arXiv subjects

Francis Liu

Publications and source records attributed to Francis Liu.

3 recordsLinked to original sources

arXiv2026

The Minimal Retroreflective Microfacet Model

We present the Minimal Retroreflective Microfacet (MRM) model, which turns any existing microfacet BSDF into a physically plausible retroreflective one by a single substitution: replacing the view direction with its reflection about the surface normal before evaluating the standard model. Based on the previously published back-vector formulation, MRM requires only minimal code changes and has been adopted in the OpenPBR and MaterialX material standards. We prove reciprocity and energy conservation under the assumption of a reflection-symmetric normal distribution function (NDF), which holds for all commonly used distributions, and validate the model against measured retroreflective material data.

cs.GR↗

arXiv2025

Jump risk premia in the presence of clustered jumps

This paper presents an option pricing model that incorporates clustered jumps using a bivariate Hawkes process. The process captures both self- and cross-excitation of positive and negative jumps, enabling the model to generate return dynamics with asymmetric, time-varying skewness and to produce positive or negative implied volatility skews. This feature is especially relevant for assets such as cryptocurrencies, so-called ``meme'' stocks, G-7 currencies, and certain commodities, where implied volatility skews may change sign depending on prevailing sentiment. We introduce two additional parameters, namely the positive and negative jump premia, to model the market risk preferences for positive and negative jumps, inferred from options data. This enables the model to flexibly match observed skew dynamics. Using Bitcoin (BTC) options, we empirically demonstrate how inferred jump risk premia exhibit predictive power for both the cost of carry in BTC futures and the performance of delta-hedged option strategies.

q-fin.MF↗

arXiv2022

Universal Behavior of Opponent Statistics and Applications to the MLB

In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's luck tends to even out over the course of a season. The other main reason is the difficulties of finding a sensible algorithm to both quantify the strengths of the opponents and incorporate such quantifications into a renormalization of a player's statistics. In this paper, we first argue that certain statistics, such as Earned Run Average (ERA) or Fielding Independent Pitching (FIP) can be significantly skewed by opponents' strengths in the MLB. We then present an algorithm to renormalize such statistics, using FIP as the main example. This is achieved by observing that certain opponent statistics for all 30 teams in the MLB (e.g. the collection of each game's opponent FIP value over the course of a season) follow a universal distribution, up to scaling and shift. This enables us to establish a data set for a hypothetical average team and to develop a pitching statistic based on FIP which accounts for the strength of a pitcher's schedule through methods based on equipercentile equating. It is called aFIP, which measures what a pitcher's FIP would have been if he had faced a league-average offensive team every time he pitched. We find that there is a significant difference between aFIP and FIP for some pitchers during the 2019 season and other seasons as well, adding a new tool for player evaluation. This could make millions of dollars of difference in player contracts and in profits for teams as they enhance the accuracy with which they make player acquisitions. The universal distribution we observed also has many possible future applications throughout the sports world.

stat.AP↗