Regime-switching Model Research Articles

Randomization and the valuation of guaranteed minimum death benefits

In this article, we focus on death-linked contingent claims (GMDBs) paying a random financial return at a random time of death in the general case where financial returns follow a regime switching model with two-sided phase-type jumps. We approximate the distribution of the remaining lifetime by either a series of Erlang distributions or a Laguerre series expansion, whose capability to fit the tail of the observed mortality data turns out to be much better than the commonly used series of exponential distributions.More precisely, we develop a Laurent series expansion of the discounted Laplace transform of the subordinated process at an Erlang distributed time, which leads to explicit formulae for European-type GMDB as well as related risk measures such as the Value-at-Risk (VaR) and the Conditional-Tail-Expectation (CTE). We further concentrate upon path-dependent GMDBs with lookback features like dynamic fund protection or dynamic withdrawal benefits, by relying on a Sylvester equation approach. The advantage of our approaches is that our results are of semi-closed form, avoiding numerical Fourier inversion or Monte-Carlo simulation, leading to fast evaluation. This is necessary in risk-management, in particularly for nested simulation in the framework of Solvency II. Several numerical experiments are included.Our results have implications beyond life-insurance and GMDBs, namely in all situations where randomization or Erlangization replaces known quantities, like, for example, model parameters, by random variables. In Finance, it is for example well-known that a random maturity time leads to much more convenient valuation formulas that well approximate its non-random counterpart.

Foreign exchange hedging using regime-switching models: the case of pound sterling

Foreign exchange hedging using regime-switching models: the case of pound sterling

Regime-Switching Model With Adaptive Adjustments for Degradation Prognosis

Inspired by the extreme reliability requirement of complex and ultra-long design lifespan equipment, degradation modeling and prognosis has emerged as a critical and essential technology in prognostics and health management (PHM) because it offers customized and individualized health assessments. However, environments with uncertainty, nonlinear phenomena, and phase-transition (or regime-switching) behavior are coupled together as a bottleneck for the implementation of degradation modeling and prognosis. To this end, this paper proposes a switching state-space model with adaptive adjustments that can adaptively simplify the patterns in original data and provide a unified framework of degradation prognosis with nonlinear phase-transition problems. Finally, some actual bearing data were used to validate the proposed method’s effectiveness. In the validation based on actual wind turbine bearing data, compared with some existing methods, the proposed method reduced the root-mean-square error of the remaining useful lifetime prediction by at least 38%.

An exact and explicit formula for pricing lookback options with regime switching

<p style='text-indent:20px;'>This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on states of the economy described by a continuous-time Markov chain process. We derive an exact, explicit and closed-form solution for European-style lookback options in a two-state regime switching model.</p>

Open-loop equilibrium strategy for mean-variance Portfolio selection with investment constraints in a non-Markovian regime-switching jump-diffusion model

<p style='text-indent:20px;'>This paper is devoted to study the open-loop equilibrium strategy for a mean-variance portfolio problem with investment constraints in a non-Markovian regime-switching jump-diffusion model. Specially, the investment strategies are constrained in a closed convex cone and all coefficients in the model are stochastic processes adapted to the filtration generated by a Markov chain. First, we provide a necessary and sufficient condition for an equilibrium strategy, which involves a system of forward and backward stochastic differential equations (FBSDEs, for short). Second, by solving these FBSDEs, we obtain a feedback representation of the equilibrium strategy. Third, we prove a theorem ensuring the almost everywhere uniqueness of the equilibrium solution. Finally, the results are applied to solve an example of the Markovian regime-switching model.</p>

A multifactor regime-switching model for inter-trade durations in the high-frequency limit order market

Modeling behaviors of inter-trade durations has been an important step to understand the market microstructure. Given that most existing models focused on intraday transaction data, we analyze limit order book (LOB) data in a high-frequency (HF) market and find that stocks’ inter-trade durations follow bimodal distributions peaking at levels of second and millisecond. To characterize this empirical property, we develop a multifactor regime-switching duration (MF-RSD) model, in which the modes of inter-trade durations are characterized as regimes and the transitions of regimes are determined by LOB-factor-dependent transition probability matrices. Using the model, we analyze the impact of LOB factors on inter-trade duration dynamics and find that the bimodal phenomenon is caused by the switchings of traders’ trading strategies between market making and price speculation. Our empirical studies show that the MF-RSD model not only produces good in-sample fit but also outperforms some benchmark models in out-of-sample predictions of inter-trade durations. • Inter-trade durations in high-frequency LOB exhibit a bimodal distribution. • A multifactor regime-switching model is built for inter-trade durations in HF. • The regimes of inter-trade durations are associated with the trader’s behaviors. • Our model has better out-of-sample performance compared with some benchmarks. • The summarized effects of LOB factors reveal principle of market microstructure.

