
Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Question
Chapter 9, Problem 22RE
To determine
(a)
Whether more or less than one-fifth of federal spending spent on health care.
To determine
(b)
The ratio of the fixed expenditures to the discretionary spending.
To determine
(c)
The amount of budget to be spent on fixed expenditure.
To determine
(d)
The amount of budget to be spent on Social Security.
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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?
Chapter 9 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 9.1 - Amy is 140 lb and 58 tall. Calculate Amys BMI....Ch. 9.1 - Roger is 511. How much should he weigh in order to...Ch. 9.1 - Prob. 3EECh. 9.1 - Felicia weighs 160 lb and is 57. She would like to...Ch. 9.1 - Finding BMI Using a Nomograph Most medical...Ch. 9.1 - Prob. 1ESCh. 9.1 - Prob. 2ESCh. 9.1 - Explain how to check the solution of an equation.Ch. 9.1 - Prob. 4ESCh. 9.1 - Prob. 5ES
Ch. 9.1 - Prob. 6ESCh. 9.1 - Prob. 7ESCh. 9.1 - Prob. 8ESCh. 9.1 - Solve the equation. 48=6zCh. 9.1 - Prob. 10ESCh. 9.1 - Prob. 11ESCh. 9.1 - Prob. 12ESCh. 9.1 - Solve the equation. x4=2Ch. 9.1 - Prob. 14ESCh. 9.1 - Prob. 15ESCh. 9.1 - Prob. 16ESCh. 9.1 - Solve the equation. 5x3=9x7Ch. 9.1 - Prob. 18ESCh. 9.1 - Prob. 19ESCh. 9.1 - Prob. 20ESCh. 9.1 - Prob. 21ESCh. 9.1 - Prob. 22ESCh. 9.1 - Solve the equation. 4b+15=32bCh. 9.1 - Prob. 24ESCh. 9.1 - Prob. 25ESCh. 9.1 - Prob. 26ESCh. 9.1 - Solve the equation. 5(32y)=34yCh. 9.1 - Prob. 28ESCh. 9.1 - Prob. 29ESCh. 9.1 - Prob. 30ESCh. 9.1 - Solve the equation. 4a+3=7(58a)Ch. 9.1 - Prob. 32ESCh. 9.1 - Prob. 33ESCh. 9.1 - Prob. 34ESCh. 9.1 - Solve the equation. 3(x4)=1(2x7)Ch. 9.1 - Solve the equation. 2y34=y61Ch. 9.1 - Solve the equation. x8+2=3x43Ch. 9.1 - Solve the equation. 2x33+12=56Ch. 9.1 - Solve the equation. 23+3x+14=53Ch. 9.1 - Prob. 40ESCh. 9.1 - Prob. 41ESCh. 9.1 - Car Payments The monthly car payment on a 60-month...Ch. 9.1 - Car Payments The monthly car payment on a 60-month...Ch. 9.1 - Deep-Sea Diving The pressure on a diver can be...Ch. 9.1 - Deep-Sea Diving The pressure on a diver can be...Ch. 9.1 - Prob. 46ESCh. 9.1 - Foot Races The world-record time for a 1-mile race...Ch. 9.1 - Black Ice Black ice is an ice covering on roads...Ch. 9.1 - Black Ice Black ice is a nice covering on roads...Ch. 9.1 - Crickets The formula N=7C30 approximates N, the...Ch. 9.1 - Crickets The formula N=7C30 approximates N, the...Ch. 9.1 - Prob. 52ESCh. 9.1 - Prob. 53ESCh. 9.1 - Prob. 54ESCh. 9.1 - Prob. 55ESCh. 9.1 - Write an equation as part of solving the problem....Ch. 9.1 - Prob. 57ESCh. 9.1 - Prob. 58ESCh. 9.1 - Prob. 59ESCh. 9.1 - Write an equation as part of solving the problem....Ch. 9.1 - Prob. 61ESCh. 9.1 - Write an equation as part of solving the problem....Ch. 9.1 - Write an equation as part of solving the problem....Ch. 9.1 - Prob. 64ESCh. 9.1 - Prob. 65ESCh. 9.1 - Prob. 66ESCh. 9.1 - Prob. 67ESCh. 9.1 - Prob. 68ESCh. 9.1 - Prob. 69ESCh. 9.1 - Prob. 70ESCh. 9.1 - Prob. 71ESCh. 9.1 - Solve the formula for the indicated variable....Ch. 9.1 - Prob. 73ESCh. 9.1 - Prob. 74ESCh. 9.1 - Prob. 75ESCh. 9.1 - Solve the formula for the indicated variable....Ch. 9.1 - Solve the formula for the indicated variable....Ch. 9.1 - Solve the formula for the indicated variable....Ch. 9.1 - Prob. 79ESCh. 9.1 - Prob. 80ESCh. 9.1 - Prob. 81ESCh. 9.1 - Prob. 82ESCh. 9.1 - Prob. 83ESCh. 9.1 - Prob. 84ESCh. 9.1 - Prob. 85ESCh. 9.1 - Prob. 86ESCh. 9.1 - Prob. 87ESCh. 9.1 - Prob. 88ESCh. 9.1 - Prob. 89ESCh. 9.1 - Prob. 90ESCh. 9.1 - Prob. 91ESCh. 9.1 - Prob. 92ESCh. 9.1 - Prob. 93ESCh. 9.2 - In 1979, his rookie year, Jeff Reardon pitched 21...Ch. 9.2 - Prob. 2EECh. 9.2 - In 1987, Nolan Ryan had the lowest ERA of any...Ch. 9.2 - During the 2015 season, Jake Arrieta of the...Ch. 9.2 - Prob. 5EECh. 9.2 - Prob. 