We demonstrate how a liquidity position in a constant product market can be closely approximated with a future (delta), a quadratic swap (gamma), and a swap for fees.The pool value behaves like an option with a constant delta and gamma and zero vega

We give a general construction for margining derivative contracts. This generalises usefully to futures, options, collateralized loans, and state contracts such as prediction markets. For partly collateralized contracts, each side is long an option on their own defaulting and short an option on...

Futures are contracts to buy or sell things in the future. Holding a futures contract gives an exposure very similar to holding the physical asset since the two prices are related by arbitrage (buying the asset and selling the future or visa-versa).Liquid exchange traded futures markets exist...

Much of the capitalist economy is funded on credit. Each different borrower, in each different currency, for loans of different lengths of time, borrows on different terms. Fixed income is the study of how to price and manage these differences. This is a short course through theory and practice...

We derive the replicating portfolio of a constant product market. This is structurally short volatility (selling options) which explains why positive transaction costs are needed to induce liquidity providers to participate. Where futures and options markets do not exist, this payoff can be used...

We define a class of margin loans and derive the distribution of defaults. The default risk from an individual loan can be priced as a series of forward starting options with a knockout. Under simple price dynamics this has an explicit solution