5 papers
Portfolio Optimization under Fast and Slow Latent Mean-Reverting and Momentum Drift
Dannin J. Eccles, Roger Lee
We consider a class of partial-information portfolio optimization problems in which the drift of a risky asset is driven by two latent stochastic factors evolving at distinct time…
All AMMs are CFMMs. All DeFi markets have invariants. A DeFi market is arbitrage-free if and only if it has an increasing invariant
Roger Lee
In a universal framework that expresses any market system in terms of state transition rules, we prove that every DeFi market system has an invariant function and is thus by defini…
Robust Replication of Volatility and Hybrid Derivatives on Jump Diffusions
Peter Carr, Roger Lee, Matthew Lorig
We price and replicate a variety of claims written on the log price and quadratic variation of a risky asset, modeled as a positive semimartingale, subject to stochastic…
Pricing Variance Swaps on Time-Changed Markov Processes
Peter Carr, Roger Lee, Matthew Lorig
We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by a…
Robust replication of barrier-style claims on price and volatility
Peter Carr, Roger Lee, Matthew Lorig
We show how to price and replicate a variety of barrier-style claims written on the price and quadratic variation of a risky asset. Our framework ass…