Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
11th Edition
ISBN: 9780137554843
Author: Allyn Washington, Richard Evans
Publisher: PEARSON+
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Chapter 31.7, Problem 24E
To determine
To solve: The differential equation
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Calculus lll
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For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram?
A
55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92
B
55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91
C
55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93
D
55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91
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 31 Solutions
Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1ECh. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4ECh. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6ECh. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8ECh. 31.1 - In Exercises 7–10, show that each function y =...
Ch. 31.1 - Prob. 10ECh. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - Prob. 14ECh. 31.1 - Prob. 15ECh. 31.1 - Prob. 16ECh. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - Prob. 19ECh. 31.1 - Prob. 20ECh. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - Prob. 22ECh. 31.1 - Prob. 23ECh. 31.1 - Prob. 24ECh. 31.1 - Prob. 25ECh. 31.1 - Prob. 26ECh. 31.1 - In Exercises 11–30, show that the given equation...Ch. 31.1 - Prob. 28ECh. 31.1 - Prob. 29ECh. 31.1 - Prob. 30ECh. 31.1 - In Exercises 31–34, determine whether or not each...Ch. 31.1 - Prob. 32ECh. 31.1 - In Exercises 31–34, determine whether or not each...Ch. 31.1 - Prob. 34ECh. 31.1 - In Exercises 35–38, solve the given...Ch. 31.1 - Prob. 36ECh. 31.1 - In Exercises 35–38, solve the given...Ch. 31.1 - In Exercises 35–38, solve the given...Ch. 31.2 -
Find the general solution of the differential...Ch. 31.2 - In Exercises 1 and 2, make the given changes in...Ch. 31.2 - Prob. 2ECh. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - Prob. 10ECh. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - Prob. 12ECh. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - Prob. 14ECh. 31.2 - Prob. 15ECh. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - Prob. 18ECh. 31.2 - Prob. 19ECh. 31.2 - Prob. 20ECh. 31.2 - Prob. 21ECh. 31.2 - Prob. 22ECh. 31.2 - Prob. 23ECh. 31.2 - Prob. 24ECh. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - Prob. 26ECh. 31.2 - Prob. 27ECh. 31.2 - Prob. 28ECh. 31.2 - Prob. 29ECh. 31.2 - Prob. 30ECh. 31.2 - Prob. 31ECh. 31.2 - Prob. 32ECh. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 3–34, solve the given differential...Ch. 31.2 - In Exercises 35–40, find the particular solution...Ch. 31.2 - In Exercises 35–40, find the particular solution...Ch. 31.2 - In Exercises 35–40, find the particular solution...Ch. 31.2 - In Exercises 35–40, find the particular solution...Ch. 31.2 - In Exercises 35–40, find the particular solution...Ch. 31.2 - In Exercises 35–40, find the particular solution...Ch. 31.2 - In Exercises 41–44, solve the given...Ch. 31.2 - In Exercises 41–44, solve the given...Ch. 31.2 - In Exercises 41–44, solve the given...Ch. 31.2 - In Exercises 41–44, solve the given...Ch. 31.3 - Find the general solution of the differential...Ch. 31.3 - Prob. 1ECh. 31.3 - In Exercises 1 and 2, make the given changes in...Ch. 31.3 -
In Exercises 3–18, solve the given differential...Ch. 31.3 - In Exercises 3–18, solve the given differential...Ch. 31.3 - In Exercises 3–18, solve the given differential...Ch. 31.3 -
In Exercises 3–18, solve the given differential...Ch. 31.3 - Prob. 7ECh. 31.3 - Prob. 8ECh. 31.3 - Prob. 9ECh. 31.3 - Prob. 10ECh. 31.3 -
