Mr. Sogi points out that prices seem to chart out along a line and that they would not have done this if they followed a random walk. My question is: If prices are DERIVED from a random walk, are trends then possible? My rationale for asking this comes from:

1. A random walk is very easy to model. Finance students use binomial trees to get an intuition of option pricing. Even the Nobel Prize winning Black-Scholes model uses a special case of this (infinitesimal time steps.)

2. Although the stock price distribution in these models obviously is wrong, the insight it offers into derivative pricing is worthwhile. But what if we for instance use the state of the world as the underlying and then derive a stock price thereof?

I am experimenting on this through a game theoretical framework. First, a price settles where everyone agrees through their beliefs and pockets. With belief I mean that everyone has his own private opinion on how the stock might perform. Instead of the standard set up of probability distributions and risk adjusted returns etc, I simply set up the market in two camps; for instance bulls vs. bears, contrarians vs. trend followers, and so on. With pocket I refer to the budget constraint one faces. Second, any participant will be willing to push the price somewhat in their own disfavor. So, through the market’s bargaining process the beliefs will indirectly be adjusted as a new price settles. This could perhaps be used to explain bubbles and crashes — and any linear paths between such highs and lows? I have posted a preliminary model, with a simulation.


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