Discussion of article "Risk Evaluation in the Sequence of Deals with One Asset. Continued"
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New article Risk Evaluation in the Sequence of Deals with One Asset. Continued has been published:
The article develops the ideas proposed in the previous part and considers them further. It describes the problems of yield distributions, plotting and studying statistical regularities.
Let us consider the simplest version of searching for deviations from a random walk. This will be a measure of how much the price moves in the gap direction until it gets filled. It is also possible to obtain an empirical distribution of this variable by the price history and compare it with the theoretical one. Some goodness-of-fit criterion can be used for comparing these two distributions.
Consider a model of a symmetric random walk with discrete time. Let large gaps be rare in it (as in real prices), and let the model be close to a walk with continuous time (Wiener process) in the intervals between the gaps. Introduce the notation: g — the gap size, m — the maximum movement in the direction of the gap before it gets filled. Then the random variable x=m/g will have a distribution function close to the function P(x) — such that P(x)=1-1/x if x≥1, and P(x)=0 if x<1. The Figure illustrates the introduced values:
Author: Aleksey Nikolayev