Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 10, Problem 6CR
To determine
The two formula to calculate the maturity value of the loan.
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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 10 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 10.I - Find the amount of interest on each of the...Ch. 10.I - Joe Hale goes to a credit union and borrows...Ch. 10.I - Prob. 3TIECh. 10.I - Prob. 4TIECh. 10.I - a. A loan was made on April 4 and had a due date...Ch. 10.I - a. What is the maturity date of a loan taken out...Ch. 10.I - Prob. 1RECh. 10.I - Prob. 2RECh. 10.I - Prob. 3RECh. 10.I - Prob. 4RE
Ch. 10.I - Principal Rate (%) Time Interest...Ch. 10.I - Prob. 6RECh. 10.I - Prob. 7RECh. 10.I - Use the exact interest method (365 days) and the...Ch. 10.I - Prob. 9RECh. 10.I - Prob. 10RECh. 10.I - Prob. 11RECh. 10.I - Prob. 12RECh. 10.I - Prob. 13RECh. 10.I - Use the exact interest method (365 days) and the...Ch. 10.I - Prob. 15RECh. 10.I - Prob. 16RECh. 10.I - Find the amount of interest and the maturity value...Ch. 10.I - Find the amount of interest and the maturity value...Ch. 10.I - Prob. 19RECh. 10.I - Prob. 20RECh. 10.I - Find the amount of interest and the maturity value...Ch. 10.I - Prob. 22RECh. 10.I - Prob. 23RECh. 10.I - Prob. 24RECh. 10.I - Prob. 25RECh. 10.I - Find the maturity value of the following loans....Ch. 10.I - Prob. 27RECh. 10.I - Find the maturity value of the following loans....Ch. 10.I - Prob. 29RECh. 10.I - Prob. 30RECh. 10.I - Prob. 31RECh. 10.I - Prob. 32RECh. 10.I - Prob. 33RECh. 10.I - Prob. 34RECh. 10.I - From the following information, determine the...Ch. 10.I - Prob. 36RECh. 10.I - Prob. 37RECh. 10.I - From the following information, determine the...Ch. 10.I - Prob. 39RECh. 10.I - Prob. 40RECh. 10.I - Prob. 41RECh. 10.I - Solve the following word problems. Round to the...Ch. 10.I - 43. What is the maturity value of a $60,000 loan...Ch. 10.I - 44. Central Auto Parts borrowed $350,000 at ...Ch. 10.I - 45. Emil Benson missed an income tax payment of...Ch. 10.I - 46. At the City National Credit Union, a , $8,000...Ch. 10.I - 47. Kyle Rohrs borrowed $1,080 on June 16 at ...Ch. 10.II - Telex Electronics borrowed money at 9% interest...Ch. 10.II - Prob. 8TIECh. 10.II - Prob. 9TIECh. 10.II - Rita Peterson borrowed $15,000 at 12% ordinary...Ch. 10.II - Prob. 1RECh. 10.II - Compute the principal for the following loans. Use...Ch. 10.II - Prob. 3RECh. 10.II - Prob. 4RECh. 10.II - Prob. 5RECh. 10.II - Prob. 6RECh. 10.II - Prob. 7RECh. 10.II - Prob. 8RECh. 10.II - Prob. 9RECh. 10.II - Prob. 10RECh. 10.II - Prob. 11RECh. 10.II - Prob. 12RECh. 10.II - Prob. 13RECh. 10.II - Prob. 14RECh. 10.II - Prob. 15RECh. 10.II - Prob. 16RECh. 10.II - Prob. 17RECh. 10.II - Prob. 18RECh. 10.II - Use the ordinary interest method to compute the...Ch. 10.II - Use the ordinary interest method to compute the...Ch. 10.II - Prob. 21RECh. 10.II - Prob. 22RECh. 10.II - Calculate the missing information for the...Ch. 10.II - Prob. 24RECh. 10.II - Prob. 25RECh. 10.II - Calculate the missing information for the...Ch. 10.II - Solve the following word problems. Round answers...Ch. 10.II - Solve the following word problems. Round answers...Ch. 10.II - Solve the following word problems. Round answers...Ch. 10.II - Solve the following word problems. Round answers...Ch. 10.II - Prob. 31RECh. 10.II - Solve the