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Zednark
I'm sorta wondering if anyone's got a system for it.
Tecumseh
I haven't gotten into this level of detail with my players but I would support it if they asked for it.

Two ideas:

1) Pick real-life corporations (or mutual funds or indices, to represent the diversified nature of megacorp holdings) and map those to in-game corporations to determine how the game-world corps are faring. You could probably leverage some of the online "Fantasy Stock" games to help make tracking things easier.

2) The back of 3E's Corporate Download (p. 124 & 125) has some rules about how to randomize the performance of the megacorps over time. The guidelines suggest only going through the performance testing every six months of game time, but I see no reason why it couldn't be done every month or so. You could use that as a basis for stock market price fluctuations in your game.
Gingivitis
Agree with Tecumseh. No reason the 3rd Ed rules wouldn't still work.

I think the number one concern when introducing the stock market is making sure that the players do not feel like they can manipulate the market to any real degree. Introducing stock market rules presupposes that the players will participate. Some may think that a run here and a murder there will manipulate stock (and net them some serious nuyen in its wake).

The reality is likely the opposite. Runs are so prevalent and corporations are so massive, so diversified, and so non-transparent that very few actions runners take will cause a corp's equity to dip or bump in value.

Some prototype goes missing? That should drop the stock, but the corp announces a large stock buy-back and some layoffs in Latvia and now they are stable before the market even opens. Or they just lie about it. It's not like the SEC is doing anything in 2076.

Plus the ECSE will have some serious SIN scrubbers. It's not likely a fake SIN would get too much action before it was tagged by Zurich. The runners would need a real SIN, or a straw man buyer (who would certainly take a cut).
Draco18s
Reminds me that I tried to work out a system to use for a board game using real stocks. Had to be something with high minute-to-minute volatility (bitcoin works for that) and you'd initialize the game using the last day/hour high-lows scaled to the game's units (so regardless of if you picked something that varied by $10 or $1000 each game-unit would cost the same).

Each player would, at the start of their turn, adjust the board to the current price of one stock based on the current trading value (so there'd be 1 option on the board per player). Even with the player knowing how the stock price has changed since their last turn, it wouldn't really give them an advantage because they'd still have to risk the duration to their next turn.

Then there'd be a few game-based modifiers; e.g. if you buy a share, you notch the game-price up a dollar, if you sell, it notches down.

Never actually tried to do it in practice, though. The goal would be ~1 hour play time. For weekly session RP stuff, you could get away with just picking an arbitrary real world company's share price and only the price at the start of the session matters.
Beta
I don't know if there has been anything about it in the official fluff, but by the sounds of things the markets in the SR era would probably not be as dynamic, liquid or important as they are currently.
- most Megas seem to have their controlling interests held in a few hands, rather than being widely dispersed, so floated shares for those would largely be for subsidiaries, which are going to tend to be manipulated from higher levels.
- there is a much higher concentration of wealth than even in the current US, which renders a lot of companies almost more like some of the earliest companies where they were almost more partnerships between relatively small numbers of wealthy people, rather than something held so broadly as we are used to now. And a lot of deals are more likely to be privately arranged, rather than done through bids on the open market.
- Much of what middle-class exists is beholden to one mega or another, which in turn suggests to me that they would have corporate savings/retirement plans invested by the corp, probably mostly in the corp's own family of companies. That helps stabilize subsidiaries in which higher level corps in the group don't have an actual majority interest.
- Due to all of the above, there is going to be less room for corporate raiders, hedge funds, and so forth. I'm sure they still exist (and probably employ shadowrunners), but that they are not apt to have as much influence on the market.
- Governments ability to regulate anything is much weaker, so the odds that the stock markets are anything remotely close to transparent and well regulated are remote.

Tycho
in the SR3 sourcebook Corporate Download (or Corporate Shadowfiles?) were Rules for the Stock Market, but they were pretty rudimentary.

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