COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)
14th Edition
ISBN: 9780135998083
Author: Barnett
Publisher: PEARSON
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Chapter 4.7, Problem 8E
To determine
To solve: The equation
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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?
The Course Name Real Analysis please Solve questions by Real Analysis
Chapter 4 Solutions
COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)
Ch. 4.1 - Solve by graphing and check:
2x − y = −3
x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing:
x...Ch. 4.1 - Prob. 3MPCh. 4.1 - Prob. 4MPCh. 4.1 - Prob. 5MPCh. 4.1 - Prob. 6MPCh. 4.1 - Prob. 7MPCh. 4.1 - Prob. 1EDCh. 4.1 - Prob. 2EDCh. 4.1 - In Problems 1–6, find the x and y coordinates of...
Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - In Problems 1–6, find the x and y coordinates of...Ch. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Match each system in Problems 9–12 with one of the...Ch. 4.1 - Solve Problems 13–16 by graphing.
13.
Ch. 4.1 - Solve Problems 13–16 by graphing.
14.
Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - In a free competitive market, if the demand for a...Ch. 4.1 - Problems 45−48 are concerned with the linear...Ch. 4.1 -
Problems 45−48 are concerned with the linear...Ch. 4.1 - Problems 45−48 are concerned with the linear...Ch. 4.1 - Problems 45–48 are concerned with the linear...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - In Problems 57−62, graph the equations in the same...Ch. 4.1 - In Problems 57−62, graph the equations in the same...Ch. 4.1 -
In Problems 57−62, graph the equations in the...Ch. 4.1 - 63. The coefficients of the three systems given...Ch. 4.1 - Repeat problem 63 for the following systems:
...Ch. 4.1 - Supply and demand for T-shirts. Suppose that the...Ch. 4.1 - Supply and demand for baseball caps. Suppose that...Ch. 4.1 - Supply and demand for soybeans. At $4.80 per...Ch. 4.1 - Supply and demand for corn. At $2.13 per bushel,...Ch. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Delivery charges. United Express, a national...Ch. 4.1 - Delivery charges. Refer to Problem 73. Federated...Ch. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Animal diet. Animals in an experiment are to be...Ch. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 81ECh. 4.1 - Prob. 82ECh. 4.1 - Prob. 83ECh. 4.1 - Prob. 84ECh. 4.1 - Prob. 85ECh. 4.2 - Solve using augmented matrix methods:
2x1 − x2 =...Ch. 4.2 - Prob. 2MPCh. 4.2 - Prob. 3MPCh. 4.2 - Prob. 4MPCh. 4.2 - Prob. 1EDCh. 4.2 - Prob. 2EDCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 13ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Perform the row operations indicated in problems...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Perform the row operations indicated in problem...Ch. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Each of the matrices in Problems 35–42 is the...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Solve Problems 47 and 48 using augmented matrix...Ch. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 64ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 66ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Solve Problems 55-74 using augmented, matrix...Ch. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Solve Problems 55-74 using augmented, matrix...Ch. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - Prob. 83ECh. 4.2 - Prob. 84ECh. 4.3 - The matrices below are not in reduced form....Ch. 4.3 - Solve by Gauss–Jordan elimination:
3x1 + x2 − 2x3...Ch. 4.3 - Solve by Gauss-Jordan elimination:
2x1 − 4x2 − x3...Ch. 4.3 - Solve by Gauss–Jordan elimination:
Ch. 4.3 - Prob. 5MPCh. 4.3 - Prob. 6MPCh. 4.3 - Prob. 1EDCh. 4.3 - Prob. 2EDCh. 4.3 - In Problems 1–4, write the augmented matrix of the...Ch. 4.3 - Prob. 2ECh. 4.3 - In Problems 1–4, write the augmented matrix of the...Ch. 4.3 - Prob. 4ECh. 4.3 - In Problems 5−8, write the system of linear...Ch. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 14ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 16ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 18ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 20ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 22ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 24ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 26ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - In which of Problems 19, 21, 23, 25, and 27 is the...Ch. 4.3 - Prob. 32ECh. 4.3 - In Problems 33–38, discuss the validity of each...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Use row operations to change each matrix in...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 52ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 54ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Consider a consistent system of three linear...Ch. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Find a, b, and c so that the graph of the...Ch. 4.3 - Prob. 72ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 74ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Construct a mathematical model for each of the...Ch. 4.3 - Prob. 78ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Taxable income. Repeat Problem 81 if tax law is...Ch. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 84ECh. 4.3 - Prob. 85ECh. 4.3 - Prob. 86ECh. 4.3 - Construct a mathematical model for each of the...Ch. 4.3 - Prob. 88ECh. 4.3 - Population growth. The U.S. population was...Ch. 4.3 - Prob. 90ECh. 4.3 - Prob. 91ECh. 4.3 - Prob. 92ECh. 4.3 - Prob. 93ECh. 4.3 - Prob. 94ECh. 4.3 - Sociology. Two sociologists have grant money to...Ch. 4.3 - Prob. 96ECh. 4.3 - Prob. 97ECh. 4.3 - Traffic flow. Refer to Problem 97. Closing...Ch. 4.4 - Add:
Ch. 4.4 - Prob. 2MPCh. 4.4 - Prob. 3MPCh. 4.4 - Prob. 4MPCh. 4.4 - Prob. 5MPCh. 4.4 - Prob. 6MPCh. 4.4 - Prob. 7MPCh. 4.4 - Find each product, if it is...Ch. 4.4 - Prob. 9MPCh. 4.4 - Prob. 10MPCh. 4.4 - Prob. 1EDCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - In Problems 1–14, perform the indicated operation,...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - In Problems 1–14, perform the indicated operation,...Ch. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - In Problems 15–22, find the matrix product. Note...Ch. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - In Problems 15–22, find the matrix product. Note...Ch. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - B Find the products in Problems 23–30.
