Speaker: David Itkin
Title: Rank-based models with listings and delistings: theory and calibration
Abstract: Rank-based models for equity markets are reduced-form models where the asset dynamics depend on the rank that asset occupies in the investment universe. Such models are able to capture certain stylized macroscopic properties of equity markets, such as stability of the capital distribution curve and collision rates of stock rank switches. However, when calibrated to real equity data the models possess undesirable features such as an “Atlas stock” effect; namely the smallest security has an unrealistically large drift. Recently, Campbell and Wong (2024) identified that listings and delistings (i.e. entrances and exists) of securities in the market are important drivers for the stability of the capital distribution curve. In this work we develop a framework for ranked-based models with listings and delistings and calibrate them to data. By incorporating listings and delistings the calibration procedure no longer leads to an “Atlas stock” behaviour. Moreover, by studying an appropriate “local model”, zooming into a specific target rank, we are able to connect collisions rates with a notion of particle density, which is more stable and easier to estimate from data than the collision rates. The calibration results are supported by novel theoretical developments such as a new master formula for functional generation of portfolios in this setting. This talk is based on joint work in progress with Martin Larsson and Licheng Zhang.