# binomial model

Discussion in 'Off-Topic Chat' started by matule, Oct 20, 2021.

1. ### matule

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Let T = {0, 1, . . . , 10}. Consider a binomial model for the price S of a share of stock.
That is: • Ω = {0, 1} 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .sample space.
• P(ω) = p k (1 − p) 10−k , where p ∈ (0, 1) and k is the number of 1’s in the sequence ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . probability distribution.
• 0 < D < 1 < U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . price ratios.
• S(t)(ω) = 100 · U kDt−k , where k is the number of 1’s among the first t entries of ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the price process.

(a) Write a program (in Mathematica or other software of your choice) such that takes as input the parameters: p, D and U; and computes:
• The price of the share S(t)(ω) at a given time t ∈ T and scenario ω ∈ Ω;
• The price of the share S(t)(k), a time t ∈ T assuming that it increased k ≤ t times.
• The probability P(s1 ≤ S(t) ≤ s2) that the price at time t ∈ T falls between s1 < s2.
• The expected price E(S(t)) at time t ∈ T

(b) Write extra features (of your own choice) to your program. For example, the program could compute (this is a suggestion only, be creative):
• The range of values of S(t).
• The full set of values of S(t).
• The distribution of S(t) (with nice graphics).

kindly assist

matule, Oct 20, 2021