Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition
11th Edition
ISBN: 9781285464657
Author: Soo T. Tan
Publisher: Brooks Cole
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Chapter 6.2, Problem 50E
To determine
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The statement “
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For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram?
A
55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92
B
55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91
C
55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93
D
55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91
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 6 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition
Ch. 6.1 - Prob. 1CQCh. 6.1 - Prob. 2CQCh. 6.1 - Prob. 3CQCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7E
Ch. 6.1 - Prob. 8ECh. 6.1 - In Exercises 9-14, state whether the statements...Ch. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Let U denotes the set of all students who applied...Ch. 6.1 - In Exercise 27-28, write an expression describing...Ch. 6.1 - In Exercise 27-28, write an expression describing...Ch. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - In Exercise 35-38, let U={1,2,3,4,5,6,7,8,9,10},...Ch. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - BEST U.S. CITY FOR ITALIAN RESTAURANTS In a reader...Ch. 6.1 - INVENTORY Loss The biggest cause of inventory...Ch. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Prob. 72ECh. 6.1 - Prob. 73ECh. 6.1 - Prob. 74ECh. 6.1 - In Exercise 71-80, determine whether the statement...Ch. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Prob. 80ECh. 6.2 - Prob. 1CQCh. 6.2 - Prob. 2CQCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - If n(A)=15, n(AB)=5 and n(AB)=30, then what is...Ch. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - NEWSPAPER SUBSCRIBERS A survey of 1000 subscribers...Ch. 6.2 - JAIL INMATES On a certain day, the Wilton County...Ch. 6.2 - Of 100 clock radios with digital tuners and/or CD...Ch. 6.2 - BRAND PREFERENCES OF CONSUMERS In a survey of 120...Ch. 6.2 - SPORTS CLUB SURVEY In a survey of 200 members of a...Ch. 6.2 - INVESTORS' USAGE OF BROKERS In a poll conducted...Ch. 6.2 - COMMUTER TRENDS Of 50 employees of a store located...Ch. 6.2 - CONSUMER SURVEY OF DESKTOP AND TABLET COMPUTER...Ch. 6.2 - CONSUMER SURVEY OF HDTV AND MP3 PLAYER OWNERS In a...Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - BRAND SWITCHING AMONG FEMALE COLLEGE STUDENTSIn a...Ch. 6.2 - Prob. 39ECh. 6.2 - FEDERAL BUDGET ALLOCATION According to the Office...Ch. 6.2 - SURVEY OF LEADING ECONOMISTS A survey of the...Ch. 6.2 - STUDENT DROPOUT RATE Data released by the...Ch. 6.2 - STUDENT MAGAZINE PREFERENCES A survey of 100...Ch. 6.2 - SAT SCORES Results of a Department of Education...Ch. 6.2 - Prob. 45ECh. 6.2 - CAFETERIA STUDENT USAGE To help plan the number of...Ch. 6.2 - 401k INVESTMENTS In a survey of 200 employees of a...Ch. 6.2 - NEWSPAPER PREFERENCES OF INVESTORS In a survey of...Ch. