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Comment by brentr | Hacker News Reader

First, options and futures involve a sub-zero game. Money leaks out via commissions.

Second, there are two types of players in this game. The first group is the speculators. They play the game for profit from the game. The second group is risk managers. They play the game for risk reduction. Speculators serve the risk managers. The speculator's strategy is starkly different than the risk manager's strategy. The speculator can profit by optimizing his strategy.

EDIT: The assumptions made by Black, Scholes, and Merton are highly idealized. There is much research to still be done in the area of behavioral finance and the game theoretic approach to derivatives pricing.

I've thought about conducting graduate research in this area because the mathematics are truly fascinating in this branch of finance/economics. When you start exploring this area from a game theory approach, you can start to understand why John Nash won the Nobel.

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My understanding is the "speculators" create liquidity for the risk managers, thereby assuming their risk.

Why does the money leaking via commissions necessarily make the game sub-zero sum? Is it because we aren't looking at the big picture where everyone wins?

It seems like the risk managers must have a positive incentive to sell their risk on the marketplace instead of assuming it themselves. I.e. hedging another investment like someone else said already.

I was thinking about how to better answer your question concerning the sub-zero game statement I made. Let's remove ourselves from finance for a minute into something that is more traditional in the game theory studies--namely poker.

If the game is played where the players arrange transfers face to face such as in a home poker game, then the game is zero-sum. Your losses are my gains. No money is created. No money is destroyed. It stays inside the game. The minute we go to a casino to play the same game, the game becomes sub-zero due to the rake. You lose X to me and Y to the rake. I gain your X and lose Y to the rake.

Your cash flows: -X - Y. My cash flows: X - Y. In a zero-sum game your cash flows are the negative of my cash flows. This implies -(-X - Y) = X + Y. This is a contradiction. Therefore, the game is not zero-sum.

I was thinking that, because the market created value, it couldn't be zero or negative sum. Now I realize that it's negative sum within the scope of the market itself, even though it may create value in a grander scheme of things.

To truly understand the implications of game theory applied to the financial markets, you should look up the concept of Pareto improvements and Pareto optimums.

Good call. My roommate and I are about to start an econ discussion site. Shoot me an email if you're interested in helping us get conversation started or just have any suggestions for us.

Email?

See profile, forgot that it doesn't show.

Liquidity is one type of risk. There exist also interest rate risk, price risk, etc.

Commissions are an expense that both sides pay to play the game. Money is not transferred from one player to another, it is transferred to outside the game.

It is true that there is a positive incentive to sell risk from the risk-manager's view. That is the whole reason the markets were initially established, both derivatives and the underlying of the derivative.

It's still zero sum. Just one of the winners is the guy charging the commission. Every dollar in commission is a dollar someone else has to lose.

No, the broker is an externality--his strategy is fixed before the game even starts.

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