This paper constructs a replicating portfolio for a portfolio rebalancing trade. The main result is that the cash-flows from a rebalancing trade on a single asset portfolio can be statically replicated with a combination of a variance swap and a quadratic return swap. Static replicating...

Many multi-population evolutionary games obtain multiple asymptotically stable equilibria. Unlike in the single population case, the size and location of the basins of attraction are determined partially by the relative speed of adjustment of the populations. This paper investigates the effect...

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...

An option gives the right to buy or sell something in the future at a fixed price. The value of an option comes from price uncertainty: if the future price is high the option to buy at a fixed lower price is valuable. An option to sell at a fixed price hedges the risk that the price will go...

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...