English

From constant to rough: A survey of continuous volatility modeling

Mathematical Finance 2025-08-22 v3 Probability

Abstract

In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.

Keywords

Cite

@article{arxiv.2309.01033,
  title  = {From constant to rough: A survey of continuous volatility modeling},
  author = {Giulia Di Nunno and Kęstutis Kubilius and Yuliya Mishura and Anton Yurchenko-Tytarenko},
  journal= {arXiv preprint arXiv:2309.01033},
  year   = {2025}
}