“If the prices do not converge, then they must oscillate infinitely around some point. A trader could exploit the logical inductor by buying the sentence at a high point on the oscillation and selling at a low one.”
I know that this is an informal summary, but I don’t find this point intuitively convincing. Wouldn’t the trader also need to be able to predict the oscillation?
One could create a program which hard-codes the point about which it oscillates (as well as some amount which it always eventually goes that far in either direction), and have it buy once when below, and then wait until the price is above to sell, and then wait until price is below to buy, etc.
The programs receive as input the prices which the market maker is offering.
It doesn’t need to predict ahead of time how long until the next peak or trough, it only needs to correctly assume that it does oscillate sufficiently, and respond when it does.
“If the prices do not converge, then they must oscillate infinitely around some point. A trader could exploit the logical inductor by buying the sentence at a high point on the oscillation and selling at a low one.”
I know that this is an informal summary, but I don’t find this point intuitively convincing. Wouldn’t the trader also need to be able to predict the oscillation?
My understanding:
One could create a program which hard-codes the point about which it oscillates (as well as some amount which it always eventually goes that far in either direction), and have it buy once when below, and then wait until the price is above to sell, and then wait until price is below to buy, etc.
The programs receive as input the prices which the market maker is offering.
It doesn’t need to predict ahead of time how long until the next peak or trough, it only needs to correctly assume that it does oscillate sufficiently, and respond when it does.
Yes, and there will always exist such a trader.