
Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 9, Problem 8AT
To determine
To calculate: Each counter employee’s total gross earnings for the week if Foremost fish market pays a straight commission of
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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…
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Chapter 9 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 9.I - An executive of a large manufacturing company...Ch. 9.I - Rick Morton works as a delivery truck driver for...Ch. 9.I - George Lopez works at a tire manufacturing plant....Ch. 9.I - You are the payroll manager for Trendy Toys, Inc.,...Ch. 9.I - Alexa Walsh sells for Supreme Designs, a...Ch. 9.I - Mike Lamb sells copiers for Royal Business...Ch. 9.I - Ed Diamond is a sales representative for Jersey...Ch. 9.I - Howard Lockwood sells for Catalina Designs, Inc....Ch. 9.I - Calculate the gross earnings per pay period for...Ch. 9.I - Calculate the gross earnings per day period for...
Ch. 9.I - Calculate the gross earnings per pay period for...Ch. 9.I - Calculate the gross earnings per day period for...Ch. 9.I - Prob. 5RECh. 9.I - Calculate the gross earnings per pay period for...Ch. 9.I - Prob. 7RECh. 9.I - Mary Jo Prenaris is an office manager with gross...Ch. 9.I - 9. Deb O’Connell is an accounting professional...Ch. 9.I - 10. Jennifer Brunner works 40 hours per week as a...Ch. 9.I - 11. Alan Kimball earns $22.34 per hour as a...Ch. 9.I - 12. Paul Curcio earns $8.25 per hour for regular...Ch. 9.I - Prob. 13RECh. 9.I - As the payroll manager for Stargate Industries,...Ch. 9.I - Prob. 15RECh. 9.I - As the payroll manager for Stargate Industries,...Ch. 9.I - Prob. 17RECh. 9.I - Calculate last week’s total gross pay for each of...Ch. 9.I - Prob. 19RECh. 9.I - Prob. 20RECh. 9.I - 21. Katrina Byrd assembles motor mounts for C-207...Ch. 9.I - 22. Bob Farrell works for a company that...Ch. 9.I - 23. What is the total gross pay for a salesperson...Ch. 9.I - Pamela Mello is paid on an incremental commission...Ch. 9.I - Dory Schrader is a buyer for Oceans of Notions....Ch. 9.I - Thomas Rendells company pays him a straight 6%...Ch. 9.I - 27. Katie Jergens works for Dynamic Designs...Ch. 9.I - 28. Jerry King is a server in a restaurant that...Ch. 9.II - What are the withholdings for social security and...Ch. 9.II - Rick Nicotera has year-to-date earnings of...Ch. 9.II - Jan McMillan is married, claims five exemptions,...Ch. 9.II - Using the combined wage bracket tables, what is...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - Use the percentage method of income tax...Ch. 9.II - Use the percentage method of income tax...Ch. 9.II - Prob. 11RECh. 9.II - Use the percentage method of income tax...Ch. 9.II - Use the combined wage bracket tables, Exhibits 9-3...Ch. 9.II - Use the combined wage bracket tables, Exhibits 9-3...Ch. 9.II - Use the combined wage bracket tables, Exhibits 9-3...Ch. 9.II - Marital Withholding Gross Combined Employee Status...Ch. 9.II - Prob. 17RECh. 9.II - ...Ch. 9.II - Marital Withholding Gross Combined Employee Status...Ch. 9.III - Big Pine Tree Service has 18 employees, 12 with...Ch. 9.III - Les Roberts, a self-employed commercial artist,...Ch. 9.III - Prob. 15TIECh. 9.III - Prob. 16TIECh. 9.III - Prob. 17TIECh. 9.III - Prob. 1RECh. 9.III - Prob. 2RECh. 9.III - 3. Arrow Asphalt & Paving Company has 24...Ch. 9.III - What are the social security and Medicare taxes...Ch. 9.III - 5. What are the social security and Medicare taxes...Ch. 9.III - Lee Sutherlin is a self-employed electrical...Ch. 9.III - Prob. 7RECh. 9.III - Prob. 8RECh. 9.III - Prob. 9RECh. 9.III - 10. Amazon Appliance Company has three installers....Ch. 9.III - Jiffy Janitorial Service employs 48 workers and...Ch. 9.III - North Beach Limousine Service employs 166 workers...Ch. 9.III - Marc Batchelor, a self-employed sales consultant,...Ch. 9 - Gross pay is the amount of earnings before payroll...Ch. 9 - 2. Annual salaries are commonly prorated to be...Ch. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - 6. A draw against commission is commission paid in...Ch. 9 - Prob. 7CRCh. 9 - Prob. 8CRCh. 9 - In addition to social security and Medicare tax...Ch. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - A plan whereby employees are given a menu of...Ch. 9 - Prob. 14CRCh. 9 - 1. Bill Pearson earns $2,800 semimonthly as a...Ch. 9 - 2. Barbara Sultan works 40 hours per week as a...Ch. 9 - Eric Shotwells company pays him $18.92 per hour...Ch. 9 - 4. Mitch Anderson is a security guard. He earns...Ch. 9 - 5. Fergie Nelson assembles toasters for the Gold...Ch. 9 - Prob. 6ATCh. 9 - Calculate the gross earnings for the following...Ch. 9 - Prob. 8ATCh. 9 - Calculate the gross earnings for the following...Ch. 9 - Prob. 10ATCh. 9 - Calculate the gross earnings for the following...Ch. 9 - Calculate the gross earnings for the following...Ch. 9 - Solve the following problems using 6.2% up to...Ch. 9 - Solve the following problems using 6.2% up to...Ch. 9 - Use the percentage method to solve the...Ch. 9 - Use the combined wage bracket tables. Exhibits 9-3...Ch. 9 - Use the combined wage bracket tables. Exhibits 9-3...Ch. 9 - Prob. 18ATCh. 9 - Prob. 19ATCh. 9 - 20. Paul Warren is a self-employed mechanic. Last...Ch. 9 - Tim Ries earns $48,320 annually as a supervisor...Ch. 9 - 22. Universal Exporting has three warehouse...Ch. 9 - Sky High Crane Company employs 150 workers and has...Ch. 9 - 24. Ransford Alda is a self-employed security...
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