binomial model

Discussion in 'Probability' started by matule, Oct 20, 2021.

  1. matule

    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
    #1
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