Transaction fee

Let’s consider the trading fee ɛ (ɛ ~0.003) impact with its four possible use cases, as follows:

Buy X:

If a trader wants to buy amount 0<ΔX<Xc:

he should pay:

If a trader wants to sell amount ΔY>0:

he will receive:

Sell X:

If a trader wants to buy amount 0<ΔY< Yc, he should pay:

If a trader wants to sell amount ΔX>0, he will receive:

Implementing fees will change the optimal arbitrage strategy as follows:

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

• if q<1 and f(q)> 1+ɛ, the sell strategy would be: