Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
11th Edition
ISBN: 9781305283831
Author: Tan
Publisher: Cengage Learning
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Chapter A.4, Problem 13E
To determine
The statement
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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?
The Course Name Real Analysis please Solve questions by Real Analysis
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 A Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
Ch. A.1 - In Exercises 114, determine whether the statement...Ch. A.1 - Prob. 2ECh. A.1 - Prob. 3ECh. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - Prob. 9ECh. A.1 - Prob. 10E
Ch. A.1 - Prob. 11ECh. A.1 - Prob. 12ECh. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - Prob. 16ECh. A.1 - Prob. 17ECh. A.1 - Prob. 18ECh. A.1 - Prob. 19ECh. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - Prob. 22ECh. A.1 - Prob. 23ECh. A.1 - Prob. 24ECh. A.1 - Prob. 25ECh. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Let p and q denote the propositions p: The...Ch. A.1 - Prob. 31ECh. A.1 - Prob. 32ECh. A.1 - Prob. 33ECh. A.2 - Prob. 1ECh. A.2 - Prob. 2ECh. A.2 - Prob. 3ECh. A.2 - Prob. 4ECh. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 6ECh. A.2 - Prob. 7ECh. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 9ECh. A.2 - Prob. 10ECh. A.2 - Prob. 11ECh. A.2 - Prob. 12ECh. A.2 - Prob. 13ECh. A.2 - Prob. 14ECh. A.2 - Prob. 15ECh. A.2 - Prob. 16ECh. A.2 - Prob. 17ECh. A.2 - Prob. 18ECh. A.2 - If a compound proposition consists of the prime...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - Prob. 3ECh. A.3 - Prob. 4ECh. A.3 - Prob. 5ECh. A.3 - In Exercises 5 and 6, refer to the following...Ch. A.3 - Prob. 7ECh. A.3 - Prob. 8ECh. A.3 - Prob. 9ECh. A.3 - Prob. 10ECh. A.3 - Prob. 11ECh. A.3 - Prob. 12ECh. A.3 - Prob. 13ECh. A.3 - Prob. 14ECh. A.3 - Prob. 15ECh. A.3 - Prob. 16ECh. A.3 - Prob. 17ECh. A.3 - Prob. 18ECh. A.3 - Prob. 19ECh. A.3 - Prob. 20ECh. A.3 - Prob. 21ECh. A.3 - Prob. 22ECh. A.3 - Prob. 23ECh. A.3 - Prob. 24ECh. A.3 - Prob. 25ECh. A.3 - Prob. 26ECh. A.3 - Prob. 27ECh. A.3 - Prob. 28ECh. A.3 - Prob. 29ECh. A.3 - Prob. 30ECh. A.3 - Prob. 31ECh. A.3 - Prob. 32ECh. A.3 - Prob. 33ECh. A.3 - Prob. 34ECh. A.3 - Prob. 35ECh. A.3 - Prob. 36ECh. A.3 - Prob. 37ECh. A.3 - Prob. 38ECh. A.4 - Prove the idempotent law for conjunction, ppp.Ch. A.4 - Prob. 2ECh. A.4 - Prove the associative law for conjunction,...Ch. A.4 - Prob. 4ECh. A.4 - Prove the commutative law for conjunction, pqqp.Ch. A.4 - Prob. 6ECh. A.4 - Prob. 7ECh. A.4 - Prob. 8ECh. A.4 - Prob. 9ECh. A.4 - Prob. 10ECh. A.4 - Prob. 11ECh. A.4 - Prob. 12ECh. A.4 - Prob. 13ECh. A.4 - Prob. 14ECh. A.4 - Prob. 15ECh. A.4 - Prob. 16ECh. A.4 - Prob. 17ECh. A.4 - In exercises 9-18, determine whether the statement...Ch. A.4 - Prob. 19ECh. A.4 - Prob. 20ECh. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 22ECh. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 26ECh. A.5 - Prob. 1ECh. A.5 - Prob. 2ECh. A.5 - Prob. 3ECh. A.5 - Prob. 4ECh. A.5 - Prob. 5ECh. A.5 - Prob. 6ECh. A.5 - Prob. 7ECh. A.5 - Prob. 8ECh. A.5 - Prob. 9ECh. A.5 - In Exercises 116, determine whether the argument...Ch. A.5 - Prob. 11ECh. A.5 - Prob. 12ECh. A.5 - Prob. 13ECh. A.5 - Prob. 14ECh. A.5 - Prob. 15ECh. A.5 - Prob. 16ECh. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 18ECh. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 22ECh. A.5 - Prob. 23ECh. A.5 - Prob. 24ECh. A.5 - Prob. 25ECh. A.6 - In Exercises 1-5, find a logic statement...Ch. A.6 - Prob. 2ECh. A.6 - Prob. 3ECh. A.6 - Prob. 4ECh. A.6 - Prob. 5ECh. A.6 - Prob. 6ECh. A.6 - Prob. 7ECh. A.6 - Prob. 8ECh. A.6 - Prob. 9ECh. A.6 - Prob. 10ECh. A.6 - Prob. 11ECh. A.6 - Prob. 12ECh. A.6 - Prob. 13ECh. A.6 - In Exercise 12-15, find a logic statement...Ch. A.6 - Prob. 15ECh. A.6 - Prob. 16E
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