From constant to rough: A survey of continuous volatility modeling
Giulia Di Nunno, K\k{e}stutis Kubilius, Yuliya Mishura, Anton Yurchenko-Tytarenko
TL;DR
This survey reviews the evolution of continuous stochastic volatility models, emphasizing fractional and rough methods, and discusses recent advances in VIX modeling and joint calibration challenges.
Contribution
It provides a comprehensive overview of the development and key features of continuous volatility models, highlighting recent innovations in fractional and rough approaches.
Findings
Fractional and rough models capture market stylized facts.
Recent advances improve VIX and SPX-VIX calibration.
Landmark models are characterized and compared.
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.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Complex Systems and Time Series Analysis · Stochastic processes and financial applications