From Constant to Rough: A Survey of Continuous Volatility Modeling

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 hindirochakkahaniya.com rough methods: without advocating for either roughness or long memory, we outline here 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.