In Exercises 3–18, solve the given differential...Ch. 31.3 - Prob. 12ECh. 31.3 - Prob. 13ECh. 31.3 - Prob. 14ECh. 31.3 - In Exercises 3–18, solve the given differential...Ch. 31.3 - Prob. 16ECh. 31.3 - In Exercises 3–18, solve the given differential...Ch. 31.3 - In Exercises 3–18, solve the given differential...Ch. 31.3 -
In Exercises 19–24, find the particular solutions...Ch. 31.3 - In Exercises 19–24, find the particular solutions...Ch. 31.3 - In Exercises 19–24, find the particular solutions...Ch. 31.3 - Prob. 22ECh. 31.3 - Prob. 23ECh. 31.3 - Prob. 24ECh. 31.3 - Prob. 25ECh. 31.3 - Prob. 26ECh. 31.3 - Prob. 27ECh. 31.3 - Prob. 28ECh. 31.4 - Find the general solution of the differential...Ch. 31.4 - In Exercises 1 and 2, make the given changes in...Ch. 31.4 - In Exercises 1 and 2, make the given changes in...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 -
In Exercises 3–18, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - Prob. 16ECh. 31.4 - Prob. 17ECh. 31.4 - Prob. 18ECh. 31.4 - Prob. 19ECh. 31.4 - Prob. 20ECh. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - Prob. 22ECh. 31.4 - Prob. 23ECh. 31.4 - Prob. 24ECh. 31.4 - Prob. 25ECh. 31.4 - In Exercises 3–28, solve the given differential...Ch. 31.4 - Prob. 27ECh. 31.4 - Prob. 28ECh. 31.4 - In Exercises 29 and 30, solve the given...Ch. 31.4 - In Exercises 29 and 30, solve the given...Ch. 31.4 - In Exercises 31–36, find the indicated particular...Ch. 31.4 - In Exercises 31–36, find the indicated particular...Ch. 31.4 - In Exercises 31–36, find the indicated particular...Ch. 31.4 - In Exercises 31–36, find the indicated particular...Ch. 31.4 - In Exercises 31–36, find the indicated particular...Ch. 31.4 - In Exercises 31–36, find the indicated particular...Ch. 31.4 - In Exercises 37–42, solve the given...Ch. 31.4 - In Exercises 37–42, solve the given...Ch. 31.4 - In Exercises 37–42, solve the given...Ch. 31.4 - In Exercises 37–42, solve the given...Ch. 31.4 - In Exercises 37–42, solve the given...Ch. 31.4 - In Exercises 37–42, solve the given...Ch. 31.5 - In Exercises 1–8, use Euler’s method to find...Ch. 31.5 - Prob. 2ECh. 31.5 - In Exercises 1–8, use Euler’s method to find...Ch. 31.5 - Prob. 4ECh. 31.5 - Prob. 5ECh. 31.5 - Prob. 6ECh. 31.5 - Prob. 7ECh. 31.5 - Prob. 8ECh. 31.5 - In Exercises 9–14, use the Runge–Kutta method to...Ch. 31.5 - Prob. 10ECh. 31.5 - In Exercises 9–14, use the Runge–Kutta method to...Ch. 31.5 - Prob. 12ECh. 31.5 - Prob. 13ECh. 31.5 - Prob. 14ECh. 31.5 - Prob. 15ECh. 31.5 - Prob. 16ECh. 31.5 - In Exercises 15–18, solve the given...Ch. 31.5 - Prob. 18ECh. 31.6 -
Find the equation of the orthogonal trajectories...Ch. 31.6 - In Exercises 1–4, make the given changes in the...Ch. 31.6 -
In Exercises 1–4, make the given changes in the...Ch. 31.6 -
In Exercises 1–4, make the given changes in the...Ch. 31.6 -
In Exercises 1–4, make the given changes in the...Ch. 31.6 -
In Exercises 5–8, find the equation of the curve...Ch. 31.6 - In Exercises 5–8, find the equation of the curve...Ch. 31.6 - In Exercises 5–8, find the equation of the curve...Ch. 31.6 - In Exercises 5–8, find the equation of the curve...Ch. 31.6 - In Exercises 9–12, find the equation of the...Ch. 31.6 - In Exercises 9–12, find the equation of the...Ch. 31.6 -
In Exercises 9–12, find the equation of the...Ch. 31.6 -
In Exercises 9–12, find the equation of the...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - Prob. 16ECh. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 -
In Exercises 13–52, solve the given problems by...Ch. 31.6 - Prob. 41ECh. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - Assuming a person expends 18 calories per pound of...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.6 - In Exercises 13–52, solve the given problems by...Ch. 31.7 - Solve the differential equation
.
