Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Textbook Question
Chapter 13.6, Problem 1PS
Level 1.
IN YOUR OWN WORDS What is a binomial random variable?
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Students have asked these similar questions
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 13 Solutions
Nature of Mathematics (MindTap Course List)
Ch. 13.1 - IN YOUR OWN WORDS What is the difference between...Ch. 13.1 - IN YOUR OWN WORDS Define probabilities?Ch. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Give the probabilities in Problems 9-11 in decimal...Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...
Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...Ch. 13.1 - Prob. 12PSCh. 13.1 - Poker is a common game in which players are dealt...Ch. 13.1 - Poker is a common game in which players are dealt...Ch. 13.1 - Poker is a common game in which players are dealt...Ch. 13.1 - Prob. 16PSCh. 13.1 - Prob. 17PSCh. 13.1 - Prob. 18PSCh. 13.1 - Prob. 19PSCh. 13.1 - Prob. 20PSCh. 13.1 - Prob. 21PSCh. 13.1 - Some numbers are shown in Table 13.1. Explain...Ch. 13.1 - a. One airline has six across seating in coach. If...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - Suppose that you toss a coin and roll a die in...Ch. 13.1 - Prob. 29PSCh. 13.1 - Suppose that you toss a coin and roll a die in...Ch. 13.1 - Suppose that you toss a coin and roll a die in...Ch. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Prob. 33PSCh. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Prob. 35PSCh. 13.1 - Prob. 36PSCh. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Prob. 42PSCh. 13.1 - Prob. 43PSCh. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Prob. 45PSCh. 13.1 - Prob. 46PSCh. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Perform the experiments in Problems 48-51, tally...Ch. 13.1 - Prob. 49PSCh. 13.1 - Perform the experiments in Problems 48-51, tally...Ch. 13.1 - Perform the experiments in Problems 48-51, tally...Ch. 13.1 - Prob. 52PSCh. 13.1 - Suppose it is certain that an earthquake will...Ch. 13.1 - Dice is a popular game in gambling casinos. Two...Ch. 13.1 - In dice, a pair of ones is called snake eyes. What...Ch. 13.1 - Consider a die with only four sides, marked one,...Ch. 13.1 - The game of Dungeons and Dragons uses nonstandard...Ch. 13.1 - A mad scientist has captured you and is showing...Ch. 13.2 - Level 1 IN YOUR OWN WORDS True or false? In...Ch. 13.2 - Level 1 IN YOUR OWN WORDS True or false? An...Ch. 13.2 - Prob. 3PSCh. 13.2 - Prob. 4PSCh. 13.2 - Prob. 5PSCh. 13.2 - Prob. 6PSCh. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Prob. 9PSCh. