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

Ömer Önalan ()
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Ömer Önalan: Marmara University, Faculty of Business Administration

Journal for Economic Forecasting, 2022, issue 1, 68-84

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

Keywords: rough volatility; fractional Ornstein-Uhlenbeck process; volatility estimation; rBergomi model; S&P500 price model (search for similar items in EconPapers)
JEL-codes: C22 C58 E37 F47 G17 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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