Ch. 31.7 - Prob. 1ECh. 31.7 - Prob. 2ECh. 31.7 -
In Exercises 3–26, solve the given differential...Ch. 31.7 - Prob. 4ECh. 31.7 -
In Exercises 3–26, solve the given differential...Ch. 31.7 - Prob. 6ECh. 31.7 - Prob. 7ECh. 31.7 - Prob. 8ECh. 31.7 - Prob. 9ECh. 31.7 - Prob. 10ECh. 31.7 - In Exercises 3–26, solve the given differential...Ch. 31.7 - Prob. 12ECh. 31.7 - Prob. 13ECh. 31.7 - Prob. 14ECh. 31.7 - Prob. 15ECh. 31.7 - Prob. 16ECh. 31.7 - Prob. 17ECh. 31.7 - Prob. 18ECh. 31.7 - Prob. 19ECh. 31.7 - Prob. 20ECh. 31.7 - Prob. 21ECh. 31.7 - Prob. 22ECh. 31.7 - In Exercises 3–26, solve the given differential...Ch. 31.7 - Prob. 24ECh. 31.7 - Prob. 25ECh. 31.7 - Prob. 26ECh. 31.7 - Prob. 27ECh. 31.7 - Prob. 28ECh. 31.7 - Prob. 29ECh. 31.7 - Prob. 30ECh. 31.7 - In Exercises 31–34, solve the given third- and...Ch. 31.7 - Prob. 32ECh. 31.7 - Prob. 33ECh. 31.7 - Prob. 34ECh. 31.7 - Prob. 35ECh. 31.7 - Prob. 36ECh. 31.7 - Prob. 37ECh. 31.7 - Prob. 38ECh. 31.8 - Solve the differential equation
.
Ch. 31.8 - Prob. 2PECh. 31.8 - Prob. 1ECh. 31.8 - Prob. 2ECh. 31.8 - Prob. 3ECh. 31.8 - Prob. 4ECh. 31.8 - In Exercises 5–32, solve the given differential...Ch. 31.8 - Prob. 6ECh. 31.8 - In Exercises 5–32, solve the given differential...Ch. 31.8 - Prob. 8ECh. 31.8 - In Exercises 5–32, solve the given differential...Ch. 31.8 - Prob. 10ECh. 31.8 - Prob. 11ECh. 31.8 - Prob. 12ECh. 31.8 - Prob. 13ECh. 31.8 - Prob. 14ECh. 31.8 - Prob. 15ECh. 31.8 - Prob. 16ECh. 31.8 - Prob. 17ECh. 31.8 - Prob. 18ECh. 31.8 - In Exercises 5–32, solve the given differential...Ch. 31.8 - Prob. 20ECh. 31.8 - Prob. 21ECh. 31.8 - Prob. 22ECh. 31.8 - Prob. 23ECh. 31.8 - Prob. 24ECh. 31.8 - Prob. 25ECh. 31.8 - Prob. 26ECh. 31.8 - Prob. 27ECh. 31.8 - Prob. 28ECh. 31.8 - Prob. 29ECh. 31.8 - Prob. 30ECh. 31.8 - In Exercises 5–32, solve the given differential...Ch. 31.8 - In Exercises 5–32, solve the given differential...Ch. 31.8 - In Exercises 33–36, find the particular solutions...Ch. 31.8 - In Exercises 33–36, find the particular solutions...Ch. 31.8 - In Exercises 33–36, find the particular solutions...Ch. 31.8 - Prob. 36ECh. 31.8 - Prob. 37ECh. 31.8 - Prob. 38ECh. 31.8 - Prob. 39ECh. 31.8 - Prob. 40ECh. 31.8 - Prob. 41ECh. 31.8 - Prob. 42ECh. 31.9 - Prob. 1PECh. 31.9 - Prob. 2PECh. 31.9 - Prob. 1ECh. 31.9 - Prob. 2ECh. 31.9 - Prob. 3ECh. 31.9 - Prob. 4ECh. 31.9 - Prob. 5ECh. 31.9 - Prob. 6ECh. 31.9 - In Exercises 5–16, solve the given differential...Ch. 31.9 - In Exercises 5–16, solve the given differential...Ch. 31.9 - Prob. 9ECh. 31.9 - Prob. 10ECh. 31.9 - In Exercises 5–16, solve the given differential...Ch. 31.9 - Prob. 12ECh. 31.9 - Prob. 13ECh. 31.9 - Prob. 14ECh. 31.9 - Prob. 15ECh. 31.9 - Prob. 