From Constant to Rough: A Survey of Continuous Volatility Modeling

Di Nunno, Giulia; Kubilius, Kestutis; Mishura, Yuliya; Yurchenko-Tytarenko, Anton
Peer reviewed, Journal article
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URI
https://hdl.handle.net/11250/3157538
Date
2023
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Original version
10.3390/math11194201
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.
 
From Constant to Rough: A Survey of Continuous Volatility Modeling
 
Journal
Mathematics