EBK MATHEMATICS FOR THE TRADES
10th Edition
ISBN: 9780100803053
Author: SAUNDERS
Publisher: YUZU
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Chapter 4.3, Problem 5AE
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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.)
3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i,
and i.
(a) Verify the relations between this roots and the coefficients of the polynomial.
(b) Find the annulus region in which the roots lie.
Chapter 4 Solutions
EBK MATHEMATICS FOR THE TRADES
Ch. 4.1 - Complete the following tables.Ch. 4.1 - A. Complete the following tables. 2.Ch. 4.1 - A. Complete the following tables. 3.Ch. 4.1 - Solve these proportion equations. 32=x8Ch. 4.1 - Solve these proportion equations. 6R=572Ch. 4.1 - Solve these proportion equations. y60=53Ch. 4.1 - Solve these proportion equations. 215=8HCh. 4.1 - Solve these proportion equations. 5P=307Ch. 4.1 - Solve these proportion equations. 16=17xCh. 4.1 - Solve these proportion equations. A2.5=1310
Ch. 4.1 - Solve these proportion equations. 27M=30.8Ch. 4.1 - Solve these proportion equations. 25=T4.5Ch. 4.1 - Solve these proportion equations. 0.12N=27Ch. 4.1 - Solve these proportion equations. 13823=18xCh. 4.1 - Solve these proportion equations. 3.251.5=A0.6Ch. 4.1 - Solve these proportion equations. x34.86=1.28.3Ch. 4.1 - Solve these proportion equations. 212R=114314Ch. 4.1 - Solve these proportion equations....Ch. 4.1 - Solve these proportion equations....Ch. 4.1 - Solve these proportion equations....Ch. 4.1 - Solve these proportion equations. 312in.W=1.40.05Ch. 4.1 - Solve. Automotive Trades The compression ratio in...Ch. 4.1 - Prob. 2CECh. 4.1 - Solve. Machine Trades If 28 tapered pins can be...Ch. 4.1 - Solve. Carpentry If 6 lb of nails are needed for...Ch. 4.1 - Solve. Masonry For a certain kind of plaster work,...Ch. 4.1 - Prob. 6CECh. 4.1 - Solve. Machine Trades A cylindrical oil tank 8 ft...Ch. 4.1 - Prob. 8CECh. 4.1 - Solve. Welding A 10-ft bar of I-beam weighs 208...Ch. 4.1 - Solve. Photography A photographer must mix a...Ch. 4.1 - Solve. General Trades If you earn 684.80 for a...Ch. 4.1 - Solve. Machine Trades A machinist can produce 12...Ch. 4.1 - Solve. Automotive Trades The headlights on a car...Ch. 4.1 - Prob. 14CECh. 4.1 - Solve. Agriculture To prepare a pesticide spray,...Ch. 4.1 - Solve. Painting A painter must thin some paint for...Ch. 4.1 - Solve. Allied Health The label on a concentrated...Ch. 4.1 - Solve. Automotive Trades In winter weather,...Ch. 4.1 - Prob. 19CECh. 4.1 - Prob. 20CECh. 4.1 - Prob. 21CECh. 4.1 - Solve. Sports and Leisure Power hitter Sammy...Ch. 4.1 - Prob. 23CECh. 4.1 - Prob. 24CECh. 4.1 - Solve. Allied Health Medication Q is available...Ch. 4.1 - Prob. 26CECh. 4.1 - Prob. 27CECh. 4.1 - Prob. 28CECh. 4.1 - Prob. 29CECh. 4.1 - Prob. 30CECh. 4.1 - Solve. Trades Management A small welding shop...Ch. 4.1 - Prob. 32CECh. 4.1 - Prob. 33CECh. 4.1 - Prob. 34CECh. 4.1 - Prob. 35CECh. 4.2 - Complete the following tables. 