STATS:DATA+MODELS(LL)-W/ACCESS>CUSTOM<
21st Edition
ISBN: 9780137643219
Author: DeVeaux
Publisher: PEARSON
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Chapter 17, Problem 8E
(a)
To determine
Find the critical value of t.
(b)
To determine
Find the critical value of t.
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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.)
Chapter 17 Solutions
STATS:DATA+MODELS(LL)-W/ACCESS>CUSTOM<
Ch. 17.2 - Every 10 years, the United States takes a census....Ch. 17.2 - Every 10 years, the United States takes a census....Ch. 17.2 - Prob. 3JCCh. 17.2 - Prob. 4JCCh. 17.2 - Prob. 5JCCh. 17.3 - In discussing estimates based on the long-form...Ch. 17 - Prob. 1ECh. 17 - 2. LSAT The LSAT (a test taken for law school...Ch. 17 - 3. Tips A waiter believes the distribution of his...Ch. 17 - 4. Groceries A grocery store’s receipts show that...
Ch. 17 - 5. More tips The waiter in Exercise 3 usually...Ch. 17 - 6. More groceries Suppose the store in Exercise 4...Ch. 17 - 7. t-models, part I Using the t tables, software,...Ch. 17 - 8. t-models, part II Using the t tables, software,...Ch. 17 - 9. t-models, part III Describe how the shape,...Ch. 17 - 10. t-models, part IV Describe how the critical...Ch. 17 - 11. Home sales The housing market recovered slowly...Ch. 17 - 12. Home sales again In the previous exercise, you...Ch. 17 - 13. Home sales revisited For the confidence...Ch. 17 - 14. Salaries A survey finds that a 95% confidence...Ch. 17 - 15. Cattle Livestock are given a special feed...Ch. 17 - 16. Teachers Software analysis of the salaries of...Ch. 17 - 17. Framingham revisited In Chapter 4, Exercise...Ch. 17 - 18. Student survey revisited Chapter 2, Exercise...Ch. 17 - 19. Shoe sizes revisited Chapter 2, Exercise 16...Ch. 17 - 20. Bird counts A biology class conducts a bird...Ch. 17 - 21. Meal plan After surveying students at...Ch. 17 - 22. Snow Based on meteorological data for the past...Ch. 17 - 23. Pulse rates A medical researcher measured the...Ch. 17 - 24. Crawling Data collected by child development...Ch. 17 - 25. CEO compensation A sample of 20 CEOs from the...Ch. 17 - 26. Credit card charges A credit card company...Ch. 17 - 27. Cholesterol In the latest National Health and...Ch. 17 - 28. Pulse rates In the latest National Health and...Ch. 17 - 29. Normal temperature The researcher described in...Ch. 17 - 30. Parking Hoping to lure more shoppers downtown,...Ch. 17 - 31. Normal temperature, part II Consider again the...Ch. 17 - 32. Parking II Suppose that, for budget planning...Ch. 17 - 33. Speed of light In 1882, Michelson measured the...Ch. 17 - 34. Michelson After his first attempt to determine...Ch. 17 - 35. Flights on time 2016 What are the chances your...Ch. 17 - 36. Flights on time 2016 revisited Will your...Ch. 17 - Prob. 37ECh. 17 - 38. Hot dogs A nutrition lab tested 40 hot dogs to...Ch. 17 - Prob. 39ECh. 17 - Prob. 40ECh. 17 - Prob. 41ECh. 17 - 42. Computer lab fees The technology committee has...Ch. 17 - Prob. 43ECh. 17 - 44. CEO compensation The total compensation of the...Ch. 17 - Prob. 45ECh. 17 - 46. CEOs, revisited In Exercise 44, you looked at...Ch. 17 - Prob. 47ECh. 17 - Prob. 48ECh. 17 - Prob. 49ECh. 17 - 50. Safe cities Allstate Insurance Company...Ch. 17 - Prob. 51ECh. 17 - 52. Rainfall Statistics from Cornell’s Northeast...Ch. 17 - 53. Pregnant again The duration of human...Ch. 17 - 54. At work Some business analysts estimate that...Ch. 17 - Prob. 55ECh. 17 - 56. Doritos Some students checked 6 bags of...Ch. 17 - 57. Popcorn Yvon Hopps ran an experiment to...Ch. 17 - Prob. 58ECh. 17 - Prob. 59ECh. 17 - Prob. 60ECh. 17 - 61. Maze Psychology experiments sometimes involve...Ch. 17 - Prob. 62ECh. 17 - 63. Golf drives 2015 The Professional Golfers...Ch. 17 - Prob. 64E
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