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.3 - Explain the multiplication principle, and...Ch. 6.3 - Prob. 2CQCh. 6.3 - RENTAL RATES Lynbrook West, an apartment complex...Ch. 6.3 - COMMUTER PASSES Five different types of monthly...Ch. 6.3 - BLACKJACK In the game of blackjack, a 2-card hand...Ch. 6.3 - Prob. 4ECh. 6.3 - WARDROBE SELECTION A female executive selecting...Ch. 6.3 - COMMUTER OPTIONS Four commuter trains and three...Ch. 6.3 - PSYCHOLOGY EXPERIMENTS A psychologist has...Ch. 6.3 - Prob. 8ECh. 6.3 - HEALTH-CARE PLAN OPTIONS A new state employee is...Ch. 6.3 - CODE WORDS How many three-letter code words can be...Ch. 6.3 - Prob. 11ECh. 6.3 - MENU CHOICES The New Shanghai Restaurant offers a...Ch. 6.3 - CHOOSING A PIN Janice needs to make up a personal...Ch. 6.3 - MENU CHOICES Marias Trattoria offers mushrooms,...Ch. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - SERIAL NUMBERS Computers manufactured by a certain...Ch. 6.3 - COMPUTER DATING A computer dating service uses the...Ch. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - TELEVISION-VIEWING POLLS An opinion poll is to be...Ch. 6.3 - LICENSE PLATE NUMBERS Over the years, the state of...Ch. 6.3 - POLITICAL POLLS An opinion poll was conducted by...Ch. 6.3 - LICENSE PLATE NUMBERS In recent years, the state...Ch. 6.3 - Exams An exam consists of ten true-or-false...Ch. 6.3 - WARRANTY NUMBERS A warranty identification number...Ch. 6.3 - CHOOSING A PASSWORD A password is to be made from...Ch. 6.3 - LOTTERIES In a state lottery, there are 15...Ch. 6.3 - COMBINATION LOCKS A rolling combination four-digit...Ch. 6.3 - COMBINATION LOCKS Lugano Leather Company makes an...Ch. 6.3 - TELEPHONE NUMBERS a. How many seven-digit...Ch. 6.3 - SLOT MACHINES A "lucky dollar" is one of the nine...Ch. 6.3 - STAFFING Student Painters, which specializes in...Ch. 6.3 - Prob. 35ECh. 6.3 - In Exercises 35 and 36, determine whether the...Ch. 6.4 - a. What is a permutation of a set of distinct...Ch. 6.4 - Prob. 2CQCh. 6.4 - a. How many combinations are there of a set of n...Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - In Exercise 1-22, evaluate the given expression....Ch. 6.4 - Prob. 22ECh. 6.4 - In Exercises 23-30, classify each problem...Ch. 6.4 - In Exercises 23-30, classify each problem...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - In Exercises 23-30, classify each problem...Ch. 6.4 - Prob. 31ECh. 6.4 - How many three-letter permutations can be formed...Ch. 6.4 - In how many ways can four students be seated in a...Ch. 6.4 - In how many ways can five people line up at a...Ch. 6.4 - Prob. 35ECh. 6.4 - In how many ways can the names of six candidates...Ch. 6.4 - In how many ways can a member of a hiring...Ch. 6.4 - In how many ways can an investor select four...Ch. 6.4 - Find the number of distinguishable permutations...Ch. 6.4 - Prob. 40ECh. 6.4 - In how many ways can the letters of the website...Ch. 6.4 - In how many ways can five people boarding a bus be...Ch. 6.4 - Prob. 43ECh. 6.4 - How many different signals can be made by hoisting...Ch. 6.4 - SUPERMARKET SITE SELECTION In how many ways can a...Ch. 6.4 - SELECTING A READING LIST A student is given a...Ch. 6.4 - QUALITY CONTROL In how many ways can a...Ch. 6.4 - STUDY GROUP ASSIGNMENTS A group of five students...Ch. 6.4 - TELEVISION PROGRAMMING In how many ways can a...Ch. 6.4 - WAITING LINES Seven people arrive at the ticket...Ch. 6.4 - SELECTING A SPECIAL OCCASION CAKE Fosselmans Ice...Ch. 6.4 - WEDDING CATERING L.A. Wedding Caterers offers a...Ch. 6.4 - MANAGEMENT DECISIONS Weaver and Kline, a stock...Ch. 6.4 - CAR POOLS A company car that has a seating...Ch. 6.4 - TRAVEL WARDROBE Kaylee is planning a wardrobe for...Ch. 6.4 - Criminology The town of Carson employs 15 police...Ch. 6.4 - Prob. 57ECh. 6.4 - CONCERT SEATING In how many ways can four married...Ch. 6.4 - NEWSPAPER