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Suppose that you roll two dice. You will...Ch. 13.2 - Level 1 A magazine subscription service is having...Ch. 13.2 - Level 1 A box contains one each of 1,5,10,20, and...Ch. 13.2 - Level 1 A box contains one each of 1,5,10,20, and...Ch. 13.2 - Level 1 Suppose that you have 5 quarters, 5 dimes,...Ch. 13.2 - Level 1 A game involves tossing two coins and...Ch. 13.2 - Level 1 Krinkles potato chips is having a Lucky...Ch. 13.2 - Level 1 A punch-out card contains 100 spaces. One...Ch. 13.2 - Level 2 What is the expectation for the 1 bets in...Ch. 13.2 - Prob. 22PSCh. 13.2 - Prob. 23PSCh. 13.2 - Prob. 24PSCh. 13.2 - Level 2 What is the expectation for the 1 bets in...Ch. 13.2 - Prob. 26PSCh. 13.2 - Prob. 27PSCh. 13.2 - Level 2 What is the expectation for the 1 bets in...Ch. 13.2 - Prob. 29PSCh. 13.2 - Prob. 30PSCh. 13.2 - Level 2 Consider the spinners in Problems 31-34....Ch. 13.2 - Prob. 32PSCh. 13.2 - Level 2 Consider the spinners in Problems 31-34....Ch. 13.2 - Level 2 Consider the spinners in Problems 31-34....Ch. 13.2 - Level 2 Assume that a dart is randomly thrown at...Ch. 13.2 - Level 2 Assume that a dart is randomly thrown at...Ch. 13.2 - Level 2 In old gangster movies on TV, you often...Ch. 13.2 - Prob. 38PSCh. 13.2 - Prob. 39PSCh. 13.2 - Level 2 A realtor who takes the listing on a house...Ch. 13.2 - Level 2 An oil-drilling company knows that it...Ch. 13.2 - Level 2 In Problem 41, suppose that the income for...Ch. 13.2 - Level 2 Consider the following game in which a...Ch. 13.2 - Level 2 A game involves drawing a single card from...Ch. 13.2 - Level 2 A company held a contest, and the...Ch. 13.2 - Level 2 A company held a bingo contest for which...Ch. 13.2 - Level 2 Heights in inches obtained by a group of...Ch. 13.2 - Level 2 In a certain school, the probabilities of...Ch. 13.2 - Level 2 Calculate the expectation to the nearest...Ch. 13.2 - Prob. 50PSCh. 13.2 - Prob. 51PSCh. 13.2 - Prob. 52PSCh. 13.2 - Prob. 53PSCh. 13.2 - Prob. 54PSCh. 13.2 - Prob. 55PSCh. 13.2 - Prob. 56PSCh. 13.2 - Problem Solving Level 3 HISTORICAL QUEST The Swiss...Ch. 13.2 - Problem Solving Level 3 HISTORICAL QUEST The Swiss...Ch. 13.2 - Prob. 59PSCh. 13.2 - Prob. 60PSCh. 13.3 - IN YOUR OWN WORDS What is the fundamental counting...Ch. 13.3 - Prob. 2PSCh. 13.3 - Prob. 3PSCh. 13.3 - Prob. 4PSCh. 13.3 - Prob. 5PSCh. 13.3 - Prob. 6PSCh. 13.3 - Which of the following is more probable? A....Ch. 13.3 - Prob. 8PSCh. 13.3 - Which of the following is more probable? A....Ch. 13.3 - Prob. 10PSCh. 13.3 - Find the requested probabilities in Problems...Ch. 13.3 - Prob. 12PSCh. 13.3 - PC ifPC-=913Ch. 13.3 - Prob. 14PSCh. 13.3 - Prob. 15PSCh. 13.3 - Choose a natural number between 1 and 100,...Ch. 13.3 - Three fair coins are tossed. What is the...Ch. 13.3 - Find the probability of obtaining at least one...Ch. 13.3 - What are the odds in favor of drawing an ace from...Ch. 13.3 - What are a four-child familys odds against having...Ch. 13.3 - The probability of drawing a heart from a deck of...Ch. 13.3 - Suppose the probability of an event is 0.80. What...Ch. 13.3 - Prob. 23PSCh. 13.3 - Racetracks quote the approximate odds for each...Ch. 13.3 - Prob. 25PSCh. 13.3 - Suppose the odds are 33 to 1 that someone will lie...Ch. 13.3 - 27. Suppose that a family want to have four...Ch. 13.3 - Prob. 28PSCh. 13.3 - Prob. 29PSCh. 13.3 - Prob. 30PSCh. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - Prob. 34PSCh. 13.3 - Prob. 35PSCh. