MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Textbook Question
Chapter 11, Problem 7P
In rectangular coordinates the equation of the hyperbola shown in the figure is given by:
x2-y2=1
(a) Use MATLAB to show that in parametric form the equation of the hyperbola can be written as:
(b) Make a plot of the hyperbola for the domain shown in the figure by using the ezplot command.
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Students have asked these similar questions
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
Chapter 11 Solutions
MATLAB: An Introduction with Applications
Ch. 11 - Prob. 1PCh. 11 - Define y as a symbolic variable and create the two...Ch. 11 - Define x and y as symbolic variables and create...Ch. 11 - Define x as a symbolic variable. (a) Derive the...Ch. 11 - Use the commands from Section 11.2 to show that:...Ch. 11 - Use the commands from Section 11.2 to show that:...Ch. 11 - In rectangular coordinates the equation of the...Ch. 11 - Prob. 8PCh. 11 - The relation between the tension T and the steady...Ch. 11 - Consider the two ellipses in the x y plane given...
Ch. 11 - A 120 in.-long beam AB is attached to the wall...Ch. 11 - A box of mass m is being pulled by a rope as...Ch. 11 - The mechanical power output P in a contracting...Ch. 11 - The equation of a circle with its center is at x=3...Ch. 11 - A tracking radar antenna is locked on an airplane...Ch. 11 - Prob. 16PCh. 11 - Evaluate the following indefinite integrals: (a)...Ch. 11 - Define x as a symbolic variable and create the...Ch. 11 - The one-dimensional diffusion equation is given...Ch. 11 - A ceramic tile has the design shown in the figure....Ch. 11 - Prob. 21PCh. 11 - 22. Consider the parabolic sector shown in the...Ch. 11 - Prob. 23PCh. 11 - The spread of an infection from a single...Ch. 11 - The Maxwell-Boltzmann probability density function...Ch. 11 - The velocity of a skydiver whose parachute is...Ch. 11 - 27. A resistor R (R = 0.4?) and an inductor L (L =...Ch. 11 - Determine the general solution of the differential...Ch. 11 - Determine the solution of the following...Ch. 11 - 30. The current, i, in a series RLC circuit when...Ch. 11 - Damped free vibrations can be modeled by a block...
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