Regime-Switching Value-at-Risk Using Hidden Markov Models: A Cross-Market Analysis of Emerging and Developed Equity Indices
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Abstract
Accurate risk measurement is essential for fi-nancial stability, particularly in markets where returns fre-quently transition between distinct volatility regimes. Thispaper applies a Hidden Markov Model (HMM) to dailylog returns of three equity indices, namely the JakartaComposite Index (JCI), Nikkei 225, and S&P 500, over theperiod January 2008 to December 2024, covering approx-imately 4,100–4,300 observations per index and multiplemajor stress episodes. Gaussian HMMs with two, three,and four hidden states are estimated, with the BayesianInformation Criterion selecting three states for JCI andNikkei 225, and four states for S&P 500, indicating thatoptimal regime granularity is market-specific. A notablestructural finding is that the JCI and S&P 500 transitionmatrices exhibit near-zero probabilities for direct calm-to-stress transitions, implying that crises are preceded byan intermediate regime of elevated uncertainty. Regimeprobabilities are used to construct a regime-conditionalValue-at-Risk (HMM-VaR), benchmarked against Histori-cal Simulation (HS-VaR) and Student-t GARCH (1,1) VaR(t-GARCH-VaR) using the Kupiec unconditional coveragetest and the Christoffersen conditional coverage test. Sub-period analysis at the 95% confidence level reveals thatduring crisis periods, static methods exceed the nominalviolation rate by up to 2.4 times the margin of adaptivemethods, with HS-VaR violation rates reaching 11.88%(JCI) and 13.55% (S&P 500) against a nominal 5%. During normal periods, HMM-VaR is the only methodthat consistently passes both coverage tests across all threemarkets, with violation rates closely approximating thenominal level (4.90%–5.61%). The findings demonstratethat regime-switching VaR provides superior and moreconsistent risk measurement across diverse market struc-tures, while also revealing that aggregate backtesting canbe misleading due to the cancellation of opposing errorsbetween crisis and normal sub-periods.
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References
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