• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.501-512
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• 2014

Stylized facts on asset return are fat-tail, asymmetry, volatility clustering and structure changes. This paper simultaneously captures these characteristics by introducing a multi-regime models: Finite mixture distribution and regime switching GARCH model. Analyzing the daily KOSPI return from $4^{th}$ January 2000 to $30^{th}$ June 2014, we find that a two-component mixture of t distribution is a good candidate to describe the shape of the KOSPI return from unconditional and conditional perspectives. Empirical results suggest that the equality assumption on the shape parameter of t distribution yields better discrimination of heterogeneity component in return data. We report the strong regime-dependent characteristics in volatility dynamics with high persistence and asymmetry by employing a regime switching GJR-GARCH model with t innovation model. Compared to two sub-samples, Pre-Crisis (January 2003 ~ December 2007) and Post-Crisis (January 2010 ~ June 2014), we find that the degree of persistence in the Pre-Crisis is higher than in the Post-Crisis along with a strong asymmetry in the low-volatility (high-volatility) regime during the Pre-Crisis (Post-Crisis).

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.711-732
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• 2013

In this paper, we are interested in finding explicit numerical formulas to evaluate defaultable bonds prices of firms. For this purpose, we use a default intensity whose values depend on the credit rating of these firms. Each credit rating corresponds to a state of the default intensity. Then, this regime switches as soon as one of the credit rating of a firm also changes. Moreover, this regime switching default intensity model allows us to capture well some market features or economics behaviors. Thus, we obtain two explicit different formulas to evaluate the conditional Laplace transform of a regime switching Cox Ingersoll Ross model. One using the property of semi-affine of the model and the other one using analytic approximation. We conclude by giving some numerical illustrations of these formulas and real data estimation results.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.29-42
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• 2018

We combine the integer-valued GARCH(1, 1) model with a generalized regime-switching model to propose a dynamic count time series model. Our model adopts Markov-chains with time-varying dependent transition probabilities to model dynamic count time series called the generalized regime-switching integer-valued GARCH(1, 1) (GRS-INGARCH(1, 1)) models. We derive a recursive formula of the conditional probability of the regime in the Markov-chain given the past information, in terms of transition probabilities of the Markov-chain and the Poisson parameters of the INGARCH(1, 1) process. In addition, we also study the forecasting of the Poisson parameter as well as the cumulative impulse response function of the model, which is a measure for the persistence of volatility. A Monte-Carlo simulation is conducted to see the performances of volatility forecasting and behaviors of cumulative impulse response coefficients as well as conditional maximum likelihood estimation; consequently, a real data application is given.

• Journal of the Korean Society for Precision Engineering
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• v.6 no.2
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• pp.30-39
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• 1989

Variable structure control (VSC) systems control the state vectors using sliding regime (SR) constructed switching logic, switching plane and control law. Saturation function switching logic is used to improve the drawback which occurs in traditional sign function switching logic. Switching plane with time-varying parameter is proposed to improve the drawback which occurs in switching plane with constant parameter and it is suggested the control law which has time-varying parameter. The stability of VSC system controlled by proposed time-varying SR is discussed, and the good control behavior was shown through computer simulation using proposed SR.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.79-95
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• 2020

The globalization of financial markets has broadened investment opportunities. International investors' investment portfolios consist of financial instruments from various countries; consequently, the risks associated with economic dependence among countries should be carefully considered. Step-down equity-linked securities (ELS) are a structured financial product that have recently become popular among Korean investors. Payoffs are based on two or three stock indices from different regions; therefore, dependence between the indices should be reflected in the risk analysis. In this study, we consider a regime-switching copula model to describe the joint behavior of two stock indices- the Eurostoxx50 and the Hang Seng China Enterprises Index (HSCEI). These indices are commonly used as underlying assets of step-down ELS. Using historical data, we analyze the risk associated with step-down ELS through the probabilities of early redemption. A regime-switching copula model can accommodate complicated dependence. Thus, it should be considered in the risk analysis of step-down ELS.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1376
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• 2019

We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1049-1068
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• 2014

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

• East Asian Economic Review
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• v.25 no.2
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• pp.205-230
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• 2021

This study examines the impact of the number of coronavirus cases on regime-switching in stock return volatility. This study documents the empirical evidence that the COVID-19 cases had an asymmetric effect on the regime of stock return volatility. When the stock return is in the low volatility regime, the probability of switching to the high volatility regime in the next trading day increases as the number of cumulative cases increases. In contrast, in the high volatility regime, the effect of cumulative cases on the transition probability is not statistically significant. This study also documents the evidence that the government measures against the pandemic contribute to promoting the high volatility regime of the KOSPI during the pandemic. Besides, this study projects future stock prices through the Monte Carlo simulation based on the estimated parameters and the predicted number of the COVID-19 new cases. Under a scenario where the number of new cases rapidly increases, stock price indices in Korea are expected to be in a downward trend over the next three months. On the other hand, under the moderate scenario and the best scenario, the stock indices are likely to continue to rise.

• International Area Studies Review
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• v.16 no.3
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• pp.53-73
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• 2012

In this study we investigate the ability of the yield spread to predict economic recessions in two Asian economies. For our purpose we use the data from two emerging economies (South Korea and Thailand) that are also known for their openness in terms of exports and imports. We employ both two-regime Markov-Switching model (MS) and three-regime MS model to estimate the probability of recessions during Asian crisis. We found that the yield spread is confirmed to be a reliable recession predictor for Thailand but not for South Korea. The three-regime MS model is better for capturing the Asian financial crisis than two-regime MS model. We also tried to find the duration of economic expansions and recessions. We tested the hypothesis of asymmetric movements of business cycles. The MS results are also compared with that of the standard probit model for comparison. The MS model does not significantly improve the forecasting ability of the yield spread in forecasting business cycles.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.737-757
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• 2011

This work is concerned with an optimal selling rule for a large position of stock in a market. Selling a large block of stock in a short period typically depresses the market, which would result in a poor filling price. In addition, the large selling intensity makes the regime more likely to be poor state in the market. In this paper, regime switching and depressing terms associated with selling intensity are considered on a set of geometric Brownian models to capture movements of underlying asset. We also consider the liquidation strategy to sell much smaller number of shares in a long period. The goal is to maximize the overall return under state constraints. The corresponding value function with the selling strategy is shown to be a unique viscosity solution to the associated HJB equations. Optimal liquidation rules are characterized by a finite difference method. A numerical example is given to illustrate the result.