03.06.2024 14:15 Lorenzo Schönleber (Collegio Carlo Alberto in Turin): Implied Impermanent Loss: A Cross-Sectional Analysis of Decentralized Liquidity Pools
We propose a continuous-time stochastic model to analyze the dynamics of impermanent loss in liquidity pools in decentralized finance (DeFi) protocols. We replicate the impermanent loss using option portfolios for the individual tokens. We estimate the risk-neutral joint distribution of the tokens by minimizing the Hansen–Jagannathan bound, which we then use for the valuation of options on relative prices and for the calculation of implied correlations. In our analyses, we investigate implied volatilities and implied correlations as possible drivers of the impermanent loss and show that they explain the cross-sectional returns of liquidity pools. We test our hypothesis on options data from a major centralized derivative exchange.
Source
03.06.2024 15:00 Maximilian Würschmidt (Universität Trier): A Probabilistic Approach to Shape Derivatives
In this talk, we introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for second-order semilinear elliptic PDEs with Dirichlet boundary conditions and a general class of target functions. The probabilistic representation derives from a boundary sensitivity result for diffusion processes due to Costantini, Gobet and El Karoui. Via so-called Taylor tests we verify the numerical accuracy of our methodology.
Source
01.07.2024 14:15 Michael Kupper (University of Konstanz): Discrete approximation of risk-based pricing under volatility uncertainty
We discuss the limit of risk-based prices of European contingent claims in discrete-time financial markets under volatility uncertainty when the number of intermediate trading periods goes to infinity. The limiting dynamics are obtained using recently developed results for the construction of strongly continuous convex monotone semigroups. We connect the resulting dynamics to the semigroups associated to G-Brownian motion, showing in particular that the worst-case bounds always give rise to a larger bid-ask spread than the risk-based bounds. Moreover, the worst-case bounds are achieved as limit of the risk-based bounds as the agent’s risk aversion tends to infinity. The talk is based on joint work with Jonas Blessing and Alessandro Sgarabottolo.
Source