Probability and Statistics for Engineers and Scientists
9th Edition
ISBN: 9780321629111
Author: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye
Publisher: Prentice Hall
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Chapter 8.8, Problem 37E
(a)
To determine
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(b)
To determine
Find
(c)
To determine
Find
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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 8 Solutions
Probability and Statistics for Engineers and Scientists
Ch. 8.2 - Define suitable populations from which the...Ch. 8.2 - The lengths of time, in minutes, that 10 patients...Ch. 8.2 - The reaction times for a random sample of 9...Ch. 8.2 - The number of tickets issued for traffic...Ch. 8.2 - The numbers of incorrect answers on a true-false...Ch. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10E
Ch. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Show that the sample variance is unchanged if a...Ch. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.4 - If all possible samples of size 16 are drawn from...Ch. 8.4 - Prob. 18ECh. 8.4 - A certain type of thread is manufactured with a...Ch. 8.4 - Given the discrete uniform population
find the...Ch. 8.4 - Prob. 21ECh. 8.4 - The heights of 1000 students are approximately...Ch. 8.4 - The random variable X, representing the number of...Ch. 8.4 - If a certain machine makes electrical resistors...Ch. 8.4 - The average life of a bread-making machine is 7...Ch. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Consider the situation described in Example 8.4 on...Ch. 8.4 - Prob. 36ECh. 8.8 - For a chi-squared distribution, find
Ch. 8.8 - For a chi-squared distribution, find
Ch. 8.8 - For a chi-squared distribution, find such that
...Ch. 8.8 - For a chi-squared distribution, find such that
...Ch. 8.8 - Assume the sample variances to be continuous...Ch. 8.8 - Prob. 42ECh. 8.8 - Prob. 43ECh. 8.8 - Prob. 44ECh. 8.8 - Find P(T < 2.365) when v = 7.
Find P(T > 1.318)...Ch. 8.8 - Find P(−t0.005 < T < t0.01) for υ = 20.
Find P(T >...Ch. 8.8 - Given a random sample of size 24 from a normal...Ch. 8.8 - Prob. 48ECh. 8.8 - Prob. 49ECh. 8.8 - A maker of a certain brand of low-fat cereal bars...Ch. 8.8 - For an F-distribution, find
f0.05 with v1 = 7 and...Ch. 8.8 - Pull-strength tests on 10 soldered leads for a...Ch. 8.8 - Prob. 53ECh. 8.8 - Prob. 54ECh. 8.8 - Prob. 55ECh. 8.8 - Prob. 56RECh. 8.8 - Prob. 57RECh. 8.8 - Prob. 58RECh. 8.8 - Prob. 59RECh. 8.8 - A random sample of 5 bank presidents indicated...Ch. 8.8 - Prob. 61RECh. 8.8 - A taxi company tests a random sample of 10...Ch. 8.8 - Prob. 63RECh. 8.8 - Prob. 64RECh. 8.8 - Prob. 65RECh. 8.8 - Consider Review Exercise 8.56. Comment on any...Ch. 8.8 - Prob. 67RECh. 8.8 - Prob. 68RECh. 8.8 - Prob. 69RECh. 8.8 - Prob. 70RECh. 8.8 - Prob. 71RECh. 8.8 - Prob. 72RECh. 8.8 - Prob. 73RECh. 8.8 - Prob. 74RECh. 8.8 - Prob. 75RE
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