Volatility: Data, Models, and the Road Ahead

Giulia Di Nunno (), Yuliya Mishura () and Anton Yurchenko-Tytarenko ()
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Giulia Di Nunno: University of Oslo, Department of Mathematics
Yuliya Mishura: Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics
Anton Yurchenko-Tytarenko: Statkraft Energi AS

Chapter 1 in Volterra Volatility Models, 2026, pp 1-49 from Springer

Abstract: Abstract In this chapter, we provide a broad overview of continuous stochastic volatility models, tracing how the field has developed and identifying the key empirical patterns that have shaped its trajectory. We pay particular attention to fractional and rough volatility approaches: while not advocating for either long memory or roughness, we explain what motivates these ideas and walk through some of the most influential models. We also briefly discuss the challenges of VIX modeling and recent progress on the SPX–VIX joint calibration puzzle. Our aim is to highlight the progress made so far and to point toward several modeling challenges that the following chapters explore in more detail.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-032-26576-0_1

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DOI: 10.1007/978-3-032-26576-0_1

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