25.
Ch. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 -
Find the products in problems 23–30.
29.
Ch. 4.4 - Prob. 30ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 36ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - If a and b are nonzero real numbers,
find AB and...Ch. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - If a, b, c, and d so that
Ch. 4.4 - Prob. 56ECh. 4.4 - If a, b, c, and d, so that
Ch. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Markup. An import car dealer sells three models of...Ch. 4.4 - Prob. 68ECh. 4.4 - Labor costs. A company with manufacturing plants...Ch. 4.4 - Inventory value. A personal computer retail...Ch. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.5 - Prob. 1MPCh. 4.5 - Prob. 2MPCh. 4.5 - Prob. 3MPCh. 4.5 - Prob. 4MPCh. 4.5 - Prob. 5MPCh. 4.5 - Prob. 1EDCh. 4.5 - Prob. 2EDCh. 4.5 - Prob. 3EDCh. 4.5 - In Problems 1-4, find the additive inverse and the...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 22ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 24ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Given M in problems 39–48, find M−1 and show that...Ch. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Given M in Problems 39–48, find M–1and show that...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Find the inverse of each matrix in Problems 49–56,...Ch. 4.5 - Prob. 50ECh. 4.5 - Find the inverse of each matrix in problem 49–56,...Ch. 4.5 - Given M in problem 39–48, find M–1 and show that...Ch. 4.5 - Find the inverse of each matrix in problems 49–56,...Ch. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - In Problems 57–60, find the inverse. Note that...Ch. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Prob. 64ECh. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Show that (A–1)–1 = A for: A =
Ch. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Cryptography. The following message was encoded...Ch. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.5 - Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.6 - Given an n × n matrix A and n × 1 column matrices...Ch. 4.6 - Prob. 2MPCh. 4.6 - Prob. 3MPCh. 4.6 - Prob. 4MPCh. 4.6 - Prob. 1EDCh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Prob. 7ECh. 4.6 - Prob. 8ECh. 4.6 - Write Problems 9–12 as systems of linear equations...Ch. 4.6 - Prob. 10ECh. 4.6 - Write problems 9–12 as system of linear equations...Ch. 4.6 - Prob. 12ECh. 4.6 - Write each system on Problems 13–16 as a matrix...Ch. 4.6 - Prob. 14ECh. 4.6 - Write each system in Problems 13–16 as a matrix...Ch. 4.6 - Prob. 16ECh. 4.6 - Find x1 and x2 in problems 17–20.
Ch. 4.6 - Prob. 18ECh. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - In Problems 21–24, find x1 and x2.
Ch. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - In Problems 21–24, find x1 and x2.
Ch. 4.6 - In Problems 25–30, solve for x1 and x2.
Ch. 4.6 - In Problems 25–30, solve for x1 and x2.
Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - In problems 25–30, solve for x1 and x2.
Ch. 4.6 - Prob. 30ECh. 4.6 - In Problems 31–38, write each system as a matrix...Ch. 4.6 - Prob. 32ECh. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - In Problems 31–38, write each system as a matrix...Ch. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Prob. 40ECh. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Prob. 44ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 46ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 48ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 50ECh. 4.6 - Prob. 51ECh. 4.6 - Prob. 52ECh. 4.6 - Prob. 53ECh. 4.6 - Prob. 54ECh. 4.6 - Prob. 55ECh. 4.6 - Prob. 56ECh. 4.6 - Prob. 57ECh. 4.6 - Prob. 58ECh. 4.6 - In Problems 59–62, write each system as a matrix...Ch. 4.6 - Prob. 60ECh. 4.6 - Prob. 61ECh. 4.6 - Prob. 62ECh. 4.6 - Concert tickets. A concert hall has 10,000 seats...Ch. 4.6 - Prob. 64ECh. 4.6 - Production scheduling. A supplier manufactures car...Ch. 4.6 - Prob. 66ECh. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - Prob. 70ECh. 4.7 - An economy is based on three sectors, coal, oil,...Ch. 4.7 - Prob. 1EDCh. 4.7 - Prob. 1ECh. 4.7 - Prob. 2ECh. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 6ECh. 4.7 - Prob. 7ECh. 4.7 - Prob. 8ECh. 4.7 - Problems 9–14 pertain to the following...Ch. 4.7 - Problems 9–14 pertain to the following input-...Ch. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Problems 15–20 pertain to the following input-...Ch. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - Repeat Problem 41 with the following table:
Four...Ch. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RE
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- 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? 2arrow_forwardQuestion 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…arrow_forwardIn 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.)arrow_forward
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