Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Forecasting VIX using interpretable Kolmogorov-Arnold networks

So-Yoon Cho, Sungchul Lee, Hyun-Gyoon Kim

TL;DR

The paper tackles the interpretability challenge in financial forecasting by introducing Kolmogorov-Arnold Networks (KANs) for predicting the $VIX$. Utilizing learnable spline-based univariate activations and a symbolification pipeline, KANs produce a sparse model with a closed-form forecast expressed in terms of explanatory variables. Empirical results across three datasets and three periods show KAN achieves competitive accuracy with far fewer parameters than MLP/LSTM, while revealing interpretable dynamics such as mean reversion via $\Delta V_t = \kappa(\theta - V_{t-1}) + \epsilon_t$ and the leverage effect when incorporating $R_{t-1}^e$. The findings underscore the value of interpretable, parsimonious time-series models in finance and point to broad applicability beyond $VIX$ forecasting.

Abstract

This paper presents the use of Kolmogorov-Arnold Networks (KANs) for forecasting the CBOE Volatility Index (VIX). Unlike traditional MLP-based neural networks that are often criticized for their black-box nature, KAN offers an interpretable approach via learnable spline-based activation functions and symbolification. Based on a parsimonious architecture with symbolic functions, KAN expresses a forecast of the VIX as a closed-form in terms of explanatory variables, and provide interpretable insights into key characteristics of the VIX, including mean reversion and the leverage effect. Through in-depth empirical analysis across multiple datasets and periods, we show that KANs achieve competitive forecasting performance while requiring significantly fewer parameters compared to MLP-based neural network models. Our findings demonstrate the capacity and potential of KAN as an interpretable financial time-series forecasting method.

Forecasting VIX using interpretable Kolmogorov-Arnold networks

TL;DR

The paper tackles the interpretability challenge in financial forecasting by introducing Kolmogorov-Arnold Networks (KANs) for predicting the . Utilizing learnable spline-based univariate activations and a symbolification pipeline, KANs produce a sparse model with a closed-form forecast expressed in terms of explanatory variables. Empirical results across three datasets and three periods show KAN achieves competitive accuracy with far fewer parameters than MLP/LSTM, while revealing interpretable dynamics such as mean reversion via and the leverage effect when incorporating . The findings underscore the value of interpretable, parsimonious time-series models in finance and point to broad applicability beyond forecasting.

Abstract

This paper presents the use of Kolmogorov-Arnold Networks (KANs) for forecasting the CBOE Volatility Index (VIX). Unlike traditional MLP-based neural networks that are often criticized for their black-box nature, KAN offers an interpretable approach via learnable spline-based activation functions and symbolification. Based on a parsimonious architecture with symbolic functions, KAN expresses a forecast of the VIX as a closed-form in terms of explanatory variables, and provide interpretable insights into key characteristics of the VIX, including mean reversion and the leverage effect. Through in-depth empirical analysis across multiple datasets and periods, we show that KANs achieve competitive forecasting performance while requiring significantly fewer parameters compared to MLP-based neural network models. Our findings demonstrate the capacity and potential of KAN as an interpretable financial time-series forecasting method.

Paper Structure

This paper contains 15 sections, 17 equations, 5 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Kolmogorov-Arnold Networks: Representation, Structure, and Training
  3. Kolmogorov-Arnold Representation Theorem
  4. Kolmogorov-Arnold Networks
  5. VIX Forecasting using KAN
  6. Data
  7. Empirical Results
  8. Experimental Setup
  9. Analysis of KAN forecasting results
  10. Statistical assessment of KAN as a forecasting model
  11. Capturing the leverage effect
  12. Comparison with traditional and deep learning benchmark methods
  13. Conclusion
  14. Training results for deep and wide KAN
  15. KAN training result before and after symbolification in Period 1 and Period 2

Figures (5)

  • Figure 1: KAN training results for Datasets 1--3 under Period 3 before (top row) and after (bottom row) symbolification. Black activation functions indicate the trained B-spline-based structure, whereas red activation functions depict the replaced symbolic functions. Vivid edges represent stronger effects, while fainter edges mean weaker ones.
  • Figure 1: KAN training results for Datasets 1--3 under Period 3 with 10 hidden nodes (top row) and with three layers and 4 hidden nodes each (bottom row). The trained activation functions predominantly exhibit a linear form, leading to the KAN model being expressed as a sum of linear terms. This structure is preserved across all Datasets.
  • Figure 2: Training results of $KAN(\hat{V}_t, R_{t-1}^e)$ across Datasets and Periods. To clearly see the activation functions, the contrast of the figures is increased by three times compared to Figure \ref{['fig: KAN before after symbolification']}.
  • Figure 2: KAN training results for Datasets 1--3 under Period 1 before (top row) and after (bottom row) symbolification. Black activation functions indicate the trained B-spline-based structure, whereas red activation functions depict the replaced symbolic functions. Vivid edges represent stronger effects, while fainter edges mean weaker ones.
  • Figure 3: KAN training results for Datasets 1--3 under Period 2 before (top row) and after (bottom row) symbolification. Black activation functions indicate the trained B-spline-based structure, whereas red activation functions depict the replaced symbolic functions. Vivid edges represent stronger effects, while fainter edges mean weaker ones.