• 충청수학회지
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• 제26권4호
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• pp.787-791
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• 2013

In this paper we present one factor model of commodity prices with a single jump regime-switching process. And we derive an analytic formula for pricing futures contracts when the parameters of commoditiy process have governed by a Markov regime-switching process.

• Communications for Statistical Applications and Methods
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• 제25권1호
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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 applied mathematics & informatics
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• 제32권5_6호
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• pp.665-673
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• 2014

Power options have payoffs that are determined by the price of the underlying asset raised to some power. In this paper, power options are considered under a regime-switching model which can capture complex asset dynamics by permitting switching between different regimes. The pricing formulas for the Laplace transforms of power options are obtained. The prices of power options are calculated using the formulas and compared with the results of the Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• 제21권6호
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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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• 제31권5_6호
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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.

• 대한산업공학회지
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• 제36권3호
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• pp.203-211
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• 2010

This study examines a cointegrated vector autoregressive (VAR) model where parameters are subject to switch across the regimes in the term structure of interest rates. To employ the regime switching framework, the Markov-switching vector error correction model (MS-VECM) is allowed to the regime shifts in the vector of intercept terms, the variance-covariance terms, the error correction terms, and the autoregressive coefficient parts. The corresponding approaches are illustrated using the term structure of interest rates in the US Treasury bonds over the period of 1958 to 2009. Throughout the modeling procedure, we find that the MS-VECM can form a statistically adequate representation of the term structure of interest rate in the US Treasury bonds. Moreover, the regime switching effects are analyzed in connection with the historical government monetary policy and with the recent global financial crisis. Finally, the results from the comparisons both in information criteria and in forecasting exercises with and without the regime switching lead us to conclude that the models in the presence of regime dependence are superior to the linear VECM model.

• Management Science and Financial Engineering
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• 제19권1호
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• pp.49-52
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• 2013

In this paper we provide a valuation formula for a variance swap with regime switching. A variance swap is a forward contract on variance, the square of realized volatility of the underlying asset. We assume that the volatility of underlying asset is governed by Markov regime-switching process with finite states. We find that the proposed model can provide ease of calculation and be superior to the models currently available.

• Communications for Statistical Applications and Methods
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• 제27권1호
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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.

• 응용통계연구
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• 제27권6호
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• pp.1049-1068
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• 2014

자기회귀 모형(autoregressive model)은 일변량(univaraite) 시계열자료의 분석에서 널리 사용되는 방법 중 하나이다. 그러나 이 방법은 자료에 일정한 추세가 있다고 가정하기 때문에 자료에 분절(structural break)이 존재할 때 적절하지 않을 수 있다. 이러한 문제점을 해결하기 위한 방법으로 국면전환(regime-switching) 모형인 임계자기회귀 모형(threshold autoregressive model)이 제안되었는데 최근 지연 모수(delay parameter)을 포함한 이 국면전환(two regime-switching) 모형으로 확장되어 많은 연구가 활발히 진행되고 있다. 본 논문에서는 이 국면전환 임계자기회귀 모형을 베이지안(Bayesian) 관점에서 살펴본다. 베이지안 분석을 위해 모수적 임계자기 회귀 모형 뿐만 아니라 디리슐레 과정(Dirichlet Process) 사전분포를 이용하는 비모수적 임계자기 회귀 모형을 고려하도록 한다. 두 가지 베이지안 임계자기 회귀 모형을 바탕으로 사후분포를 유도하고 마코프 체인 몬테 카를로(Markov chain Monte Carlo) 방법을 통해 사후추론을 실시한다. 모형 간의 성능을 비교하기 위해 모의실험을 통한 자료 분석을 고려하고, 더 나아가 한국과 미국의 국내 총생산(Gross Domestic Product)에 대한 실증적 자료 분석을 실시한다.

• 국제지역연구
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• 제16권3호
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• pp.53-73
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• 2012

본 논문에서는 금리 스프레드가 두 아시아 국가의 경기불황을 예측할 수 있는가를 살펴보았다. 이를 위해 세계시장에 상대적으로 개방이 많이 되어 있고 무역활동이 활발한 두 개의 신흥경제국가인 한국과 태국을 선정 하였다. 본 논문에서는 두 개의 국면(Two-regime Markov-Switching model)과 세 개의 국면(Three-regime Markov-Switching model)이 있는 마코프 국면 전환 모형을 이용하여 아시아 경제위기의 불황확률을 추정해 보았다. 추정결과 태국의 금리스프레드는 태국의 불황 확률을 반영하였으나 한국의 금리스프레드는 불황 예측을 하지 못하는 것으로 나타났다. 또한, 세 개의 국면이 있는 모형이 두 개의 국면 있는 모형보다 아시아 금융위기의 불황예측에서 우수함을 밝혔다. 또한 본 논문에서는 경기상승과 경기불황이 있을 때 얼마나 지속되는가의 지속성(Duration)을 추정하였다. 이는 경기가 불황으로 움직일 때는 생산이 급격히 감소하는 반면 저점을 찍고 경기가 살아날 때는 생산이 천천히 오른다는 경기불황과 호황의 비대칭적 움직임을 테스트 하였다. 한편 마코프 국면 전환 모형의 결과와 전통적으로 많이 사용되어 왔던 프로빗(Probit) 모형의 결과를 비교 분석 하였다. 마코프 국면전환 모형이 프로빗 모형보다 경기변동의 예측력을 크게 향상시키지는 못하는 것으로 나타났다.