Articlegold2023

From Constant to Rough: A Survey of Continuous Volatility Modeling

Giulia Di Nunno · Kęstutis Kubilius · Yuliya Stepanovna Mishura · Anton Yurchenko-Tytarenko

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Complex Systems and Time Series Analysis

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.

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1973The Pricing of Options and Corporate Liabilities 1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1952PORTFOLIO SELECTION*1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1965The Behavior of Stock-Market Prices 1985A Theory of the Term Structure of Interest Rates

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