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A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes

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  • Giuseppe Orlando
  • Michele Bufalo

Abstract

This work aims to forecast (over 1, 5, and 15 years) the extremes, the expected value, and the volatility of natural disasters occurrences. To achieve this objective, we adopt a generalized two‐factor square‐root model linking together occurrences and volatility through stochastic correlation (Brownian motion). We use a generalized Pareto distribution (GPD) to forecast the maximum number of occurrences as a measure of value at risk (VaR). The results are checked in terms of accuracy, compared versus some baseline models (i.e., the Poisson process and the extreme value model) and backtested.

Suggested Citation

  • Giuseppe Orlando & Michele Bufalo, 2022. "A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1608-1622, December.
    • Handle: RePEc:wly:jforec:v:41:y:2022:i:8:p:1608-1622
    DOI: 10.1002/for.2880
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    References listed on IDEAS

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    1. Giuseppe Orlando & Rosa Maria Mininni & Michele Bufalo, 2020. "Forecasting interest rates through Vasicek and CIR models: A partitioning approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(4), pages 569-579, July.
    2. Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
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    4. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Giuseppe Orlando & Michele Bufalo, 2021. "Interest rates forecasting: Between Hull and White and the CIR#—How to make a single‐factor model work," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1566-1580, December.
    7. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    8. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
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    11. Ju-Liang Jin & Jian Cheng & Yi-Ming Wei, 2008. "Forecasting flood disasters using an accelerated genetic algorithm: Examples of two case studies for China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 44(1), pages 85-92, January.
    12. Giuseppe Orlando & Rosa Maria Mininni & Michele Bufalo, 2019. "Interest rates calibration with a CIR model," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 20(4), pages 370-387, September.
    13. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
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    1. Willi Semmler & Fabio Della Rossa & Giuseppe Orlando & Gabriel R. Padro Rosario & Levent Kockesen, 2023. "Endogenous Economic Resilience, Loss of Resilience, Persistent Cycles, Multiple Attractors, and Disruptive Contractions," Working Papers 2309, New School for Social Research, Department of Economics.

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