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...

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...

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

We derive bounds for profitable manipulation of a constant product market used as a reference provider (oracle) for a margin position. Such bounds exist in terms of limits imposed on deposits the constant product market and the margin position, and depend on the elasticity of the underlying spot...

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...