From Constant to Rough: A Survey of Continuous Volatility Modeling

From Constant to Rough: A Survey of Continuous Volatility Modeling

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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 arcade smokey the bear belt 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 jerome brown jersey touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.