MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Chapter 7, Problem 19P
Write a user-defined MATLAB
(a) 100 (b) 1002 (c) 52,601 (d) 200,090
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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 7 Solutions
MATLAB: An Introduction with Applications
Ch. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - In the U.S. fuel efficiency of cars is specified...Ch. 7 - Pressure in U.S. customary units is measured in...Ch. 7 - Tables of material properties list density, in...Ch. 7 - Write a user-defined MATLAB function that converts...Ch. 7 - The body surface area (BSA) in m2 of a person...Ch. 7 - The fuel tank shown in the figure in shad as a...Ch. 7 - A paper cup is designed to have a geometry of a...Ch. 7 - The relative humidity, RH, at sea level can be...
Ch. 7 - Write a user-defined function that calculates...Ch. 7 - Write a user-defined MATLAB function that...Ch. 7 - Write a user-defined MATLAB function that...Ch. 7 - Write a user-defined MATLAB function that...Ch. 7 - Prob. 15PCh. 7 - The area of a triangle ABC can be calculated by:...Ch. 7 - As shown in the figure, the area of a convex...Ch. 7 - Write a user-defined function that determines the...Ch. 7 - Write a user-defined MATLAB function that converts...Ch. 7 - Write a user-defined function that plots a...Ch. 7 - Write a user-defined function that plots an...Ch. 7 - Prob. 22PCh. 7 - Write a user-defined function that determines if a...Ch. 7 - The harmonic mean H of a set of n positive numbers...Ch. 7 - Write a user-defined function that determines the...Ch. 7 - Write a user-defined function that determines the...Ch. 7 - Write a user-defined function that sorts the...Ch. 7 - Write a user-defined function that sorts the...Ch. 7 - Write a user-defined MATLAB function that finds...Ch. 7 - Write a user-defined MATLAB function that...Ch. 7 - The shortest distance between two points on the...Ch. 7 - Delta rosette is a set of three strain gages...Ch. 7 - In a lottery the player has to select several...Ch. 7 - 34. The Taylor series expansion for sin x about x...Ch. 7 - Write a user-defined function that determines the...Ch. 7 - The area moment of inertia Ixe of a rectangle...Ch. 7 - The simple RC high-pass filter shown in the figure...Ch. 7 - A circuit that filters out a certain frequency is...Ch. 7 - The first derivative df(x)dx a function f(x) at a...Ch. 7 - In lottery the player has to guess correctly r...
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