Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 10.III, Problem 12RE
To determine
To calculate: The amount of bank discount, proceeds value and effective rate of interest where face value is
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Students have asked these similar questions
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?
2
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…
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 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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