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State your assumptions. 5.29. A model for the movement of a stock supposes that if the present price of the stock is s, then after one period, it will be either us with probability por ds with probability 1 - p. Assuming that successive movements are independent, approximate the probability that the stock's price will be up at least 30 percent after the next 1000 periods if u = 1.012, d = 0.990, and p = .52. 5.20 I partitioned into two regions one white and the other black

State your assumptions. 5.29. A model for the movement of a stock supposes that if the present price of the stock is s, then after one period, it will be either us with probability por ds with probability 1 - p. Assuming that successive movements are independent, approximate the probability that the stock's price will be up at least 30 percent after the next 1000 periods if u = 1.012, d = 0.990, and p = .52. 5.20 I partitioned into two regions one white and the other black

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How can I solve this question 5.29

**5.29. Stock Movement Model** This model examines the movement of a stock's price. It assumes that if the current price of the stock is \( s \), then after one period, the price will either be \( us \) with probability \( p \), or \( ds \) with probability \( 1-p \). The model assumes that these successive movements are independent. **Objective:** Approximate the probability that the stock's price will increase by at least 30% after 1000 periods. The given parameters are \( u = 1.012 \), \( d = 0.990 \), and \( p = 0.52 \). ### Explanation of Parameters: - **\( u \):** The factor by which the stock price will increase if it moves up. - **\( d \):** The factor by which the stock price will decrease if it moves down. - **\( p \):** The probability that the stock price will increase in a given period. ### Calculation Approach: To determine the chance of a 30% increase over 1000 periods, calculate the compounded effect of repeated applications of the factors \( u \) and \( d \), considering their respective probabilities.
Transcribed Image Text:**5.29. Stock Movement Model** This model examines the movement of a stock's price. It assumes that if the current price of the stock is \( s \), then after one period, the price will either be \( us \) with probability \( p \), or \( ds \) with probability \( 1-p \). The model assumes that these successive movements are independent. **Objective:** Approximate the probability that the stock's price will increase by at least 30% after 1000 periods. The given parameters are \( u = 1.012 \), \( d = 0.990 \), and \( p = 0.52 \). ### Explanation of Parameters: - **\( u \):** The factor by which the stock price will increase if it moves up. - **\( d \):** The factor by which the stock price will decrease if it moves down. - **\( p \):** The probability that the stock price will increase in a given period. ### Calculation Approach: To determine the chance of a 30% increase over 1000 periods, calculate the compounded effect of repeated applications of the factors \( u \) and \( d \), considering their respective probabilities.
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How " P(Z>= -3.1965) " became " 1-symbol(-3.1965)"? Could you explain how you got the three last lines? Which symbol is that?

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