From Constant to Rough: A Survey of Continuous Volatility Modeling

Giulia Di Nunno, Kęstutis Kubilius, Yuliya Mishura and Anton Yurchenko-Tytarenko ()
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Giulia Di Nunno: Department of Mathematics, University of Oslo, 0851 Oslo, Norway
Kęstutis Kubilius: Faculty of Mathematics and Informatics, Vilnius University, LT-03225 Vilnius, Lithuania
Yuliya Mishura: Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
Anton Yurchenko-Tytarenko: Department of Mathematics, University of Oslo, 0851 Oslo, Norway

Mathematics, 2023, vol. 11, issue 19, 1-35

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: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.

Keywords: stochastic volatility; implied volatility smile; rough volatility; fractional processes; VIX; option pricing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:19:p:4201-:d:1255656

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