MATLAB: An Introduction with Applications
5th Edition
ISBN: 9781118629864
Author: Amos Gilat
Publisher: WILEY
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Chapter 3, Problem 16P
The area of a triangle ABC can be calculated by
First, define the vectors rOA, rOB, and rOCfrom knowing the coordinates of points A, B, and C. Then determine the vectors rABand rACfrom rOA, rOBand rOC. Finally, determine the area by using MATLAB’s built-in
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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?
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…
Chapter 3 Solutions
MATLAB: An Introduction with Applications
Ch. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - 8. The length |u| (magnitude) of a vector is given...Ch. 3 - Prob. 9PCh. 3 - Prob. 10P
Ch. 3 - Prob. 11PCh. 3 - Define the vector v = [2 3 4 5 6]. Then use the...Ch. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Define r and s as scalars r = 1.6 × 103 and s =...Ch. 3 - The area of a triangle ABC can be calculated by...Ch. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Create the following three matrices:...Ch. 3 - 30. Use the matrices A, B, and C from the previous...Ch. 3 - 31. Create a 4 × 4 matrix A having random integer...Ch. 3 - 32. The magic square is an arrangement of numbers...Ch. 3 - 33. Solve the following system of three linear...Ch. 3 - 34. Solve the following system of five linear...Ch. 3 - A food company manufactures five types of 8 oz...Ch. 3 - Prob. 36PCh. 3 -
37. The electrical circuit shown consists of...
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