Practical Business Math Procedures with Business Math Handbook
12th Edition
ISBN: 9781259725067
Author: Jeffrey Slater, Sharon M. Wittry
Publisher: McGraw-Hill Education
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Chapter 9.1, Problem 2AH
a.
To determine
The total hours, regular pay, overtime pay, and gross pay of Adams.
b.
To determine
The total hours, regular pay, overtime pay, and gross pay of Card.
c.
To determine
The total hours, regular pay, overtime pay, and gross pay of Kline.
d.
To determine
The total hours, regular pay, overtime pay, and gross pay of Mack.
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Construct a know-show table for each statement below that appears to be true.
Problem 3. Pricing a multi-stock option the Margrabe formula
The purpose of this problem is to price a swap option in a 2-stock model, similarly as
what we did in the example in the lectures. We consider a two-dimensional Brownian
motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices
are modeled by the following equations:
dX
=
dY₁ =
X₁ (rdt+
rdt+0₁dW!)
(²)),
Y₁ (rdt+dW+0zdW!"),
with Xo
xo and Yo =yo. This corresponds to the multi-stock model studied in class,
but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure
P is already the risk-neutral measure (Both stocks have rate of return r). We write
σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to
exchange one share of X for one share of Y. That is, the option has payoff
F=(Yr-XT).
(a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for
the process Xt.
Reminder before proceeding to question (b): Girsanov's theorem…
Problem 1. Multi-stock model
We consider a 2-stock model similar to the one studied in class. Namely, we consider
=
S(1)
S(2)
=
S(¹) exp (σ1B(1) + (M1 - 0/1 )
S(²) exp (02B(2) + (H₂-
M2
where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with
t≥0
Cov (B(¹), B(2)) = p min{t, s}.
"
The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian
motion (W+)+20 (W(1), W(2))+20 such that
=
S(1)
S(2)
=
=
S(¹) exp (011W(¹) + (μ₁ - 01/1) t)
롱)
S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t).
where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p).
Hint: The constants will follow the formulas developed in the lectures.
(a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2)
functions of (B(1), B(²)).
as
(b) Using the formulas obtained in (a), show that the process (WA) is actually a 2-
dimensional standard Brownian motion (i.e. show that each component is normal,
with mean 0, variance t, and that their…
Chapter 9 Solutions
Practical Business Math Procedures with Business Math Handbook
Ch. 9.1 - Jill Foster worked 52 hours in one week for Delta...Ch. 9.1 - Matt Long had $180,000 in sales for the month....Ch. 9.1 - Bob Meyers receives a $1,000 monthly salary. He...Ch. 9.1 - Jill Foster worked 54 hours in one week for Delta...Ch. 9.1 - Matt Long had $210,000 in sales for the month....Ch. 9.1 - Bob Myers receives a $1,200 monthly salary. He...Ch. 9.1 - Fill in the missing amounts for each of the...Ch. 9.1 - Prob. 2AHCh. 9.1 - Calculate the gross wages of the following...Ch. 9.1 - Using the given differential scale, calculate the...
Ch. 9.1 - Calculate the following salespersons’ gross...Ch. 9.1 - Prob. 6AHCh. 9.1 - Prob. 7AHCh. 9.1 - Prob. 8AHCh. 9.1 - Prob. 9AHCh. 9.1 - Prob. 10AHCh. 9.1 - Prob. 11AHCh. 9.1 - Prob. 12AHCh. 9.2 - Calculate Social Security taxes, Medicare taxes,...Ch. 9.2 - Prob. 2PQCh. 9.2 - Prob. 1EPQCh. 9.2 - Jim Brewer, owner of Arrow Company, has three...Ch. 9.2 - Prob. 1AHCh. 9.2 - Prob. 2AHCh. 9.2 - Prob. 3AHCh. 9.2 - Prob. 4AHCh. 9.2 - Prob. 5AHCh. 9.2 - Prob. 6AHCh. 9.2 - Prob. 7AHCh. 9.2 - If Cynthia (Problem 7) earns $1,050 the following...Ch. 9.2 - Prob. 9AHCh. 9.2 - Nicole Mariotte is unmarried and claimed one...Ch. 9.2 - Gerald Knowlton had total gross earnings of...Ch. 9 - Prob. 1ECPCh. 9 - Complete the following table:
Ch. 9 - Complete the following table (assume the overtime...Ch. 9 - Complete the following table (assume the overtime...Ch. 9 - Calculate gross earnings:
Ch. 9 - Calculate gross earnings:
Ch. 9 - Calculate the gross earnings for each apple picker...Ch. 9 - Calculate the gross earnings for each apple picker...Ch. 9 - Calculate the end-of-month commission.
Ch. 9 - Ron Company has the following commission...Ch. 9 - Ron Company has the following commission...Ch. 9 - Complete the following table, given that A...Ch. 9 - Complete the following table, given that A...Ch. 9 - Calculate the Social Security and Medicare...Ch. 9 - Calculate the Social Security and Medicare...Ch. 9 - Calculate the Social Security and Medicare...Ch. 9 - Complete the following payroll register. Calculate...Ch. 9 - Complete the following payroll register. Calculate...Ch. 9 - Given the following, calculate the state (assume...Ch. 9 - Lai Xiaodong, a 22-year-old college-educated man,...Ch. 9 - Rhonda Brennan found her first job after...Ch. 9 - The Social Security Administration increased the...Ch. 9 - Calculate Social Security taxes, Medicare taxes,...Ch. 9 - Maggie Vitteta, single, works 38 hours per week at...Ch. 9 - Robin Hartman earns $600 per week plus 3% of sales...Ch. 9 - Pat Maninen earns a gross salary of $3,000 each...Ch. 9 - Richard Gaziano is a manager for Health Care. Inc....Ch. 9 - Larren Bullett is concerned after receiving her...Ch. 9 - Westway Company pays Suzie Chan $3,000 per week....Ch. 9 - Sarah Jones earns $525 per week selling life...Ch. 9 - Prob. 31ECPCh. 9 - Prob. 32ECPCh. 9 - Bill Rose is a salesperson for Boxes, Inc. He...Ch. 9 - Prob. 1PTCh. 9 - Prob. 2PTCh. 9 - Prob. 3PTCh. 9 - Prob. 4PTCh. 9 - Prob. 5PTCh. 9 - Jean Michaud pays his two employees $900 and...
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