STATS:DATA+MODELS-MY LAB ACC >CUSTOM<
STATS:DATA+MODELS-MY LAB ACC >CUSTOM<
21st Edition
ISBN: 9780137643127
Author: DeVeaux
Publisher: PEARSON
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Chapter 22, Problem 46E

a.

To determine

Find the sensible way to combine some cells that will make the expected counts acceptable.

b.

To determine

Test the appropriate hypothesis and state the conclusion for the data.

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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 22 Solutions

STATS:DATA+MODELS-MY LAB ACC >CUSTOM<

Ch. 22 - 2. Bank cards At a major credit card bank, the...Ch. 22 - 3. Human births, again For the births in Exercise...Ch. 22 - 4. Bank cards, again For the customers in Exercise...Ch. 22 - 5. Customer ages An analyst at a local bank...Ch. 22 - 6. Bank cards, once more A market researcher...Ch. 22 - Prob. 7ECh. 22 - Prob. 8ECh. 22 - Prob. 9ECh. 22 - 10. Iliad weapons The Iliad also reports the cause...Ch. 22 - Prob. 11ECh. 22 - 12. Which test, again? For each of the following...Ch. 22 - 13. Dice After getting trounced by your little...Ch. 22 - 14. M&M’s As noted in an earlier chapter, Mars...Ch. 22 - Prob. 15ECh. 22 - 16. Mileage A salesman who is on the road visiting...Ch. 22 - 17. NYPD and race Census data for New York City...Ch. 22 - Prob. 18ECh. 22 - 19. Fruit flies Offspring of certain fruit flies...Ch. 22 - 20. Pi Many people know the mathematical constant...Ch. 22 - Prob. 21ECh. 22 - 22. Lottery numbers The fairness of the South...Ch. 22 - Prob. 23ECh. 22 - Prob. 24ECh. 22 - Prob. 25ECh. 22 - Prob. 26ECh. 22 - 27. Childbirth, part 3 In Exercises 23 and 25,...Ch. 22 - 28. Does your doctor know? (part 3) In Exercises...Ch. 22 - Prob. 29ECh. 22 - Prob. 30ECh. 22 - Prob. 31ECh. 22 - Prob. 32ECh. 22 - Prob. 33ECh. 22 - Prob. 34ECh. 22 - Prob. 35ECh. 22 - 36. NYPD again Examine and comment on this table...Ch. 22 - Prob. 37ECh. 22 - 38. Car origins A random survey of autos parked in...Ch. 22 - 39. Montana A poll conducted by the University of...Ch. 22 - 40. Fish diet Medical researchers followed 6272...Ch. 22 - Prob. 41ECh. 22 - 42. Working parents In April 2009, Gallup...Ch. 22 - Prob. 43ECh. 22 - Prob. 44ECh. 22 - Prob. 45ECh. 22 - 46. Full moon, next phase In Exercise 44, you...Ch. 22 - Prob. 47ECh. 22 - Prob. 48ECh. 22 - Prob. 49ECh. 22 - Prob. 50E
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