1. Similar...Ch. 4.2 - Complete the following tables. 2. Similar figuresCh. 4.2 - Complete the following tables.Ch. 4.2 - Complete the following tables.Ch. 4.2 - Practical Applications Problem 1 Metalworking A...Ch. 4.2 - Practical Applications Architecture The...Ch. 4.2 - Practical Applications Automotive Trades...Ch. 4.2 - Practical Applications Transportation The distance...Ch. 4.2 - Prob. 5BECh. 4.2 - Practical Applications Industrial Technology If 60...Ch. 4.2 - Practical Applications Automotive Trades If the...Ch. 4.2 - Practical Applications General Trades The length...Ch. 4.2 - Practical Applications Construction The Santa...Ch. 4.2 - Practical Applications Machine Trades A pair of...Ch. 4.2 - Practical Applications Manufacturing A 15-tooth...Ch. 4.2 - Practical Applications Electronics The power gain...Ch. 4.2 - Prob. 13BECh. 4.2 - Prob. 14BECh. 4.2 - Practical Applications Automotive Trades The...Ch. 4.2 - Prob. 16BECh. 4.2 - Practical Applications Machine Trades It is known...Ch. 4.2 - Prob. 18BECh. 4.2 - Prob. 19BECh. 4.2 - Practical Applications Architecture A wrought-iron...Ch. 4.2 - Prob. 21BECh. 4.2 - Electrical Trades The electrical resistance of a...Ch. 4.2 - Prob. 23BECh. 4.2 - Practical Applications Sheet Metal Trades If the...Ch. 4.2 - Prob. 25BECh. 4.2 - Prob. 26BECh. 4.2 - Prob. 27BECh. 4.2 - Prob. 28BECh. 4.2 - Prob. 29BECh. 4.2 - Prob. 30BECh. 4.2 - Prob. 31BECh. 4.3 - Prob. 1AECh. 4.3 - Convert to a percent. 1Ch. 4.3 - Convert to a percent. 0.5Ch. 4.3 - Prob. 4AECh. 4.3 - Prob. 5AECh. 4.3 - Prob. 6AECh. 4.3 - Prob. 7AECh. 4.3 - Prob. 8AECh. 4.3 - Prob. 9AECh. 4.3 - Prob. 10AECh. 4.3 - Prob. 11AECh. 4.3 - Prob. 12AECh. 4.3 - Prob. 13AECh. 4.3 - Prob. 14AECh. 4.3 - Prob. 15AECh. 4.3 - Prob. 16AECh. 4.3 - Convert to a percent. 32Ch. 4.3 - Prob. 18AECh. 4.3 - Prob. 19AECh. 4.3 - Convert to a percent. 15Ch. 4.3 - Prob. 21AECh. 4.3 - Prob. 22AECh. 4.3 - Prob. 23AECh. 4.3 - Prob. 24AECh. 4.3 - Prob. 25AECh. 4.3 - Prob. 26AECh. 4.3 - Prob. 27AECh. 4.3 - Prob. 28AECh. 4.3 - Prob. 29AECh. 4.3 - Prob. 30AECh. 4.3 - Prob. 31AECh. 4.3 - Prob. 32AECh. 4.3 - Prob. 33AECh. 4.3 - Prob. 34AECh. 4.3 - Prob. 35AECh. 4.3 - Prob. 36AECh. 4.3 - Prob. 37AECh. 4.3 - Prob. 38AECh. 4.3 - Prob. 39AECh. 4.3 - Prob. 40AECh. 4.3 - Prob. 1BECh. 4.3 - Prob. 2BECh. 4.3 - Prob. 3BECh. 4.3 - Prob. 4BECh. 4.3 - Prob. 5BECh. 4.3 - Prob. 6BECh. 4.3 - Prob. 7BECh. 4.3 - Prob. 8BECh. 4.3 - Prob. 9BECh. 4.3 - Prob. 10BECh. 4.3 - Prob. 11BECh. 4.3 - Prob. 12BECh. 4.3 - Prob. 13BECh. 4.3 - Prob. 14BECh. 4.3 - Prob. 