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Prob. 40PSCh. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - What is the probability of getting a license plate...Ch. 13.3 - What is the probability of getting a license plate...Ch. 13.3 - 45. Consider the following table showing the...Ch. 13.3 - 46. Suppose a single die is rolled. Find the...Ch. 13.3 - Prob. 47PSCh. 13.3 - Prob. 48PSCh. 13.3 - 49. Suppose a pair of dice is rolled. Consider the...Ch. 13.3 - 50. Suppose a pair of dice is rolled. Consider the...Ch. 13.3 - Prob. 51PSCh. 13.3 - Show that the odds against an event E can be found...Ch. 13.3 - Prob. 53PSCh. 13.3 - A sorority has 35 members, 25 of whom are full...Ch. 13.3 - IN YOUR OWN WORDS The odds against winning a...Ch. 13.3 - Prob. 57PSCh. 13.3 - Prob. 58PSCh. 13.3 - Prob. 60PSCh. 13.4 - IN YOUR OWN WORDS What do we mean by independent...Ch. 13.4 - What is the formula for the probability of an...Ch. 13.4 - Prob. 3PSCh. 13.4 - Prob. 4PSCh. 13.4 - Prob. 5PSCh. 13.4 - Prob. 6PSCh. 13.4 - Prob. 7PSCh. 13.4 - Prob. 8PSCh. 13.4 - Prob. 9PSCh. 13.4 - Prob. 10PSCh. 13.4 - Suppose events A, B, and C are independent and...Ch. 13.4 - Suppose events A, B, and C are independent and...Ch. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - Prob. 16PSCh. 13.4 - Prob. 17PSCh. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - Prob. 19PSCh. 13.4 - Prob. 20PSCh. 13.4 - Prob. 21PSCh. 13.4 - Prob. 22PSCh. 13.4 - Prob. 23PSCh. 13.4 - Prob. 24PSCh. 13.4 - Prob. 25PSCh. 13.4 - Prob. 26PSCh. 13.4 - Prob. 27PSCh. 13.4 - Prob. 28PSCh. 13.4 - Prob. 29PSCh. 13.4 - Prob. 30PSCh. 13.4 - Prob. 31PSCh. 13.4 - Prob. 32PSCh. 13.4 - Prob. 33PSCh. 13.4 - Prob. 34PSCh. 13.4 - Prob. 35PSCh. 13.4 - Prob. 36PSCh. 13.4 - A certain slot machine has three identical...Ch. 13.4 - Suppose slot machine has three identical...Ch. 13.4 - Prob. 39PSCh. 13.4 - The one coin payoffs for the slot machine shown in...Ch. 13.4 - A high rollers Keno is offered in which you pay...Ch. 13.4 - A special catch all Keno ticket allows you to play...Ch. 13.4 - What is the expectation for playing Keno by...Ch. 13.4 - What is the expectation for playing a four-spot...Ch. 13.4 - What is the probability of obtaining five tails...Ch. 13.4 - Prob. 46PSCh. 13.4 - Assume a jar has five red marbles and three black...Ch. 13.4 - Suppose that in an assortment of 20 calculators...Ch. 13.4 - a. A game consists of at most three cuts with a...Ch. 13.4 - Prob. 50PSCh. 13.4 - Prob. 51PSCh. 13.4 - Prob. 52PSCh. 13.4 - Prob. 53PSCh. 13.4 - Prob. 54PSCh. 13.4 - Prob. 55PSCh. 13.4 - Prob. 56PSCh. 13.4 - Prob. 57PSCh. 13.4 - Prob. 58PSCh. 13.4 - Prob. 59PSCh. 13.4 - Prob. 60PSCh. 13.5 - Prob. 1PSCh. 13.5 - Prob. 2PSCh. 13.5 - Prob. 3PSCh. 13.5 - Prob. 4PSCh. 13.5 - Prob. 5PSCh. 13.5 - Prob. 6PSCh. 13.5 - Prob. 7PSCh. 13.5 - Prob. 8PSCh. 13.5 - Prob. 9PSCh. 13.5 - Prob. 10PSCh. 13.5 - Prob. 11PSCh. 13.5 - Prob. 12PSCh. 13.5 - Prob. 13PSCh. 13.5 - Prob. 14PSCh. 13.5 - Prob. 15PSCh. 13.5 - Prob. 16PSCh. 13.5 - Prob. 17PSCh. 