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Estimating stochastic volatility: the rough side to equity returns

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Abstract

This paper evaluates the forecasting performance of a Brownian semi-stationary (BSS) process in modelling the volatility of 21 equity indices. We implement a hybrid scheme to simulate BSS processes with high efficiency and precision. These simulations are useful to price derivatives, accounting for rough volatility. We then calibrate the BSS parameters for the realised kernel of 21 equity indices, using data from the Oxford-Man Institute. Finally, we conduct one-step and ten-step ahead forecasts on six indices and find that the BSS outperforms benchmarks, including a Log-HAR specification, in most cases.

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Notes

  1. This has been done using the autocorr and fmincon commands in MATLAB.

  2. To implement this matrix multiplication in practice, the ‘fliplr’ command in MATLAB is used on the \(\varGamma _{12} \) matrix to ensure the correct time order of correlation lags.

  3. Note that estimation error is a delicate issue here, which is what Patton (2011) aims to address with robust loss functions. Patton (2011) derives a class of loss functions which, when used with an unbiased volatility proxy such as realised kernels, can be used to rank volatility models (see Sect. 3.1).

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Authors and Affiliations

  1. Barcelona Graduate School of Economics, Barcelona, Spain

    Jonathan Haynes, Daniel Schmitt & Lukas Grimm

  2. Oxera Consulting LLP, Oxford, UK

    Jonathan Haynes

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  1. Jonathan Haynes
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  2. Daniel Schmitt
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  3. Lukas Grimm
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Correspondence to Jonathan Haynes.

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The authors would like to thank Christian Brownlees, Eulalia Nualart, Alex Badran and two anonymous referees for their detailed comments and valuable suggestions.

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Haynes, J., Schmitt, D. & Grimm, L. Estimating stochastic volatility: the rough side to equity returns. Decisions Econ Finan 42, 449–469 (2019). https://doi.org/10.1007/s10203-019-00261-y

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