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Empirical Economics

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26-04-2021

Time connectedness of fear

Authors: Julián Andrada-Félix, Adrian Fernandez-Perez, Fernando Fernández-Rodríguez, Simón Sosvilla-Rivero

Published in: Empirical Economics | Issue 3/2022

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Abstract

This paper examines the interconnection between four implied volatility indices representative of the investors' consensus view of expected stock market volatility at different maturities during the period from 3 January 2011 to 4 May 2018. To this end, we first perform static analysis to measure the total volatility connectedness in the entire period using a framework proposed by Diebold and Yilmaz (J Econ 182: 119–134, 2014). Second, we apply a dynamic analysis to evaluate both the net directional connectedness for each market using the TVP-VAR connectedness approach developed by Antonakakis and Gabauer (Refined measures of dynamic connectedness based on TVP-VAR. MPRA, Working Paper No. 78282, 2017). Our results suggest that 72.27% of the total variance of the forecast errors is explained by shocks across the examined maturities, indicating that the remainder 27.73% of the variation is due to idiosyncratic shocks. Furthermore, we find that volatility connectedness varies over time, with a surge during periods of increasing economic and financial instability. Our results are robust to control by macroeconomic and uncertainty factors, and persistent across US and European implied volatility indices.

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For excellent primers on the VIX, see Whaley (2009) and Gonzalez-Perez (2015). Carr and Lee (2009) provide an exemplary history of the market for volatility derivatives and a survey of the relevant methodologies for pricing and hedging volatility derivatives products.

Poon and Granger (2003) concluded that the VIX is the best predictor of realized volatility, although it may be a biased one.

See http://www.cboe.com/micro/vix/vixwhite.pdf.

Note that by falsely assuming normality, we risk underestimating responses to shocks in the tails of the distribution and may be unable to identify differences in the responses to positive and negative shocks. Therefore, the Diebold–Yilmaz framework may suggest low connectedness, while there is in fact high connectedness for negative events and low connectedness for positive events. Nevertheless, the empirical literature has consistently used the log transformation to make data conform to normality and as a variance stabilizing transformation as documented by Diebold and Yilmaz (2015).

All results are based on a VAR model of order 2 and generalized variance decompositions of 10-day ahead volatility forecast errors. To check for the sensitivity of the results to the choice of the order of VAR, we also calculate the spillover index for orders 2 through 4, as well as for forecast horizons varying from 4 to 10 days. The main results of our paper are not affected by these choices. Detailed results are available from the authors upon request.

To eliminate the effect of the non-informative initial conditions in the Kalman filter, we have skipped the first 200 days of the sample and plot the results from 12 October 2011 to 4 May 2018. This number is somehow arbitrary but conservative.

In the black-and-white version of the paper the colours of lines in Fig. 4 range from black (black) to dark grey (red), grey (blue) and light grey (green).

Recall that VIX9D provides a market-based gauge of expectations of 9-day volatility, making it particularly responsive to the short-term changes in the S&P 500 index.

These concerns were mainly fueled by the outcome of the Greek elections in May, by several downgrades of Spanish and Italian banks and by Moody’s downgrade of the Spanish sovereign rating in June.

Figures 8, 9, 10, 11 in "Appendix 3" provide a detailed account of the time-varying evolution of the spillovers from each implied volatility index to the others.

Recall that, due to the use of the Kalman filter to eliminate the effect of the non-informative initial conditions, we have skipped the first 200 days of the sample and therefore we cannot examine the debt ceiling crisis experienced in August 2011.

To construct the impulse-response functions and their confidence bounds, we use the MATLAB toolbox MFE Toolbox provided by Prof. Kevin Sheppard (source: https://www.kevinsheppard.com/code/matlab/mfe-toolbox/). Specifically, we estimate the asymptotic confidence bounds (Hamilton 1994) from the error covariance estimator in the VAR (corrected by heteroskedasticity and correlated errors), and the impulse-response functions based on the generalized impulse response of Koop et al. (1996) and Pesaran and Shin (1998). From the former, we obtain the standard errors for the estimated impulse-response coefficient with forecasting horizon H, and the upper (lower) confidence bound is calculated as the impulse-response value for that particular forecasting horizon plus (minus) 1.96 times its standard error.

We are grateful to an anonymous referee for suggesting this robustness analysis.

This measure is constructed by counting the number of US newspaper articles achieved by the NewsBank Access World News database with at least one term from each of the following three categories: (i) “economic” or “economy”; (ii) “uncertain” or “uncertainty”; and (iii) “legislation”, “deficit”, “regulation”, “congress”, “Federal Reserve”, or “White House”. Baker et al. (2016) provide evidence that EPU captures perceived economic policy uncertainty. Source: https://www.policyuncertainty.com.

This index extracts the latent state of macroeconomic activity from a large number of macroeconomic variables (jobless claims, payroll employment, industrial production, personal income less transfer payments, manufacturing and trade sales, and quarterly real gross domestic product) using a dynamic factor model. Source: https://www.philadelphiafed.org/surveys-and-data/real-time-data-research/ads.

Source: https://fred.stlouisfed.org/series/DFF.

We are grateful to an anonymous referee for suggesting this robustness analysis.

We are not aware of a short-term Euro Stoxx 50 implied volatility index at 9-day maturity, so we have added the 2-month maturity, instead, to study the European implied volatility connectedness with a similar set of maturities.

Following Koop and Korobilis (2014), we use the same non-informative initial conditions in the Kalman filter, a decay factor of 0.96 and a forgetting factor of 0.99 (see online appendix in Koop and Korobilis 2014, for the technical details). Without loss of generality, we normalize the series \({Y}_{t}\) to get a faster convergence in the Kalman filter and smoother. This normalization does not have any effect on the connectedness matrix.

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Title: Time connectedness of fear
Authors: Julián Andrada-Félix
Adrian Fernandez-Perez
Fernando Fernández-Rodríguez
Simón Sosvilla-Rivero
Publication date: 26-04-2021
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 3/2022
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-021-02056-w

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