An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Chapter 2.8, Problem 20E
In Exercises 2.20–2.22, identify whether the design is a completely randomized design, randomized complete block design, or Latin square design. If there is a factorial structure for the treatments, specify whether it has a two-factor or three-factor structure. If the measurement units are different from the experimental units, identify both.
2.20. The researchers design an experiment to evaluate the effect of applying fertilizer having varying levels of nitrogen, potassium, and phosphorus on the yields of orange trees. There were three, four, and three different levels of N, P, and K, respectively, yielding 36 distinct combinations. Ten orange groves were randomly selected for the experiment. Each grove was then divided into 36 distinct plots, and the 36 fertilizer combinations were randomly assigned to the plots within each grove. The yield of five randomly selected trees in each plot is recorded to assess the variation within each of the 360 plots.
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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 2 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 2.8 - In the following descriptions of a study,...Ch. 2.8 - In the following descriptions of a study,...Ch. 2.8 - A news report states that minority children who...Ch. 2.8 - A study was conducted to determine if the...Ch. 2.8 - Prob. 5ECh. 2.8 - A large auto parts supplier with distribution...Ch. 2.8 - The circuit judges in a rural county are...Ch. 2.8 - Prob. 8ECh. 2.8 - Time magazine, in an article in the late 1950s,...Ch. 2.8 - The New York City school district is planning a...
Ch. 2.8 - A professional society, with a membership of...Ch. 2.8 - For each of the following situations, decide what...Ch. 2.8 - For each of the following situations, decide what...Ch. 2.8 - The process engineer designed a study to evaluate...Ch. 2.8 - Prob. 15ECh. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - A research specialist for a large seafood company...Ch. 2.8 - In Exercises 2.20–2.22, identify whether the...Ch. 2.8 - In Exercises 2.202.22, identify whether the design...Ch. 2.8 - In Exercises 2.20–2.22, identify whether the...Ch. 2.8 - A bakery wants to evaluate new recipes for carrot...Ch. 2.8 - Prob. 24SECh. 2.8 - Prob. 25SECh. 2.8 - Prob. 26SECh. 2.8 - Prob. 27SECh. 2.8 - Prob. 28SECh. 2.8 - Prob. 29SECh. 2.8 - A forester wants to estimate the total number of...Ch. 2.8 - A transportation researcher is funded to estimate...Ch. 2.8 - The department of agriculture in a midwestern...Ch. 2.8 - Prob. 33SECh. 2.8 - A Yankelovich, Skelly, and White poll taken in the...
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