The risk premium in times of financial crisis: an assessment from ICAPM on the MENA region

The purpose of our research is to study the impact of financial crisis on Risk premium evolution for a set of emerging countries of MENA (Middle East and North Africa), giving special attention to the appreciation of the local risk premium in addition to the currency risk premium through the study of the dynamics of the financial integration under two assumptions: perfect integration and partial segmentation. At the methodological level, we test a conditional version of the international model of the financial assets ICAPM of De initially proposed by Adler and Dumas 1983 [Adler, M., & Dumas, B. (1983). International portfolio choice and corporation finance: A synthesis. The Journal of Finance, 38(3), 925-984.]. Our analysis is based on the conditional model of regime change of Bekaert and Harvey (1995) [Bekaert, G., & Harvey, C. R. (1995). Time‐varying world market integration. The Journal of Finance, 50(2), 403-444.], we follow the econometric modeling using the Kalman filter and the Markov regime-switching model with variable transition probabilities.

A second-order ADI method for pricing options under fractional regime-switching models

<abstract><p>Fractional regime-switching option models have recently attracted much attention because they can capture the sudden state movement of the market, and deal with the non-stationary behavior. A second-order numerical scheme is proposed to solve the regime-switching option pricing models with fractional derivatives in space. The sufficient conditions of the stability and convergence of the proposed scheme are studied in details. An alternating direction implicit (ADI) method is implemented to accelerate the computation in every time layer. Numerical experiments are presented to verify the convergence and efficiency of the proposed method, compared with classical Krylov subspace solvers.</p></abstract>

단일변량 모형을 이용한 토지가격 예측력 비교

The Purpose of this paper is to compare different models’ forecasting performance of ARIMA, ARIMA-GARCH, ARIMA-RS models in Korean land market covering the period from the first quarter of 1987 to the first quarter of 2022. I carry out in-sample and out-of-sample forecasting power to Korean land price index. For the comparison of forecast powers, I calculate root mean squared forecast errors and mean absoute forecast errors for each forecasting horizon of the second quarter of 2021 to the first quarter of 2022. I test the statistical signification of the predictive comparison results using DM test. The empirical results are as follows: First, the forecasting power of the ARIMA(1,1,0)-GARCH model is the best in all horzions in- and out-of-sample. Second, within the sample, the forecasting power of the ARIMA(1,0) model is relatively better than that of the ARIMA(2,1,0) model, but outside the sample, it is the opposite. In addition, within the sample, the forecasting power of the ARIMA(3,1,0)-RS model is relatively better than that of the ARIMA(1,0)-RS model, but it is contrary to the sample. Third, it is found that the predictive power of the regime-switching model(RSM) is significantly decreased in all predictive horzions in- and out-of-sample. In order to stabilize the real estate market, it is necessary to consider the ARIMA(1,0)-GARCH model as an alternative to the prediction model.

Forecasting the real prices of crude oil: What is the role of parameter instability?

Parameter instability due to potential structural breaks is an important problem affecting out-of-sample forecasting performance of econometric models. This paper uses four types of methods addressing parameter instability, including rolling window, regime switching model, time-varying parameter model, and the time-dependent weighted least squares. The hyperparameters in each method which control the degree of parameter variation are determined via a simple machine learning approach of cross-validation and forecast combination. Our results show significant improvement in predictability of oil prices using these methods accounting for parameter instability except the rolling window method. Forecast combination for models with different hyperparameters produces more robust results than the cross-validation selecting the ex-ante optimal hyperparameters.

How does economic policy uncertainty drive time–frequency connectedness across commodity and financial markets?

