Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 12, Problem 30AT
To determine
To calculate: The amount of sinking fund payment where payment frequency is
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Students have asked these similar questions
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.)
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?
The Course Name Real Analysis please Solve questions by Real Analysis
Chapter 12 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 12.I - Freeport Bank is paying 8% interest compounded...Ch. 12.I - Vista Savings Loan is paying 6% interest...Ch. 12.I - Katrina Byrd invested $250 at the end of every...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...
Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Use Table 12-1 to calculate the future value of...Ch. 12.I - Solve the following exercises by using Table 12-1....Ch. 12.I - Solve the following exercises by using Table 12-1....Ch. 12.I - Solve the following exercises by using Table...Ch. 12.I - Solve the following exercises by using Table 12-1....Ch. 12.I - Solve the following exercises by using Table...Ch. 12.I - Solve the following exercises by using formulas....Ch. 12.I - Solve the following exercises by using...Ch. 12.I - Solve the following exercises by using formulas....Ch. 12.I - Annuities Due Annuity Payment Time Nominal...Ch. 12.I - Annuities...Ch. 12.I - Annuities Due Annuity Payment Time Nominal...Ch. 12.I - To establish a "rainy day" cash reserve account....Ch. 12.I - 23. As a part of his retirement planning strategy....Ch. 12.I - Hi-Tech Hardware has been in business for a few...Ch. 12.II - Prob. 4TIECh. 12.II - Prob. 5TIECh. 12.II - Prob. 6TIECh. 12.II - Use Table 12-2 to calculate the present value of...Ch. 12.II - Prob. 2RECh. 12.II - Prob. 3RECh. 12.II - Prob. 4RECh. 12.II - Prob. 5RECh. 12.II - Prob. 6RECh. 12.II - Prob. 7RECh. 12.II - Prob. 8RECh. 12.II - Prob. 9RECh. 12.II - Prob. 10RECh. 12.II - Prob. 11RECh. 12.II - Solve the following exercises by using Table...Ch. 12.II - Solve the following exercises by using Table 12-2....Ch. 12.II - Prob. 14RECh. 12.II - Solve the following exercises by using Table...Ch. 12.II - Solve the following exercises by using Table...Ch. 12.II - Prob. 17RECh. 12.II - Prob. 18RECh. 12.II - Prob. 19RECh. 12.II - Prob. 20RECh. 12.II - Prob. 21RECh. 12.II - Prob. 22RECh. 12.II - As part of an inheritance. Joan Townsend will...Ch. 12.II - Norm Legend has been awarded a scholarship from...Ch. 12.III - Prob. 7TIECh. 12.III - Prob. 8TIECh. 12.III - Prob. 9TIECh. 12.III - Apex Manufacturing recently purchased a new...Ch. 12.III - Prob. 1RECh. 12.III - Prob. 2RECh. 12.III - Prob. 3RECh. 12.III - Prob. 4RECh. 12.III - Prob. 5RECh. 12.III - Prob. 6RECh. 12.III - You have just been hired as a loan officer at the...Ch. 12.III - Prob. 8RECh. 12.III - Prob. 9RECh. 12.III - Loan Payment Term of Nominal Present...Ch. 12.III - Prob. 11RECh. 12.III - Solve the following exercises by using tables.
12....Ch. 12.III - Solve the following exercises by using tables.
13....Ch. 12.III - Solve the following exercises by using tables....Ch. 12.III - Solve the following exercises by using tables.
15....Ch. 12.III - Solve the following exercises by using the sinking...Ch. 12.III - Prob. 17RECh. 12.III - Prob. 18RECh. 12.III - Prob. 19RECh. 12.III - Prob. 20RECh. 12.III - Prob. 21RECh. 12.III - Prob. 22RECh. 12.III - Randy Scott purchased a motorcycle for $8,500 with...Ch. 12.III - Prob. 24RECh. 12.III - Prob. 25RECh. 12 - Payment or receipt of equal amounts of money per...Ch. 12 - Prob. 2CRCh. 12 - Prob. 3CRCh. 12 - Prob. 4CRCh. 12 - Prob. 5CRCh. 12 - The table factor for an annuity due is found by...Ch. 12 - 7. Write the formula for calculating the future...Ch. 12 - Prob. 8CRCh. 12 - Prob. 9CRCh. 12 - Prob. 10CRCh. 12 - 11. A(n) ____ fund is an account used to set aside...Ch. 12 - Prob. 12CRCh. 12 - Prob. 13CRCh. 12 - Prob. 14CRCh. 12 - Prob. 1ATCh. 12 - Prob. 2ATCh. 12 - Prob. 3ATCh. 12 - Prob. 4ATCh. 12 - Prob. 5ATCh. 12 - Prob. 6ATCh. 12 - Prob. 7ATCh. 12 - Use Table 12-2 to calculate the present value of...Ch. 12 - Prob. 9ATCh. 12 - Use Table 12-1 to calculate the amount of the...Ch. 12 - Prob. 11ATCh. 12 - Prob. 12ATCh. 12 - Prob. 13ATCh. 12 - Prob. 14ATCh. 12 - Prob. 15ATCh. 12 - Prob. 16ATCh. 12 - Solve the following exercises by using tables.
17....Ch. 12 - Prob. 18ATCh. 12 - Prob. 19ATCh. 12 - Solve the following exercises by using tables....Ch. 12 - Solve the following exercises by using formulas....Ch. 12 - Prob. 22ATCh. 12 - Prob. 23ATCh. 12 - Prob. 24ATCh. 12 - Prob. 25ATCh. 12 - Prob. 26ATCh. 12 - Prob. 27ATCh. 12 - Prob. 28ATCh. 12 - Prob. 29ATCh. 12 - Prob. 30ATCh. 12 - Prob. 31ATCh. 12 - Prob. 32ATCh. 12 - Prob. 33ATCh. 12 - Prob. 34ATCh. 12 - Prob. 35AT
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- 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? 2arrow_forwardQuestion 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_forward
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