Imagine the options market where every put was exactly matched to every call, pending interest is always zero. Any value of put and call is acceptable. That is an infinite world. We have a Godot.
Market size is finite, fuzzy, and constant. In this case, there is a finite queue of puts and calls to match. The pit boss needs to deliver bids at rates to keep the queues from diverging. The pit boss has to find the closest match, and bear the market making risk.
The pit boss wants his pouts and calls to arrive like centered binomials so the pay off is split the difference. In that case the pit boss only carries the risk of known unknowns, the floaters who skipped the betting sequence. That risk, show up, as a slight skew between the optimum binomials arrivals of puts and calls. The pit boss at optimum should carry a uniform bound small fraction, and queue variances stable, mostly bound.
You we will see that is an encoding problem, solving the economies of scale an deriving an encoder trees. he pit boss maintains the indifference curve. These solutions should be be Markov nodes.
The pit boss carries a finite round off error so the puts and calls carry a basket, fractionally dividable. It is the maximum entropy compression effect, minimize transaction by making agent keep their basket 2/3 full. Very similar to the atomic orbitals in topology rules. The orbital is like an indifference surface oi a topology. The structure of the put and call coding trees should be the 'imaginary' points of the known unknowns running loose. I am matching kinetic energy to known unknowns uncertainty.
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