From constant to rough: A survey of continuous volatility modeling

Paper: arXiv 2309.01033

Authors: Giulia Di Nunno, Kęstutis Kubilius, Yuliya Mishura, Anton Yurchenko-Tytarenko

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: As a comprehensive survey paper, it provides high mathematical density covering fractional calculus and rough volatility models, but lacks original empirical backtesting or novel primary research. Its clarity and thoroughness in summarizing the development from constant to rough volatility are high.

Research Flowchart

  flowchart TD
    A[Goal: Survey Continuous Stochastic Volatility Models] --> B[Input: Financial Time Series, SPX & VIX Data]
    B --> C[Methodology: Analyze Historical Evolution & Stylized Facts]
    C --> D[Evaluate Model Frameworks: Standard vs. Rough Volatility]
    D --> E[Address SPX-VIX Joint Calibration Puzzle]
    E --> F[Outcomes: Justify Rough Volatility Models & Future Directions]