10.14489/vkit.2022.05.pp.026-035

DOI: 10.14489/vkit.2022.05.pp.026-035

Глушенко А. А., Куликов А. В.
РАЗРАБОТКА МОДЕЛИ С МАРКОВСКИМ ПЕРЕКЛЮЧЕНИЕМ РЕЖИМОВ ДЛЯ АНАЛИЗА КОЛИЧЕСТВА ДЕФОЛТОВ КОМПАНИЙ СПЕКУЛЯТИВНОГО И ИНВЕСТИЦИОННОГО РЕЙТИНГОВ
(с. 26-35)

Аннотация. Построена комбинированная модель с переключениями режимов, учитывающая как информацию о количестве дефолтов спекулятивного и инвестиционного класса, так и статистику VIX. Проведен бэктестинг модели и построен прогноз о количестве дефолтов в 2021 г. на основе параметров модели и информации о VIX.

Ключевые слова: кредитный рейтинг; дефолт; модель с марковской сменой режима; VIX; инвестиционный рейтинг; спекулятивный рейтинг.

Glushenko A. A., Kulikov A. V.
MARKOV REGIME-SWITCHING MODEL DEVELOPMENT FOR NUMBER OF DEFAULTS OF INVESTMENT AND SPECULATIVE GRADE ANALYSIS
(pp. 26-35)

Abstract. In this paper the Markov regime-switching model was constructed for the main classes of credit ratings – speculative and investment. Estimates of the model parameters were obtained based on statistics on credit ratings and the number of defaults from the annual reports of S&P Global. The VIX volatility index was taken into account for a more accurate prediction of the probability of default. A similar model was constructed for the average annual value of VIX. Also a combined regime-switching model was considered, taking into account both statistics on the number of defaults of the speculative and investment grade and statistics on the average annual value of the VIX index for the period from 1990 to 2019. 10 parameters were estimated using the maximum likelihood method: the probability of the onset of a crisis and the probability of overcoming it; the probability of default in a crisis and non-crisis year for counterparties of the investment and speculative rating classes; the mathematical expectation and standard deviation of the VIX value in a crisis and non-crisis year. Two-stage backtesting of these models was carried out based on the obtained values of the parameter estimates. The first step was to check if the number of defaults falls between the quantiles of a mixed distribution consisting of a mixture of two binomials for the number of defaults and a mixture of two Gaussians for the VIX value. The second step was to check whether the number of misses in the first step falls within the two-sided confidence intervals of the binomial distribution. Finally, the number of defaults in 2020 and 2021 was forecasted and a comparison was made of the forecast for 2020 with the real numbers of defaults from the S&P Global report 2020.

Keywords: Credit rating; Default; Markov regime-switching model; VIX; Investment rating; Speculative rating.

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А. А. Глушенко, А. В. Куликов (Московский физико-технический институт (национальный исследовательский университет), Долгопрудный, Россия) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript

Eng

А. A. Glushenko, A. V. Kulikov (The Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript

+ - Библиографический список (References) Click to collapse

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1. Kuepper J. CBOE Volatility Index (VIX) Definition. Investopedia. URL: https://www. investopedia. com/terms/v/vix.asp (дата обращения: 20.04.2022).
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5. Maringer D., Ramtohul T. Regime-Switching Recurrent Reinforcement Learning for Investment Decision Making. Universitӓt Basel, 2011. URL: https://link.springer.com/article/10.1007/s10287-011-0131-1 (дата обращения: 20.04.2022).
6. Papanicolaou A., Sircar R. A Regime-Switching Heston Model for VIX and S&P 500 Implied Volatilities. Quantitative Finance, 2013. URL: https:// papers.ssrn.com/sol3/papers.cfm?abstract_id=2164500 (дата обращения: 20.04.2022).
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Eng

1. Kuepper J. CBOE Volatility Index (VIX) Definition. Investopedia. Available at: https://www.investopedia. com/terms/v/vix.asp (Accessed: 20.04.2022).
2. Staff C. (2019). Whitepaper: Cboe Volatility Index. Available at: http://www.cboe.com/micro/vix/vix-white.pdf (Accessed: 20.01.2022).
3. Hamilton J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, Vol. 57, (2), pp. 357 ‒ 384. Available at: http://www.jstor.org/stable/1912559 (Accessed: 20.04.2022).
4. Huisman R., Mahieu R. (2003). Regime Jumps in Electricity Prices. Erasmus University Rotterdam. Available at: https://core.ac.uk/download/pdf/43314909.pdf (Accessed: 20.04.2022).
5. Maringer D., Ramtohul T. (2011). Regime-Switching Recurrent Reinforcement Learning for Investment Decision Making. Universitӓt Basel. Available at: https://link.springer.com/article/10.1007/s10287-011-0131-1 (Accessed: 20.04.2022).
6. Papanicolaou A., Sircar R. (2013). A Regime-Switching Heston Model for VIX and S&P 500 Implied Volatilities. Quantitative Finance. Available at: https:// papers.ssrn.com/sol3/papers.cfm?abstract_id=2164500 (Accessed: 20.04.2022).
7. Goutte S., Ismail A., Pham H. (2017). Regime-Switching Stochastic Volatility Model: Estimation and Calibration to VIX options. HAL. Available at: https://hal. archives-ouvertes.fr/hal-01212018/file/RS_Vol_AMFrev. pdf (Accessed: 20.04.2022).
8. Supervisory Framework for the Use of “Back-testing” in Conjunction with the Internal Models Approach to Market Risk Capital Requirements. Available at: https://www.bis.org/publ/bcbs22.htm (Accessed: 20.04.2022).

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