Actuarial Finance by Boudreault Mathieu;Renaud Jean-Francois; & Jean-François Renaud

Author:Boudreault, Mathieu;Renaud, Jean-Francois; & Jean-François Renaud
Language: eng
Format: epub
ISBN: 9781119137023
Publisher: John Wiley & Sons, Inc.
Published: 2019-03-13T19:00:00+00:00

11.1.2.1 Probability distribution

We now look at the probability distribution of the risky asset time-k price, where k = 1, 2, …, n. We can write

where the random variable Ik counts the number of upward movements in the trajectory after k periods. Mathematically, it is defined as

If there are i upward movements after k time steps, then

where i can be as little as 0 but at most equal to k (k up-moves in k trials).

It is clear that Ik follows a binomial distribution (with respect to ) with parameters (k, p):

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