Pricing exchanges of cryptocurrency

[mtbc]

At work, I had to learn about a particular distributed cryptocurrency exchange. Liquidity is provided by set of reserves that each contain coins of two different kinds, an equal value of each.

For pricing an exchange "from" the coin we hold "to" the coin we want, using one of these reserves of two different kinds of coin, we have:

r_f

how much of the "from" coin is in the reserve

r_t

how much of the "to" coin is in the reserve

a_f

how much of the "from" coin we want to exchange

a_t

how much of the "to" coin we are to receive

c_n

a constant determining the transaction cost

c_d

another constant determining the transaction cost, a little larger than c_n

It turns out that we decide how much currency users receive by,

a_t = (a_f × r_t × c_n) / (a_f × c_n + r_f × c_d)

I found this quite interesting. In my ignorance, I don't know if it's a standard approach for such currency exchanges. The formula seems to have some reasonable properties, in terms of things like how the price increases as one's swapping to a currency that there is now less of (or would be less of after the swap).

(Dreamwidth doesn't appear to allow <math> markup so I did what I could.)