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Joint Modelling of S&P500 and VIX Indices with Rough Fractional Ornstein-Uhlenbeck Volatility Model

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  • Ömer ÖNALAN

    (Marmara University, Faculty of Business Administration)

Abstract

In this paper, we study the joint modelling problem of S&P500 and VIX indices, under rough volatility dynamics by a stochastic model with continuous paths. Our aim is to improve the future values’ forecast of S&P500 index using the VIX index estimates. The present study is built on the estimation with the rough volatility models of the noise component which is included in financial models. The main stylized facts of the volatility can be captured well by fractional Brownian motions with a Hurst index, lower than 0.5. The H parameter governs the realized volatility roughness of time series. In the rough volatility approach, the Hurst exponent H is estimated by using the scaling properties of the volatility series. We describe the log-volatility of S&P500 index using a rough fractional Ornstein-Uhlenbeck model. The VIX index is a measure of the market’s expected volatility on the S&P 500 Index. When the rBergomi model is empirically calibrated to daily data of the proxy, realized volatility and the VIX index, it is found that the VIX index is rough with H

Suggested Citation

  • Ömer ÖNALAN, 2022. "Joint Modelling of S&P500 and VIX Indices with Rough Fractional Ornstein-Uhlenbeck Volatility Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 68-84, April.
    • Handle: RePEc:rjr:romjef:v::y:2022:i:1:p:68-84
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    rough volatility; fractional Ornstein-Uhlenbeck process; volatility estimation; rBergomi model; S&P500 price model;
    All these keywords.

    JEL classification:

    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F47 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Forecasting and Simulation: Models and Applications

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