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Tail-Risk Indicators with Time-Variant Volatility Models: the case of the Chilean Peso

Author

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  • Rodrigo Alfaro
  • Catalina Estefó

Abstract

In this paper we propose a framework for building tail-risk indicators for the Chilean Peso (CLP) based on time-variant volatility models [e.g., Engle (1982), Taylor (1982), Nelson (1991), Heston and Nandi (2000)], which we estimate by combining: (i) daily returns, (ii) option-implied volatility (IV), and (iii) intraday realized volatility (RV). Our empirical results show that the in-sample fit of the models improves when volatility measures (IV or RV) are added. We provide an application of the framework to evaluate extreme scenarios.

Suggested Citation

  • Rodrigo Alfaro & Catalina Estefó, 2025. "Tail-Risk Indicators with Time-Variant Volatility Models: the case of the Chilean Peso," Working Papers Central Bank of Chile 1041, Central Bank of Chile.
  • Handle: RePEc:chb:bcchwp:1041
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    References listed on IDEAS

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    1. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    3. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    5. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
    6. Mozumder, Sharif & Frijns, Bart & Talukdar, Bakhtear & Kabir, M. Humayun, 2024. "On practitioners closed-form GARCH option pricing," International Review of Financial Analysis, Elsevier, vol. 94(C).
    7. Li, Chenxing & Zhang, Zehua & Zhao, Ran, 2024. "Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?," Finance Research Letters, Elsevier, vol. 67(PB).
    8. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    11. Romain Lafarguette & Mr. Romain M Veyrune, 2021. "Foreign Exchange Intervention Rules for Central Banks: A Risk-based Framework," IMF Working Papers 2021/032, International Monetary Fund.
    12. Jinji Hao & Jin E. Zhang, 2013. "GARCH Option Pricing Models, the CBOE VIX, and Variance Risk Premium," Journal of Financial Econometrics, Oxford University Press, vol. 11(3), pages 556-580, June.
    13. Jara, Alejandro & Piña, Marco, 2023. "Exchange rate volatility and the effectiveness of FX interventions: The case of Chile," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 4(2).
    14. Suk Joon Byun & Jung‐Soon Hyun & Woon Jun Sung, 2021. "Estimation of stochastic volatility and option prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(3), pages 349-360, March.
    15. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    16. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    17. Alfaro, Rodrigo & Inzunza, Alejandra, 2023. "Modeling S&P500 returns with GARCH models," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 4(3).
    18. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    19. Luis Gonzales C. & Daniel Oda Z., 2015. "Medición del Riesgo (Neutral) Cambiario Chileno: Incorporación de la Información de Mercado de las Opciones," Notas de Investigación Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 18(3), pages 90-103, December.
    20. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    21. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    22. Christoffersen, Peter & Feunou, Bruno & Jacobs, Kris & Meddahi, Nour, 2014. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 663-697, June.
    23. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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