IMM - Arbitrage Trades

Let’s calculate how the pool assets’ total value changes as a result of an infinitely small amount trade: dX or dY.

As the trader and the pool are engaged in a 0 sum game, if dV<0, the trader has a profit |dV| and if dV>0, the trader has a loss |dV|.

Where , (In this case q ≠ 1) a trader theoretically has an arbitrage opportunity.

The optimal arbitrage strategy is as follows:

If q>1 and f(q)<1, the buy strategy would be:

If q<1 and f(q)>1, the sell strategy would be:

The arbitrageurs’ activity returns the pool towards balance.