13.5 - Prob. 18PSCh. 13.5 - Prob. 19PSCh. 13.5 - Prob. 20PSCh. 13.5 - Prob. 21PSCh. 13.5 - Prob. 22PSCh. 13.5 - Prob. 23PSCh. 13.5 - Prob. 24PSCh. 13.5 - Prob. 25PSCh. 13.5 - Prob. 26PSCh. 13.5 - Prob. 27PSCh. 13.5 - Prob. 28PSCh. 13.5 - Prob. 29PSCh. 13.5 - Prob. 30PSCh. 13.5 - Prob. 31PSCh. 13.5 - Prob. 32PSCh. 13.5 - Prob. 33PSCh. 13.5 - Prob. 34PSCh. 13.5 - Prob. 35PSCh. 13.5 - Prob. 36PSCh. 13.5 - Prob. 37PSCh. 13.5 - Prob. 38PSCh. 13.5 - Prob. 39PSCh. 13.5 - Prob. 40PSCh. 13.5 - Prob. 41PSCh. 13.5 - Prob. 42PSCh. 13.5 - Prob. 43PSCh. 13.5 - Prob. 44PSCh. 13.5 - Prob. 45PSCh. 13.5 - Prob. 46PSCh. 13.5 - Prob. 47PSCh. 13.5 - Prob. 48PSCh. 13.5 - Prob. 49PSCh. 13.5 - Prob. 50PSCh. 13.5 - Suppose the people in a room are divided into two...Ch. 13.5 - Prob. 52PSCh. 13.5 - Prob. 53PSCh. 13.5 - Prob. 54PSCh. 13.5 - Prob. 55PSCh. 13.5 - Prob. 56PSCh. 13.5 - Prob. 57PSCh. 13.5 - Prob. 58PSCh. 13.5 - Prob. 59PSCh. 13.5 - Prob. 60PSCh. 13.6 - Level 1. IN YOUR OWN WORDS What is a binomial...Ch. 13.6 - Prob. 2PSCh. 13.6 - Level 1. Find the binomial probabilities in...Ch. 13.6 - Prob. 4PSCh. 13.6 - Prob. 5PSCh. 13.6 - Prob. 6PSCh. 13.6 - Prob. 7PSCh. 13.6 - Prob. 8PSCh. 13.6 - Prob. 9PSCh. 13.6 - Prob. 10PSCh. 13.6 - Level 1. Find the probability of obtaining exactly...Ch. 13.6 - Prob. 12PSCh. 13.6 - Prob. 13PSCh. 13.6 - Prob. 14PSCh. 13.6 - Prob. 15PSCh. 13.6 - Prob. 16PSCh. 13.6 - Prob. 17PSCh. 13.6 - Prob. 18PSCh. 13.6 - Prob. 19PSCh. 13.6 - Prob. 20PSCh. 13.6 - Prob. 21PSCh. 13.6 - Prob. 22PSCh. 13.6 - Level 1. Suppose a jar contains 3 pens: 1 red, 1...Ch. 13.6 - Level 1. Suppose a jar contains 3 pens: 1 red, 1...Ch. 13.6 - Prob. 25PSCh. 13.6 - Level 1. Suppose a jar contains 3 pens: 1 red, 1...Ch. 13.6 - Prob. 27PSCh. 13.6 - Prob. 28PSCh. 13.6 - Prob. 29PSCh. 13.6 - Prob. 30PSCh. 13.6 - Prob. 31PSCh. 13.6 - Prob. 32PSCh. 13.6 - Prob. 33PSCh. 13.6 - Prob. 34PSCh. 13.6 - Prob. 35PSCh. 13.6 - Prob. 36PSCh. 13.6 - Prob. 37PSCh. 13.6 - Prob. 38PSCh. 13.6 - Prob. 39PSCh. 13.6 - Prob. 40PSCh. 13.6 - Level 2. What is the probability that if a pair of...Ch. 13.6 - Level 2. What is the probability that if a pair of...Ch. 13.6 - Prob. 43PSCh. 13.6 - Prob. 44PSCh. 13.6 - Prob. 45PSCh. 13.6 - Prob. 46PSCh. 13.6 - Prob. 47PSCh. 13.6 - Prob. 48PSCh. 13.6 - Prob. 49PSCh. 13.6 - Prob. 50PSCh. 13.6 - Prob. 51PSCh. 13.6 - Prob. 52PSCh. 13.6 - Prob. 53PSCh. 13.6 - Prob. 54PSCh. 13.6 - Prob. 55PSCh. 13.6 - Prob. 56PSCh. 13.6 - Prob. 57PSCh. 13.6 - Prob. 58PSCh. 13.6 - Prob. 59PSCh. 13.6 - Prob. 60PSCh. 13.CR - Prob. 1CRCh. 13.CR - Prob. 2CRCh. 13.CR - Prob. 3CRCh. 13.CR - Prob. 4CRCh. 13.CR - Prob. 5CRCh. 13.CR - Prob. 6CRCh. 13.CR - Prob. 7CRCh. 13.CR - Prob. 8CRCh. 13.CR - Prob. 9CRCh. 13.CR - Prob. 10CRCh. 13.CR - Prob. 11CRCh. 13.CR - Prob. 12CRCh. 13.CR - Prob. 13CRCh. 13.CR - Prob. 14CRCh. 13.CR - The probability that an individual who is selected...Ch. 13.CR - Prob. 16CRCh. 13.CR - Prob. 17CRCh. 13.CR - Prob. 18CRCh. 13.CR - Prob. 19CRCh. 13.CR - Prob. 20CR
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