16ECh. 31.9 - Prob. 17ECh. 31.9 - Prob. 18ECh. 31.9 - Prob. 19ECh. 31.9 - Prob. 20ECh. 31.9 - Prob. 21ECh. 31.9 - Prob. 22ECh. 31.9 - Prob. 23ECh. 31.9 - Prob. 24ECh. 31.9 - Prob. 25ECh. 31.9 - Prob. 26ECh. 31.9 - In Exercises 17–32, solve the given differential...Ch. 31.9 - Prob. 28ECh. 31.9 - Prob. 29ECh. 31.9 - Prob. 30ECh. 31.9 - Prob. 31ECh. 31.9 - Prob. 32ECh. 31.9 - Prob. 33ECh. 31.9 - Prob. 34ECh. 31.9 - Prob. 35ECh. 31.9 - Prob. 36ECh. 31.9 - Prob. 37ECh. 31.9 - Prob. 38ECh. 31.9 - Prob. 39ECh. 31.9 - In Exercises 37–40, solve the given problems.
40....Ch. 31.10 - In Example 1, find the solution if x = 0 and Dx =...Ch. 31.10 - Prob. 1ECh. 31.10 - Prob. 2ECh. 31.10 - In Exercises 3–28, solve the given problems.
3. An...Ch. 31.10 - Prob. 4ECh. 31.10 - In Exercises 3–28, solve the given problems.
5....Ch. 31.10 - Prob. 6ECh. 31.10 - Prob. 7ECh. 31.10 - In Exercises 3–28, solve the given problems.
8. A...Ch. 31.10 - Prob. 9ECh. 31.10 - In Exercises 3–28, solve the given problems.
10....Ch. 31.10 - Prob. 11ECh. 31.10 - Prob. 12ECh. 31.10 - In Exercises 3–28, solve the given problems.
13. A...Ch. 31.10 - Prob. 14ECh. 31.10 - Prob. 15ECh. 31.10 - Prob. 16ECh. 31.10 - Prob. 17ECh. 31.10 - Prob. 18ECh. 31.10 - Prob. 19ECh. 31.10 - Prob. 20ECh. 31.10 - In Exercises 3–28, solve the given problems.
21....Ch. 31.10 - Prob. 22ECh. 31.10 - Prob. 23ECh. 31.10 - In Exercises 3–28, solve the given problems.
24....Ch. 31.10 - Prob. 25ECh. 31.10 - In Exercises 3–28, solve the given problems.
26....Ch. 31.10 - Prob. 27ECh. 31.10 - Prob. 28ECh. 31.11 - Prob. 1PECh. 31.11 - Prob. 2PECh. 31.11 - Prob. 1ECh. 31.11 - Prob. 2ECh. 31.11 - Prob. 3ECh. 31.11 - Prob. 4ECh. 31.11 - In Exercises 5–12, find the transforms of the...Ch. 31.11 - Prob. 6ECh. 31.11 - Prob. 7ECh. 31.11 - Prob. 8ECh. 31.11 - Prob. 9ECh. 31.11 - Prob. 10ECh. 31.11 - Prob. 11ECh. 31.11 - Prob. 12ECh. 31.11 - In Exercises 13–16, express the transforms of the...Ch. 31.11 - Prob. 14ECh. 31.11 - Prob. 15ECh. 31.11 - Prob. 16ECh. 31.11 - In Exercises 17–28, find the inverse transforms of...Ch. 31.11 - Prob. 18ECh. 31.11 - Prob. 19ECh. 31.11 - Prob. 20ECh. 31.11 - In Exercises 17–28, find the inverse transforms of...Ch. 31.11 - Prob. 22ECh. 31.11 - Prob. 23ECh. 31.11 - Prob. 24ECh. 31.11 - Prob. 25ECh. 31.11 - In Exercises 17–28, find the inverse transforms of...Ch. 31.11 - In Exercises 17–28, find the inverse transforms of...Ch. 31.11 - Prob. 28ECh. 31.11 - Prob. 29ECh. 31.11 - Prob. 30ECh. 31.12 - In Example 2, find the solution if
