Quadratic regression models for Profile Picture NFT valuation

Abstract

In this study, we propose a valuation methodology for Non-Fungible Tokens (NFTs), focusing on the profile picture (PFP) NFT category represented by the Bored Ape Yacht Club (BAYC). To identify the attributes that influence the value of individual BAYC NFTs, we develop a hedonic pricing model that uses the NFT’s value as the dependent variable and its properties as independent variables. We apply Term Frequency-Inverse Document Frequency (TF-IDF) to quantify attributes of NFTs. Three hedonic models—linear, quadratic, and full quadratic—are proposed. For the full quadratic model, we introduce a systematic procedure to select first-order, second-order, and interaction terms in the model. To evaluate the performance of the proposed models, we carried out comparative computational experiments. We collected actual BAYC transaction data and split it into a training set (70%) and a validation set (30%). For benchmarking purposes, we compare the proposed models against four machine learning algorithms: Random Forest, Support Vector Regression (SVR), XGBoost, and LightGBM. The machine learning models perform well on the training set, however, this was largely due to overfitting. In contrast, the proposed hedonic models maintained consistent performance with minimal degradation from the training to the validation set. Among them, the full quadratic model demonstrates the highest explanatory power on the validation set in terms of adjusted R² and other evaluation metrics.