STATS:DATA+MODELS-W/DVD
4th Edition
ISBN: 9780321986498
Author: DeVeaux
Publisher: PEARSON
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Chapter 14, Problem 9E
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Explain why table is better than a tree here.
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We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
Negate the following compound statement using De Morgans's laws.
Chapter 14 Solutions
STATS:DATA+MODELS-W/DVD
Ch. 14.1 - 1. Back in Chapter 1, we suggested that you sample...Ch. 14.3 - JUST CHECKING
4. The American Association for...Ch. 14.4 - JUST CHECKING
5. Remember our sample of pages in...Ch. 14 - Prob. 1ECh. 14 - Cooking and shopping Forty-five percent of...Ch. 14 - Sports What is the probability that a person likes...Ch. 14 - Sports again From Exercise 3, if someone doesn’t...Ch. 14 - Late to the train A student figures that he has a...Ch. 14 - Field goals A nervous kicker usually makes 70% of...Ch. 14 - Titanic On the Titanic, the probability of...
Ch. 14 - Births If the sex of a child is independent of all...Ch. 14 - Facebook Facebook reports that 70% of its users...Ch. 14 - Online banking A national survey indicated that...Ch. 14 - Facebook again Suppose that the information in...Ch. 14 - Online banking again Suppose that the information...Ch. 14 - Facebook final Given the probabilities in Exercise...Ch. 14 - Online banking last time Given the probabilities...Ch. 14 - Phones Recent research suggests that 73% of...Ch. 14 - Travel Suppose the probability that a U.S....Ch. 14 - Amenities A check of dorm rooms on a large college...Ch. 14 - Workers Employment data at a large company reveal...Ch. 14 - Global survey The marketing research organization...Ch. 14 - Birth order A survey of students in a large...Ch. 14 - 21. Cards You draw a card at random front a...Ch. 14 - Pets In its monthly report, the local animal...Ch. 14 - 59. Health The probabilities that an adult...Ch. 14 - 60. Immigration The table shows the political...Ch. 14 - 25. Global survey, take 2 Look again at the table...Ch. 14 - 26. Birth order, take 2 Look again at the data...Ch. 14 - Sick kids Seventy percent of kids who visit a...Ch. 14 - Sick cars Twenty percent of cars that are...Ch. 14 - 29. Cards You are dealt a hand of three cards, one...Ch. 14 - 30. Another hand You pick three cards at random...Ch. 14 - 63. Batteries A junk box in your room contains a...Ch. 14 - 64. Shirts The soccer team’s shirts have arrived...Ch. 14 - 65. Eligibility A university requires its biology...Ch. 14 - 66. Benefits Fifty-six percent of all American...Ch. 14 - 35. Cell phones in the home A survey found that...Ch. 14 - Prob. 36ECh. 14 - Prob. 37ECh. 14 - Prob. 38ECh. 14 - Prob. 39ECh. 14 - 40. Birth order, finis In Exercises 20 and 26, we...Ch. 14 - Prob. 41ECh. 14 - Prob. 42ECh. 14 - Prob. 43ECh. 14 - Prob. 44ECh. 14 - Prob. 45ECh. 14 - Prob. 46ECh. 14 - Prob. 47ECh. 14 - Prob. 48ECh. 14 - Prob. 49ECh. 14 - Prob. 50ECh. 14 - Prob. 51ECh. 14 - Prob. 52ECh. 14 - Prob. 53ECh. 14 - Prob. 54ECh. 14 - Prob. 55ECh. 14 - 82. No-shows An airline offers discounted...Ch. 14 - Prob. 57ECh. 14 - Prob. 58ECh. 14 - Prob. 59ECh. 14 - Prob. 60E
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- Question 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forwardCharacterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forward
- Let G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forwardLet G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forward
- We consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forwardDetermine if the two statements are equivalent using a truth tablearrow_forwardQuestion 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forward
- Determine if the two statements are equalivalent using a truth tablearrow_forwardQuestion 3: p and q represent the following simple statements. p: Calgary is the capital of Alberta. A) Determine the value of each simple statement p and q. B) Then, without truth table, determine the va q: Alberta is a province of Canada. for each following compound statement below. pvq р^~q ~рл~q ~q→ p ~P~q Pq b~ (d~ ← b~) d~ (b~ v d) 0 4arrow_forward2. Let X be a random variable. (a) Show that, if E X2 = 1 and E X4arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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