Statistics: Informed Decisions Using Data (5th Edition)
Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 6.3, Problem 1AYU
To determine

To define: The conditions needed for a random variable X to follow Poisson distribution.

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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?
We 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? 2

Chapter 6 Solutions

Statistics: Informed Decisions Using Data (5th Edition)

Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 15 and 16, determine the required...Ch. 6.1 - In Problems 15 and 16, determine the required...Ch. 6.1 - NW 17. Televisions In the Sullivan Statistics...Ch. 6.1 - 18. Marriage In the following probability...Ch. 6.1 - 19. Ichiro's Hit Parade In the 2004 baseball...Ch. 6.1 - 20. Waiting in Line A Wendy's manager performed a...Ch. 6.1 - In Problems 21 and 22, (a) construct a discrete...Ch. 6.1 - In Problems 21 and 22, (a) construct a discrete...Ch. 6.1 - 23. Number of Births The graph of the discrete...Ch. 6.1 - 24. Rental Units The graph of the discrete...Ch. 6.1 - 25. Life Insurance A life insurance company sells...Ch. 6.1 - 26. Life Insurance A life insurance company sells...Ch. 6.1 - 27. BlackJack BlackJack is a popular casino game...Ch. 6.1 - 28. Investment An investment counselor calls with...Ch. 6.1 - 29. Roulette In the game of roulette, a player can...Ch. 6.1 - 30. Connecticut Lottery In the Cash Five Lottery...Ch. 6.1 - 31. Powerball Powerball is a multistate lottery....Ch. 6.1 - 32. SAT Test Penalty Some standardized tests, such...Ch. 6.1 - Prob. 33AYUCh. 6.1 - Prob. 34AYUCh. 6.1 - Prob. 35AYUCh. 6.1 - 36. 2014 Senate Election In the 2014 election,...Ch. 6.2 - 1. A binomial experiment is performed a fixed...Ch. 6.2 - 2. For each trial of a binomial experiment, there...Ch. 6.2 - 3. True or False: In the binomial probability...Ch. 6.2 - 4. The phrase “no more than” is represented by the...Ch. 6.2 - 5. The expected number of successes in a binomial...Ch. 6.2 - 6. As a rule of thumb, if ______, the probability...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - Prob. 16AYUCh. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - Prob. 22AYUCh. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - Prob. 24AYUCh. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - Prob. 28AYUCh. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - 35. On-Time Flights According to flightstats.com,...Ch. 6.2 - 36. Morality In a recent poll, the Gallup...Ch. 6.2 - 37. Toilet Flushing In the Healthy Handwashing...Ch. 6.2 - 38. Allergy Sufferers Clarinex-D is a medication...Ch. 6.2 - 39. Sneeze According to a study done by Nick...Ch. 6.2 - 40. Sneeze Revisited According to a study done by...Ch. 6.2 - 41. Jury Selection Twelve jurors are randomly...Ch. 6.2 - 42. Sullivan Survey: Car Color According to paint...Ch. 6.2 - 43. On-Time Flights According to flightstats.com,...Ch. 6.2 - 44. Morality In a recent poll, the Gallup...Ch. 6.2 - 45. Toilet Flushing In the Healthy Handwashing...Ch. 6.2 - Prob. 46AYUCh. 6.2 - Prob. 47AYUCh. 6.2 - Prob. 48AYUCh. 6.2 - Prob. 49AYUCh. 6.2 - Prob. 50AYUCh. 6.2 - 51. Overbooking Flights Historically, the...Ch. 6.2 - Prob. 52AYUCh. 6.2 - Prob. 53AYUCh. 6.2 - Prob. 54AYUCh. 6.2 - Prob. 55AYUCh. 6.2 - Prob. 56AYUCh. 6.2 - Prob. 57AYUCh. 6.2 - Prob. 58AYUCh. 6.2 - Prob. 59AYUCh. 6.2 - 60. When can the Empirical Rule be used to...Ch. 6.3 - Prob. 1AYUCh. 6.3 - 2. Explain the role of λ and t in the Poisson...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 7 and 8, the random variable X follows...Ch. 6.3 - Prob. 8AYUCh. 6.3 - Prob. 9AYUCh. 6.3 - Prob. 10AYUCh. 6.3 - 11. Hits to a Website The number of hits to a...Ch. 6.3 - Prob. 12AYUCh. 6.3 - Prob. 13AYUCh. 6.3 - 14. Potholes The potholes on a major highway in...Ch. 6.3 - Prob. 15AYUCh. 6.3 - 16. Traffic Fatalities According to...Ch. 6.3 - 17. Florida Hurricanes From 1900 to 2014 (115...Ch. 6.3 - Prob. 18AYUCh. 6.3 - Prob. 19AYUCh. 6.3 - Prob. 20AYUCh. 6.3 - Prob. 21AYUCh. 6.3 - Prob. 22AYUCh. 6.3 - 23. Simulation According to the National Center...Ch. 6.3 - Prob. 24AYUCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - 6. Emergency Room Visits The probability that a...Ch. 6 - 7. Driving Age According to a Gallup poll, 60% of...Ch. 6 - Prob. 8RECh. 6 - 9. State the condition required to use the...Ch. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 1CSCh. 6 - 2. Does it appear that, on average, the Neuländers...Ch. 6 - Prob. 3CSCh. 6 - Prob. 4CSCh. 6 - Prob. 5CSCh. 6 - Prob. 6CS
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