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 8.2, Problem 13E
To determine
Find the standard deviation.
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Problem1
We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.
Problem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%.
We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…
What is the standard scores associated to the left of z is 0.1446
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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- Note: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forwardshow work in paperarrow_forwardshow all work (...or what you entered into your calculator...)arrow_forward
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