ADS Four items from five different...Ch. 6.4 - MANAGEMENT DECISIONS C ** J Realty has received 12...Ch. 6.4 - SELECTING A BASEBALL TEAM A Little League baseball...Ch. 6.4 - TENNIS MATCH In the mens tennis tournament at...Ch. 6.4 - Prob. 63ECh. 6.4 - JURY SELECTION In how many different ways can a...Ch. 6.4 - Prob. 65ECh. 6.4 - EXAMS A student taking an examination is required...Ch. 6.4 - TEACHING ASSISTANTSHIPS Twelve graduate students...Ch. 6.4 - SENATE COMMITTIES In how many ways can a...Ch. 6.4 - CONTRACT BIDDING UBS Television Company is...Ch. 6.4 - PERSONNEL SELECTION JCL. Computers has five...Ch. 6.4 - Prob. 71ECh. 6.4 - Prob. 72ECh. 6.4 - Prob. 73ECh. 6.4 - Prob. 74ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - WORLD SERIES In the World Series, one National...Ch. 6.4 - VOTING QUORUMS A quorum minimum of 6 voting...Ch. 6.4 - Prob. 82ECh. 6.4 - Prob. 83ECh. 6.4 - Prob. 84ECh. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - Prob. 90ECh. 6.4 - Prob. 1TECh. 6.4 - Prob. 2TECh. 6.4 - Prob. 3TECh. 6.4 - Prob. 4TECh. 6.4 - Prob. 5TECh. 6.4 - Prob. 6TECh. 6.4 - In Exercises 110, evaluate the expression. C(52,7)Ch. 6.4 - Prob. 8TECh. 6.4 - In Exercises 110, evaluate the expression....Ch. 6.4 - In Exercises 110, evaluate the expression....Ch. 6.4 - Prob. 11TECh. 6.4 - Prob. 12TECh. 6.CRQ - Fill in the blanks. A well-defined collection of...Ch. 6.CRQ - Prob. 2CRQCh. 6.CRQ - Prob. 3CRQCh. 6.CRQ - Prob. 4CRQCh. 6.CRQ - Prob. 5CRQCh. 6.CRQ - Prob. 6CRQCh. 6.CRQ - Prob. 7CRQCh. 6.CRQ - Prob. 8CRQCh. 6.CRE - Prob. 1CRECh. 6.CRE - Prob. 2CRECh. 6.CRE - Prob. 3CRECh. 6.CRE - Prob. 4CRECh. 6.CRE - Prob. 5CRECh. 6.CRE - Prob. 6CRECh. 6.CRE - Prob. 7CRECh. 6.CRE - Prob. 8CRECh. 6.CRE - Prob. 9CRECh. 6.CRE - Prob. 10CRECh. 6.CRE - Prob. 11CRECh. 6.CRE - Prob. 12CRECh. 6.CRE - Prob. 13CRECh. 6.CRE - Prob. 14CRECh. 6.CRE - Prob. 15CRECh. 6.CRE - Prob. 16CRECh. 6.CRE - Prob. 17CRECh. 6.CRE - Prob. 18CRECh. 6.CRE - Prob. 19CRECh. 6.CRE - Prob. 20CRECh. 6.CRE - Prob. 21CRECh. 6.CRE - Prob. 22CRECh. 6.CRE - Prob. 23CRECh. 6.CRE - Prob. 24CRECh. 6.CRE - Prob. 25CRECh. 6.CRE - Let A and B be subsets of a universal set U and...Ch. 6.CRE - Prob. 27CRECh. 6.CRE - Prob. 28CRECh. 6.CRE - Prob. 29CRECh. 6.CRE - Prob. 30CRECh. 6.CRE - CREDIT CARD COMPARISONS A comparison of five major...Ch. 6.CRE - STUDENT SURVEYS The Department of Foreign...Ch. 6.CRE - In how many ways can six different DVDs be...Ch. 6.CRE - Prob. 34CRECh. 6.CRE - In how many ways can six different books, four of...Ch. 6.CRE - Prob. 36CRECh. 6.CRE - Find the number of distinguishable permutations...Ch. 6.CRE - Prob. 38CRECh. 6.CRE - AUTOMOBILE SELECTION An automobile manufacturer...Ch. 6.CRE - MENU SELECTIONS Two soups, five entres, and three...Ch. 6.CRE - Prob. 41CRECh. 6.CRE - POKER From a standard 52-card deck, how many...Ch. 6.CRE - Prob. 43CRECh. 6.CRE - TEAM SELECTION There are eight seniors and six...Ch. 6.CRE - Prob. 45CRECh. 6.CRE - SEATING ARRANGEMENTS In how many ways can seven...Ch. 6.CRE - Prob. 47CRECh. 6.CRE - Prob. 48CRECh. 6.CRE - Prob. 49CRECh. 6.CRE - Prob. 50CRECh. 6.BMO - Prob. 1BMOCh. 6.BMO - Prob. 2BMOCh. 6.BMO - In how many ways can four compact discs be...Ch. 6.BMO - Prob. 4BMOCh. 6.BMO - Prob. 5BMO
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- The Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardWe 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_forward
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