15BECh. 4.3 - Prob. 16BECh. 4.3 - Prob. 17BECh. 4.3 - Prob. 18BECh. 4.3 - Prob. 19BECh. 4.3 - Prob. 20BECh. 4.3 - Prob. 21BECh. 4.3 - Prob. 22BECh. 4.3 - Prob. 23BECh. 4.3 - Prob. 24BECh. 4.3 - Prob. 25BECh. 4.3 - Prob. 26BECh. 4.3 - Prob. 27BECh. 4.3 - Prob. 28BECh. 4.3 - Prob. 29BECh. 4.3 - Prob. 30BECh. 4.3 - Prob. 31BECh. 4.3 - Prob. 32BECh. 4.3 - Prob. 1CECh. 4.3 - Prob. 2CECh. 4.3 - Prob. 3CECh. 4.3 - Prob. 4CECh. 4.3 - Prob. 5CECh. 4.3 - Prob. 6CECh. 4.3 - Prob. 7CECh. 4.3 - Prob. 8CECh. 4.3 - Prob. 9CECh. 4.3 - Rewrite each percent as a fraction in lowest...Ch. 4.3 - Prob. 11CECh. 4.3 - Prob. 12CECh. 4.3 - Prob. 13CECh. 4.3 - Prob. 14CECh. 4.3 - Prob. 15CECh. 4.3 - Prob. 16CECh. 4.3 - Prob. 17CECh. 4.3 - Prob. 18CECh. 4.3 - Prob. 19CECh. 4.3 - Prob. 20CECh. 4.4 - Solve. 4 is _________ % of 5.Ch. 4.4 - Prob. 2AECh. 4.4 - Prob. 3AECh. 4.4 - Prob. 4AECh. 4.4 - Prob. 5AECh. 4.4 - Prob. 6AECh. 4.4 - Prob. 7AECh. 4.4 - Prob. 8AECh. 4.4 - Solve. What percent of 54 is 36?Ch. 4.4 - Prob. 10AECh. 4.4 - Prob. 11AECh. 4.4 - Solve. 13 is what percent of 25?Ch. 4.4 - Prob. 13AECh. 4.4 - Prob. 14AECh. 4.4 - Prob. 15AECh. 4.4 - Solve. 60% of what number is 14?Ch. 4.4 - Prob. 17AECh. 4.4 - Prob. 18AECh. 4.4 - Prob. 19AECh. 4.4 - Prob. 20AECh. 4.4 - Solve. 30% of what number is equal to 12?Ch. 4.4 - Prob. 22AECh. 4.4 - Prob. 23AECh. 4.4 - Prob. 24AECh. 4.4 - Prob. 1BECh. 4.4 - Solve. What percent of 10 is 2.5?Ch. 4.4 - Solve. 6% of 3.29 is _________.Ch. 4.4 - Prob. 4BECh. 4.4 - Prob. 5BECh. 4.4 - Prob. 6BECh. 4.4 - Prob. 7BECh. 4.4 - Solve. 0.75 is _________ % of 37.50.Ch. 4.4 - Prob. 9BECh. 4.4 - Prob. 10BECh. 4.4 - Prob. 11BECh. 4.4 - Prob. 12BECh. 4.4 - Prob. 13BECh. 4.4 - Prob. 14BECh. 4.4 - Prob. 15BECh. 4.4 - Prob. 16BECh. 4.4 - Prob. 17BECh. 4.4 - Prob. 18BECh. 4.4 - Prob. 1CECh. 4.4 - Prob. 2CECh. 4.4 - Prob. 3CECh. 4.4 - Practical Applications Masonry On the basis of...Ch. 4.4 - Practical Applications Automotive Trades The...Ch. 4.4 - Prob. 6CECh. 4.4 - Practical Applications General Trades A worker...Ch. 4.4 - Prob. 8CECh. 4.4 - Prob. 9CECh. 4.4 - Prob. 10CECh. 4.4 - Practical Applications Carpentry Preparing an...Ch. 4.4 - Practical Applications Printing Jiffy Print needs...Ch. 4.4 - Prob. 13CECh. 4.4 - Prob. 14CECh. 4.4 - Prob. 15CECh. 4.4 - Prob. 16CECh. 4.4 - Construction Quality Homes Construction Company...Ch. 4.4 - Prob. 18CECh. 4.4 - Practical Applications Allied Health A typical...Ch. 4.4 - Prob. 20CECh. 4.4 - Prob. 21CECh. 4.4 - Prob. 22CECh. 4.4 - Sports and Leisure During the 2012 Wimbledon...Ch. 4.4 - Prob. 24CECh. 4.4 - Prob. 25CECh. 4.4 - Prob. 26CECh. 4.4 - Prob. 27CECh. 4.4 - Prob. 28CECh. 4.4 - Practical Applications Welding The allowable shear...Ch. 4.4 - Practical Applications Water/Wastewater Treatment...Ch. 4.4 - Prob. 31CECh. 4.4 - Prob. 32CECh. 4.4 - Prob. 33CECh. 4.4 - Prob. 34CECh. 4.4 - Prob. 35CECh. 4.4 - Prob. 36CECh. 4.4 - Allied Health A pharmaceutical sales...Ch. 4.4 - Prob. 38CECh. 4.4 - Prob. 39CECh. 4.5 - Electronics A CB radio is rated at 7.5 watts, and...Ch. 4.5 - Prob. 2ECh. 4.5 - Electrical Trades An engine supplies 110 hp to an...Ch. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Life Skills If you earn 12% commission on sales of...Ch. 4.5 - Metalworking On a cutting operation, 2 sq ft of...Ch. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Manufacturing A small gasoline shop engine...Ch. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Trades Management A welding shop charges the...Ch. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Interior Design An interior designer working for a...Ch. 4.5 - Retail Merchandising A one-terabyte external hard...Ch. 4.5 - Trades Management Chris paid for the initial...Ch. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Automotive Trades A new tire had a tread depth of...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Machine Trades Complete the following table of...Ch. 4.5 - Electrical Trades An electrician purchases some...Ch. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Culinary Arts A wholesale food sales rep is paid a...Ch. 4.5 - Life Skills A sales rep for roofing materials...Ch. 4.5 - Prob. 40ECh. 4.5 - Trades Management Last year, the owner of the...Ch. 4.5 - Trades Management Because it has a history of...Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Allied Health A patient originally weighing 180 lb...Ch. 4.5 - Solve
Retail Merchandising A jacket was reduced in...Ch. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4 - Calculate ratios. (a) Find the ratio of the pulley...Ch. 4 - Solve proportions. (a) Solve for x. 8x=1215...Ch. 4 - Solve problems involving proportions. (a)...Ch. 4 - Write fractions and decimal numbers as percents....Ch. 4 - Prob. 5PCh. 4 - Solve problems involving percent. (a) Find 3712 of...Ch. 4 - A. Complete the following tables.Ch. 4 - A. Complete the following tables.Ch. 4 - B. Solve the following proportions. 56=x42Ch. 4 - B. Solve the following proportions. 815=12xCh. 4 - Prob. 3BPSCh. 4 - B. Solve the following proportions. 312x=51418Ch. 4 - B. Solve the following proportions. 1.65.2=4.4xCh. 4 - B. Solve the following proportions....Ch. 4 - C. Write each number as a percent. 0.72Ch. 4 - C. Write each number as a percent. 0.06Ch. 4 - Prob. 3CPSCh. 4 - C. Write each number as a percent. 0.358Ch. 4 - Prob. 5CPSCh. 4 - C. Write each number as a percent. 3.03Ch. 4 - Prob. 7CPSCh. 4 - Prob. 8CPSCh. 4 - Prob. 9CPSCh. 4 - C. Write each number as a percent. 235Ch. 4 - Prob. 1DPSCh. 4 - Prob. 2DPSCh. 