1ESCh. 9.2 - Prob. 2ESCh. 9.2 - Write the expression as a unit rate. 582mi in 12hCh. 9.2 - Write the expression as a unit rate. 138mi on 6...Ch. 9.2 - Write the expression as a unit rate. 544 words...Ch. 9.2 - Write the expression as a unit rate. 100m in 8sCh. 9.2 - Write the expression as a unit rate. 9100 for 350...Ch. 9.2 - Write the expression as a unit rate. 1000 ft2 of...Ch. 9.2 - Wages A machinist earns 682.50 for working a...Ch. 9.2 - Space Vehicles The Space Shuttles solid rocket...Ch. 9.2 - Photography During filming, an IMAX camera uses...Ch. 9.2 - Consumerism Which is the more economical purchase,...Ch. 9.2 - Consumerism Which is the more economical purchase,...Ch. 9.2 - Wages You have a choice of receiving a wage of...Ch. 9.2 - Baseball Baseball statisticians calculate a...Ch. 9.2 - Population Density The table below shows the...Ch. 9.2 - E-mail The Radicati Group compiled the following...Ch. 9.2 - Prob. 18ESCh. 9.2 - Prob. 19ESCh. 9.2 - Exchange Rates The table below shows the exchange...Ch. 9.2 - Exchange Rates The table below shows the exchange...Ch. 9.2 - Real Estate Dean Baker, co-director at the Center...Ch. 9.2 - Real Estate Dean Baker, co-director at the Center...Ch. 9.2 - Prob. 24ESCh. 9.2 - Prob. 25ESCh. 9.2 - Prob. 26ESCh. 9.2 - Solve the proportion. 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If...Ch. 9.4 - Prob. 2ESCh. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - Prob. 5ESCh. 9.4 - Prob. 6ESCh. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - Prob. 12ESCh. 9.4 - Prob. 13ESCh. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - Prob. 16ESCh. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - Prob. 18ESCh. 9.4 - First try to solve the equation by factoring. If...Ch. 9.4 - Prob. 20ESCh. 9.4 - Prob. 21ESCh. 9.4 - Prob. 22ESCh. 9.4 - Prob. 23ESCh. 9.4 - Prob. 24ESCh. 9.4 - Prob. 25ESCh. 9.4 - Prob. 26ESCh. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Prob. 28ESCh. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Prob. 32ESCh. 9.4 - Prob. 33ESCh. 9.4 - Prob. 34ESCh. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Prob. 36ESCh. 9.4 - Prob. 37ESCh. 9.4 - Prob. 38ESCh. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Round answers to nearest hundredth where...Ch. 9.4 - Prob. 41ESCh. 9.4 - Prob. 42ESCh. 9.4 - Prob. 43ESCh. 9.4 - Prob. 44ESCh. 9.4 - Prob. 45ESCh. 9.4 - Prob. 46ESCh. 9.4 - Prob. 47ESCh. 9.4 - Prob. 48ESCh. 9.4 - Prob. 49ESCh. 9.4 - Prob. 50ESCh. 9 - Solve the equation. 5x+3=10x17Ch. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Solve the formula for the given variable....Ch. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Chemistry A chemist mixes 100g of water at 80C...Ch. 9 - Telemarketing At a telemarketing firm, an employee...Ch. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Social Media In July 2012, Instagram announced 80...Ch. 9 - City Populations The table below shows the...Ch. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Gardening Three tablespoons of a liquid plant...Ch. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Diet Americans consume 7 billion hot dogs from...Ch. 9 - Boston Marathon In the 2015 Boston Marathon,...Ch. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Vacation Days In Italy, workers take an average of...Ch. 9 - Model Rockets A small rocket is shot from the edge...Ch. 9 - Prob. 32RECh. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - Energy The cost of electricity in a certain city...Ch. 9 - Prob. 10TCh. 9 - Prob. 11TCh. 9 - Prob. 12TCh. 9 - Social Media In 2015, Twitter announced that they...Ch. 9 - Prob. 14TCh. 9 - Gardening The directions on a bag of plant food...Ch. 9 - Prob. 16TCh. 9 - Prob. 17TCh. 9 - Prob. 18TCh. 9 - Compact Disc Sales In 2005, the total number of...Ch. 9 - Prob. 20T
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