following word problems. Round answers...Ch. 10.II - Prob. 33RECh. 10.II - 34. Steve Perry borrowed $10,000 at ordinary...Ch. 10.II - Prob. 35RECh. 10.II - 36. The Mutt Hut Pet Shop borrowed $60,000 on...Ch. 10.II - Prob. 37RECh. 10.III - Erin Lang signed a $20,000 simple discount...Ch. 10.III - What is the effective interest rate of a simple...Ch. 10.III - Legacy Lumber received a $35,000 promissory note...Ch. 10.III - Bob Schuller purchased $10,000 in U.S. Treasury...Ch. 10.III - Calculate the bank discount and proceeds for the...Ch. 10.III - Calculate the bank discount and proceeds for the...Ch. 10.III - Prob. 3RECh. 10.III - Calculate the bank discount and proceeds for the...Ch. 10.III - Prob. 5RECh. 10.III - Prob. 6RECh. 10.III - Prob. 7RECh. 10.III - Prob. 8RECh. 10.III - Using ordinary interest, 360 days, calculate the...Ch. 10.III - Prob. 10RECh. 10.III - Using ordinary interest, 360 days, calculate the...Ch. 10.III - Prob. 12RECh. 10.III - Using ordinary interest, 360 days, calculate the...Ch. 10.III - Prob. 14RECh. 10.III - Prob. 15RECh. 10.III - The following interest-bearing promissory notes...Ch. 10.III - The following interest-bearing promissory notes...Ch. 10.III - Prob. 18RECh. 10.III - The following interest-bearing promissory notes...Ch. 10.III - Prob. 20RECh. 10.III - Prob. 21RECh. 10.III - Calculate the interest, purchase price, and...Ch. 10.III - Calculate the interest, purchase price, and...Ch. 10.III - Prob. 24RECh. 10.III - Prob. 25RECh. 10.III - Use the ordinary interest method, 360 days, to...Ch. 10.III - Boz Foster signed a $10.000 simple discount...Ch. 10.III - Prob. 28RECh. 10.III - Prob. 29RECh. 10 - 1. The price or rental fee charged by a lender to...Ch. 10 - List the three factors that determine the amount...Ch. 10 - Prob. 3CRCh. 10 - The interest calculation method that uses 365 days...Ch. 10 - 5. The interest calculation method that uses 360...Ch. 10 - Prob. 6CRCh. 10 - Prob. 7CRCh. 10 - Prob. 8CRCh. 10 - Prob. 9CRCh. 10 - Prob. 10CRCh. 10 - The amount of money that the borrower receives at...Ch. 10 - 12. The actual interest rate charged on a...Ch. 10 - Prob. 13CRCh. 10 - Prob. 14CRCh. 10 - Prob. 1ATCh. 10 - Prob. 2ATCh. 10 - Prob. 3ATCh. 10 - Prob. 4ATCh. 10 - Prob. 5ATCh. 10 - What is the maturity value of the following loans?...Ch. 10 - Prob. 7ATCh. 10 - Prob. 8ATCh. 10 - Prob. 9ATCh. 10 - Prob. 10ATCh. 10 - Prob. 11ATCh. 10 - Prob. 12ATCh. 10 - Prob. 13ATCh. 10 - Prob. 14ATCh. 10 - Prob. 15ATCh. 10 - Prob. 16ATCh. 10 - Prob. 17ATCh. 10 - Prob. 18ATCh. 10 - Calculate the missing information for the...Ch. 10 - Prob. 20ATCh. 10 - Prob. 21ATCh. 10 - Prob. 22ATCh. 10 - Prob. 23ATCh. 10 - Prob. 24ATCh. 10 - Prob. 25ATCh. 10 - Prob. 26ATCh. 10 - Calculate the interest, purchase price, and...Ch. 10 - Solve the following word problems. Round to the...Ch. 10 - 29. Ronald Brown missed an income tax payment of...Ch. 10 - 30. Katie Chalmers borrowed money from her credit...Ch. 10 - 31. Ryan Roberts took out a loan for $5.880 at the...Ch. 10 - 32. Alicia Eastman deposited $2,000 in a savings...Ch. 10 - 33. Laurie Carron borrowed $16,000 at 14% ordinary...Ch. 10 - 34. Euromart Tile Company borrowed $40,000 on...Ch. 10 - Brandi Lee signed a $30,000 simple discount...Ch. 10 - Varsity Press, a publisher of college textbooks,...Ch. 10 - 37. Fernando Rodriguez purchased $64,000 in U.S....
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