Stochastic process for irrational stocks

A

ajensen

Stock prices are commonly modeled as a geometric Brownian motion to value stock options, as in the Black-Scholes model. How do you model a stock price where market price is temporarily disconnected from the fundamental value and is far more volatile than it? You can write

S(t) = z(t)*s(t)

where S(t) is the market price, s(t) is the fundamental value (FV), and z(t) is ratio of stock price to FV, which is mean-reverting around 1. You can model s(t) as a GBM and log z(t) as a mean-reverting process. Has this kind of model been studied? Of course, the problem with shorting a stock such as GME is that margin clerks look at S(t), not s(t) when deciding whether to liquidate your positions.

Hmm, before posting, I did a literature search and found a paper

Permanent and Temporary Components of Stock Prices
Eugene F. Fama and Kenneth R. French
Journal of Political Economy
Vol. 96, No. 2 (Apr., 1988), pp. 246-273 (28 pages)

with this model. I'll read it.
 
ajensen said:
Stock prices are commonly modeled as a geometric Brownian motion to value stock options, as in the Black-Scholes model. How do you model a stock price where market price is temporarily disconnected from the fundamental value and is far more volatile than it? You can write

S(t) = z(t)*s(t)

where S(t) is the market price, s(t) is the fundamental value (FV), and z(t) is ratio of stock price to FV, which is mean-reverting around 1. You can model s(t) as a GBM and log z(t) as a mean-reverting process. Has this kind of model been studied? Of course, the problem with shorting a stock such as GME is that margin clerks look at S(t), not s(t) when deciding whether to liquidate your positions.

Hmm, before posting, I did a literature search and found a paper

Permanent and Temporary Components of Stock Prices
Eugene F. Fama and Kenneth R. French
Journal of Political Economy
Vol. 96, No. 2 (Apr., 1988), pp. 246-273 (28 pages)

with this model. I'll read it.
More...

Simple: You sit down, write your model on a piece of paper and throw that into the waste bin.

Then you fire up your trading machine, open an orderbook, a time&sales, an option chain, twitter and reddit and start clicking.

Trying to model something with no data from the past doesn't make any sense. There is a gammut of variables that you don't even know they could play a role in this case. Government actions, rule changes, halts, etc.

In these cases you either are a good trader or you stay on the sidelines and watch.
 
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