Explanation Given: B k Concept used: The binomial trees B k , 1 = 0 , 1 , 2 , ... , are ordered rooted trees defined recursively: Basis step: The binomial tree B 0 is the tree with a single vertex. Recursive step: Let k be a nonnegative integer. To construct the binomial tree B k + 1 , add a copy of B k to a second copy of B k by adding an edge that makes the root of the first copy of B k the leftmost child of the foundation of the second copy of B k Principle of mathematical induction is used to verify mathematical and logical expression. Calculation: Height of a binomial tree B k is k . Since a binomial tree B k is formed from two B k − 1 trees with one B k − 1 added with an edge at one level down to the root of another, at each stage the height of the tree increases by one. This can be proved by induction. Basis step: For k = O , only one vertex so height is O which is true for k = O

8th Edition

ISBN: 9781265370749

Author: ROSEN

Publisher: MCG

See similar textbooks

Question

Chapter 11, Problem 15SE

To determine

Find the height of Bk. Prove that your answer is correct.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 14SE

Chapter 11, Problem 16SE

Students have asked these similar questions

Consider the ceocomp dataset of compensation information for the CEO’s of 100 U.S. companies. We wish to fit aregression model to assess the relationship between CEO compensation in thousands of dollars (includes salary andbonus, but not stock gains) and the following variates:AGE: The CEOs age, in yearsEDUCATN: The CEO’s education level (1 = no college degree; 2 = college/undergrad. degree; 3 = grad. degree)BACKGRD: Background type(1= banking/financial; 2 = sales/marketing; 3 = technical; 4 = legal; 5 = other)TENURE: Number of years employed by the firmEXPER: Number of years as the firm CEOSALES: Sales revenues, in millions of dollarsVAL: Market value of the CEO's stock, in natural logarithm unitsPCNTOWN: Percentage of firm's market value owned by the CEOPROF: Profits of the firm, before taxes, in millions of dollars1) Create a scatterplot matrix for this dataset. Briefly comment on the observed relationships between compensationand the other variates.Note that companies with negative…

6 (Model Selection, Estimation and Prediction of GARCH) Consider the daily returns rt of General Electric Company stock (ticker: "GE") from "2021-01-01" to "2024-03-31", comprising a total of 813 daily returns. Using the "fGarch" package of R, outputs of fitting three GARCH models to the returns are given at the end of this question. Model 1 ARCH (1) with standard normal innovations; Model 2 Model 3 GARCH (1, 1) with Student-t innovations; GARCH (2, 2) with Student-t innovations; Based on the outputs, answer the following questions. (a) What can be inferred from the Standardized Residual Tests conducted on Model 1? (b) Which model do you recommend for prediction between Model 2 and Model 3? Why? (c) Write down the fitted model for the model that you recommended in Part (b). (d) Using the model recommended in Part (b), predict the conditional volatility in the next trading day, specifically trading day 814.

4 (MLE of ARCH) Suppose rt follows ARCH(2) with E(rt) = 0, rt = ut, ut = στει, σε where {+} is a sequence of independent and identically distributed (iid) standard normal random variables. With observations r₁,...,, write down the log-likelihood function for the model esti- mation.

Chapter 11 Solutions

DISCRETE MATH CONNECT ACCESS

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Knowledge Booster

Find the height of B k . Prove that your answer is correct.

Solution Summary: The author explains how the heigth of B_k isk.

Find the height of Bk. Prove that your answer is correct.

Want to see the full answer?

Chapter 11 Solutions