y(0) = 1 and...Ch. 31.12 - Prob. 1ECh. 31.12 - Prob. 2ECh. 31.12 - Prob. 3ECh. 31.12 - Prob. 4ECh. 31.12 - In Exercises 5–38, solve the given differential...Ch. 31.12 - Prob. 6ECh. 31.12 - In Exercises 5–38, solve the given differential...Ch. 31.12 - Prob. 8ECh. 31.12 - In Exercises 5–38, solve the given differential...Ch. 31.12 - Prob. 10ECh. 31.12 - Prob. 11ECh. 31.12 - Prob. 12ECh. 31.12 - Prob. 13ECh. 31.12 - Prob. 14ECh. 31.12 - Prob. 15ECh. 31.12 - Prob. 16ECh. 31.12 - Prob. 17ECh. 31.12 - Prob. 18ECh. 31.12 - Prob. 19ECh. 31.12 - Prob. 20ECh. 31.12 - Prob. 21ECh. 31.12 - Prob. 22ECh. 31.12 - Prob. 23ECh. 31.12 - Prob. 24ECh. 31.12 - Prob. 25ECh. 31.12 - Prob. 26ECh. 31.12 - Prob. 27ECh. 31.12 - Prob. 28ECh. 31.12 - Prob. 29ECh. 31.12 - Prob. 30ECh. 31.12 - Prob. 31ECh. 31.12 - In Exercises 5–38, solve the given differential...Ch. 31.12 - Prob. 33ECh. 31.12 - Prob. 34ECh. 31.12 - In Exercises 5–38, solve the given differential...Ch. 31.12 - In Exercises 5–38, solve the given differential...Ch. 31.12 - Prob. 37ECh. 31.12 - Prob. 38ECh. 31 - Prob. 1RECh. 31 - Prob. 2RECh. 31 - Prob. 3RECh. 31 - Prob. 4RECh. 31 - Prob. 5RECh. 31 - Prob. 6RECh. 31 - Prob. 7RECh. 31 - Prob. 8RECh. 31 - Prob. 9RECh. 31 - Prob. 10RECh. 31 - Prob. 11RECh. 31 - Prob. 12RECh. 31 - Prob. 13RECh. 31 - Prob. 14RECh. 31 - Prob. 15RECh. 31 - Prob. 16RECh. 31 - Prob. 17RECh. 31 - Prob. 18RECh. 31 - Prob. 19RECh. 31 - Prob. 20RECh. 31 - Prob. 21RECh. 31 - Prob. 22RECh. 31 - Prob. 23RECh. 31 - Prob. 24RECh. 31 - Prob. 25RECh. 31 - Prob. 26RECh. 31 - Prob. 27RECh. 31 - Prob. 28RECh. 31 - Prob. 29RECh. 31 - Prob. 30RECh. 31 - Prob. 31RECh. 31 - Prob. 32RECh. 31 - Prob. 33RECh. 31 - Prob. 34RECh. 31 - Prob. 35RECh. 31 - Prob. 36RECh. 31 - Prob. 37RECh. 31 - Prob. 38RECh. 31 - Prob. 39RECh. 31 - Prob. 40RECh. 31 - Prob. 41RECh. 31 - Prob. 42RECh. 31 - Prob. 43RECh. 31 - Prob. 44RECh. 31 - Prob. 45RECh. 31 - Prob. 46RECh. 31 - In Exercises 41–48, find the indicated particular...Ch. 31 - Prob. 48RECh. 31 - Prob. 49RECh. 31 - Prob. 50RECh. 31 - Prob. 51RECh. 31 - Prob. 52RECh. 31 - Prob. 53RECh. 31 - Prob. 54RECh. 31 - Prob. 55RECh. 31 - Prob. 56RECh. 31 - Prob. 57RECh. 31 - Prob. 58RECh. 31 - Prob. 59RECh. 31 - Prob. 60RECh. 31 - Prob. 61RECh. 31 - Prob. 62RECh. 31 - Prob. 63RECh. 31 - Prob. 64RECh. 31 - Prob. 65RECh. 31 - Prob. 66RECh. 31 - Prob. 67RECh. 31 - Prob. 68RECh. 31 - Prob. 69RECh. 31 - Prob. 70RECh. 31 - Prob. 71RECh. 31 - Prob. 72RECh. 31 - Prob. 73RECh. 31 - Prob. 74RECh. 31 - Prob. 75RECh. 31 - Prob. 76RECh. 31 - Prob. 77RECh. 31 - Prob. 78RECh. 31 - Prob. 79RECh. 31 - Prob. 80RECh. 31 - Prob. 81RECh. 31 - Prob. 82RECh. 31 - Prob. 83RECh. 31 - Prob. 84RECh. 31 - Prob. 85RECh. 31 - Prob. 86RECh. 31 - Prob. 87RECh. 31 - Prob. 88RECh. 31 - Prob. 89RECh. 31 - Prob. 90RECh. 31 - Prob. 91RECh. 31 - Prob. 92RECh. 31 - Prob. 93RECh. 31 - Prob. 94RECh. 