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Structural GARCH: The Volatility-Leverage Connection

Author

Listed:
  • Robert Engle

    (New York University Stern School of Business)

  • Emil Siriwardane

    (Office of Financial Research)

Abstract
We propose a new model of volatility where financial leverage amplifies equity volatility by what we call the "leverage multiplier." The exact specification is motivated by standard structural models of credit; however, our parametrization departs from the classic Merton (1974) model and can accommodate environments where the firm's asset volatility is stochastic, asset returns can jump, and asset shocks are nonnormal. In addition, our specification nests both a standard GARCH and the Merton model, which allows for a statistical test of how leverage interacts with equity volatility. Empirically, the Structural GARCH model outperforms a standard asymmetric GARCH model for approximately 74 percent of the financial firms we analyze. We then apply the Structural GARCH model to two empirical applications: the leverage effect and systemic risk measurement. As a part of our systemic risk analysis, we define a new measure called "precautionary capital" that uses our model to quantify the advantages of regulation aimed at reducing financial firm leverage.

Suggested Citation

  • Robert Engle & Emil Siriwardane, 2014. "Structural GARCH: The Volatility-Leverage Connection," Working Papers 14-07, Office of Financial Research, US Department of the Treasury.
    • Handle: RePEc:ofr:wpaper:14-07
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    3. Özbekler, Ali Gencay & Kontonikas, Alexandros & Triantafyllou, Athanasios, 2021. "Volatility forecasting in European government bond markets," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1691-1709.
    4. Gao, Jiti & Peng, Bin & Wu, Wei Biao & Yan, Yayi, 2024. "Time-varying multivariate causal processes," Journal of Econometrics, Elsevier, vol. 240(1).
    5. Gemmill, Gordon & Marra, Miriam, 2019. "Explaining CDS prices with Merton’s model before and after the Lehman default," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 93-109.
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    7. Durrani, Agha & Ongena, Steven & Ponte Marques, Aurea, 2022. "The certification role of the EU-wide stress testing exercises in the stock market. What can we learn from the stress tests (2014-2021)?," Working Paper Series 2711, European Central Bank.
    8. Forte, Santiago & Lovreta, Lidija, 2023. "Credit default swaps, the leverage effect, and cross-sectional predictability of equity and firm asset volatility," Journal of Corporate Finance, Elsevier, vol. 79(C).

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    Keywords

    Structural GARCH; Volatility; Leverage;
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