated from the air...Ch. 4 - The stress intensity factor K at a crack is given...
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- The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forwardUsing the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. LOADING... Click the icon to view the Home Market Value data. Question content area bottom Part 1 Construct a frequency distribution of the errors, e Subscript iei. (Type whole numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0 minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5 minus−50005000less than< e Subscript iei less than or equals≤0 21 0less than< e Subscript iei less than or equals≤50005000 9…arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000arrow_forward
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