31 - Prob. 95RECh. 31 - Prob. 96RECh. 31 - Prob. 97RECh. 31 - Prob. 98RECh. 31 - Prob. 99RECh. 31 - Prob. 100RECh. 31 - Prob. 101RECh. 31 - Prob. 102RECh. 31 - An electric circuit contains an inductor L, a...Ch. 31 - Prob. 1PTCh. 31 - Prob. 2PTCh. 31 - In Problems 1–6, find the general solution of each...Ch. 31 - Prob. 4PTCh. 31 - Prob. 5PTCh. 31 - Prob. 6PTCh. 31 - Prob. 7PTCh. 31 - Prob. 8PTCh. 31 - Prob. 9PTCh. 31 - Prob. 10PTCh. 31 - Prob. 11PTCh. 31 - Prob. 12PT
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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?arrow_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardWe 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_forward
- 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…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_forward3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forward
- The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward3. Consider the polynomial equation 6-iz+7z2-iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forwardWrite the equation of the trigonometric function shown in the graph. LO 5 4 3 2 1 y -5 -5 4 8 8 500 -1 -2 -3 -4 -5 x 5 15л 5л 25л 15л 35π 5л 4 8 2 8 4 8arrow_forward
- c) Using only Laplace transforms solve the following Samuelson model given below i.e., the second order difference equation (where yt is national income): - Yt+2 6yt+1+5y₁ = 0, if y₁ = 0 for t < 0, and y₁ = 0, y₁ = 1 1-e-s You may use without proof that L-1[s(1-re-s)] = f(t) = r² for n ≤tarrow_forward5. 156 m/WXY = 59° 63 E 7. B E 101 C mFE = 6. 68° 8. C 17arrow_forwardScoring: MATH 15 FILING /10 COMPARISON /10 RULER I 13 Express EMPLOYMENT PROFESSIONALS NAME: SKILLS EVALUATION TEST- Light Industrial MATH-Solve the following problems. (Feel free to use a calculator.) DATE: 1. If you were asked to load 225 boxes onto a truck, and the boxes are crated, with each crate containing nine boxes, how many crates would you need to load? 2. Imagine you live only one mile from work and you decide to walk. If you walk four miles per hour, how long will it take you to walk one mile? 3. Add 3 feet 6 inches + 8 feet 2 inches + 4 inches + 2 feet 5 inches. 4. In a grocery store, steak costs $3.85 per pound. If you buy a three-pound steak and pay for it with a $20 bill, how much change will you get? 5. Add 8 minutes 32 seconds + 37 minutes 18 seconds + 15 seconds. FILING - In the space provided, write the number of the file cabinet where the company should be filed. Example: File Cabinet #4 Elson Co. File Cabinets: 1. Aa-Bb 3. Cg-Dz 5. Ga-Hz 7. La-Md 9. Na-Oz 2. Bc-Cf…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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