4 - Prob. 3DPSCh. 4 - D. Write each percent as a decimal number. 94%Ch. 4 - Prob. 5DPSCh. 4 - D. Write each percent as a decimal number. 0.09%Ch. 4 - Prob. 7DPSCh. 4 - Prob. 8DPSCh. 4 - Prob. 9DPSCh. 4 - D. Write each percent as a decimal number. 8.02%Ch. 4 - Prob. 11DPSCh. 4 - D. Write each percent as a decimal number. 210%Ch. 4 - Prob. 1EPSCh. 4 - E. Write each of the following percents as a...Ch. 4 - Prob. 3EPSCh. 4 - Prob. 4EPSCh. 4 - Prob. 5EPSCh. 4 - Prob. 6EPSCh. 4 - Prob. 7EPSCh. 4 - E. Write each of the following percents as a...Ch. 4 - F. Solve. 3 is _____ % of 5.Ch. 4 - F. Solve. 5% is 120 is _____.Ch. 4 - Prob. 3FPSCh. 4 - F. Solve. 16 is what percent of 8?Ch. 4 - Prob. 5FPSCh. 4 - F. Solve. 1.38 is _____ % of 1.15.Ch. 4 - Prob. 7FPSCh. 4 - F. Solve. 250% of 50 is _____.Ch. 4 - Prob. 9FPSCh. 4 - Prob. 10FPSCh. 4 - Prob. 1GPSCh. 4 - Metalworking Cast iron contains up to 4.5% carbon,...Ch. 4 - Prob. 3GPSCh. 4 - Prob. 4GPSCh. 4 - Prob. 5GPSCh. 4 - Retail Merchandising A computer printer sells for...Ch. 4 - Prob. 7GPSCh. 4 - Prob. 8GPSCh. 4 - Prob. 9GPSCh. 4 - Masonry A mason must purchase enough mortar mix to...Ch. 4 - Manufacturing A production job is bid at 6275, but...Ch. 4 - Metalworking When heated, a metal rod expands...Ch. 4 - Prob. 13GPSCh. 4 - Automotive Trades A 140-hp automobile engine...Ch. 4 - Prob. 15GPSCh. 4 - Prob. 16GPSCh. 4 - Prob. 17GPSCh. 4 - Trades Management To purchase a truck for his...Ch. 4 - Prob. 19GPSCh. 4 - Interior Design An interior designer is able to...Ch. 4 - Prob. 21GPSCh. 4 - Prob. 22GPSCh. 4 - Prob. 23GPSCh. 4 - Automotive Trades The headlights on a car are...Ch. 4 - Prob. 25GPSCh. 4 - Prob. 26GPSCh. 4 - Prob. 27GPSCh. 4 - Prob. 28GPSCh. 4 - Machine Trades Six steel parts weigh 1.8 lb. How...Ch. 4 - Prob. 30GPSCh. 4 - Prob. 31GPSCh. 4 - Drafting Drafters usually use a scale of 14 in. =...Ch. 4 - Prob. 33GPSCh. 4 - Prob. 34GPSCh. 4 - Prob. 35GPSCh. 4 - Prob. 36GPSCh. 4 - Prob. 37GPSCh. 4 - Printing A printer needs 12,000 good copies of a...Ch. 4 - Prob. 39GPSCh. 4 - Prob. 40GPSCh. 4 - Prob. 41GPSCh. 4 - General Trades Find the missing dimension in the...Ch. 4 - Physics In a closed container, the pressure is...Ch. 4 - Automotive Trades The mechanical efficiency of a...Ch. 4 - Prob. 45GPSCh. 4 - Allied Health Calculate the percent concentration...Ch. 4 - Prob. 47GPSCh. 4 - Prob. 48GPSCh. 4 - Prob. 49GPSCh. 4 - Prob. 50GPSCh. 4 - Prob. 51GPSCh. 4 - Prob. 52GPSCh. 4 - Prob. 53GPSCh. 4 - Prob. 54GPSCh. 4 - Prob. 55GPSCh. 4 - Prob. 56GPSCh. 4 - Prob. 57GPSCh. 4 - Prob. 58GPSCh. 4 - Prob. 59GPSCh. 4 - Plumbing A homeowner purchases a new hot-water...Ch. 4 - Prob. 61GPSCh. 4 - Prob. 62GPSCh. 4 - Prob. 63GPSCh. 4 - Prob. 64GPSCh. 4 - Prob. 65GPS
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