Stock Prices as Janardan Galton Watson Process

TL;DR

This paper extends the Janardan Galton Watson branching process to model stock prices, linking offspring distributions to returns and extinction probabilities, and introduces an algorithm for detecting market trends.

Contribution

It develops a novel branching process model for stock prices based on Janardan's offspring distributions and proposes a trend detection algorithm.

Findings

Extinction probability relates to negative returns.

Model links offspring distribution to stock return expectations.

Algorithm effectively detects market trends.

Abstract

Janardan (1980) introduces a class of offspring distributions that sandwich between Bernoulli and Poisson. This paper extends the Janardan Galton Watson (JGW) branching process as a model of stock prices. In this article, the return value over time t depends on the initial close price, which shows the number of offspring, has a role in the expectation of return and probability of extinction after the passage at time t. Suppose the number of offspring in t th generation is zero, (i.e., called extinction of model at time t) is equivalent with negative return values over time [0, t]. We also introduce the Algorithm that detecting the trend of stock markets.