This study provides novel insight to the prior literature on the time–frequency connectedness across commodity and financial markets while considering the effect of economic policy uncertainty (EPU). We utilize DY and BK methods combined with the rolling window technique to examine how the connectedness varies over time and across frequencies. Subsequently, we establish regime-switching models to evaluate the influence of EPU on the connectedness and provide implications under different economic states. Our empirical results unveil robust short-term information, volatility, or risk transmission among commodity and financial markets, as they are the main contributors and receivers of shocks, especially during the crisis. Moreover, we identify EPU as a remarkable driver of the interactions among these markets in static and switching regimes. Finally, the optimal weight and hedge ratio responses to EPU are regime-dependent and EPU is more economically important in determining short-term investment. Our findings present vital implications that all market participants should consider the EPU level and prevailing economic conditions when selecting hedging strategies.

American options pricing under regime-switching jump-diffusion models with meshfree finite point method

In an incomplete market construction and by no-arbitrage assumption, the American options pricing problem under the jump-diffusion regime-switching process is formulated by a variational form of coupled partial integro-differential equations. In this paper, a valuation algorithm is developed for American options when the dynamics of underlying assets follow the regime-switching jump-diffusion processes. Using the fact that the price of an American option under jump-diffusion regime-switching processes is formulated by a collection of coupled variational partial integro-differential equations with the free boundary characteristic, we combine the moving least-squares approximation with an operator splitting method to treat American constraints. Numerical experiments with American options under three, five, and seven regimes demonstrate the efficiency and effectiveness of our computational scheme for pricing American options under the regime-switching models.

A revisit to sovereign risk contagion in eurozone with mutual exciting regime-switching model

This paper proposes a new mutual exciting regime-switching model where crises can spread contagiously across countries. Each country has its own hidden stochastic process that determines whether it is in a normal or crisis regime. The mutual-excitation component allows interactions in the Markov chains, and a crisis in one country could increase the likelihood of a crisis in another country. Using this new approach, I revisit the sovereign risk contagion in the euro area. I find striking shifts in market pricing functions for the sovereign bond spreads. Multi-country contagion plays a dominant role in driving such shifts, while common risk factors and country-specific fundamentals are less important.

Stock market volatility predictability in a data-rich world: A new insight

This study develops a shrinkage method, LASSO with a Markov regime-switching model (MRS-LASSO), to predict US stock market volatility. A set of 17 well-known macroeconomic and financial factors are used. The out-of-sample results reveal that the MRS-LASSO model yields statistically and economically significant volatility predictions. We further investigate the predictability of MRS-LASSO with respect to different market conditions, business cycles, and variable selection. Three factors (equity market returns, a short-term reversal factor, and a consumer sentiment index) are the most frequent predictors. To investigate the practical implications, we construct the expected variance risk premium (VRP) by using volatility forecasts generated from the LASSO and MRS-LASSO models to forecast future stock returns and find that those models are also powerful.

Time-Varying Risks in ESG Equity Investments during the COVID-19 Pandemic

We analyse the time-varying risks associated with ESG equity investments in developed, emerging and BRIC equity markets in the wake of the COVID-19 pandemic which has once again underscored the vulnerability of the financial space to shocks. For this purpose, the nonlinear Markov regime switching model is used to analyse the time-varying beta and idiosyncratic volatility of the World ESG Leaders, Emerging Markets ESG Leaders and BRIC ESG Leaders equity portfolios provided by Morgan Stanley Capital International (MSCI). To further complement the evidence, we also refer to the global ACWI ESG Leaders index which represents both developed markets and emerging markets. The evidence suggests that the risk dynamics of the ESG equity portfolios representing the developed markets, emerging markets, BRIC markets and the global markets are distinct during the crisis and calm period. ESG equity investments have higher systematic risk exposure in emerging markets and BRIC markets during the crisis period as well as calm periods. On the other hand, ESG equity investments have higher systematic risk exposure during the crisis period only in case of developed markets. The results of the study provide insights on the time -varying risk dynamics of ESG investing and thus, facilitate informed investment decisions.

Macroeconomic Determinants of Credit Risk: Evidence on the Impact on Consumer Credit in Central and Eastern European Countries

Although empirical studies show that different types of loans have different risks (moreover, consumer credit risk is higher compared to other types of loans), it is common to study the credit risk of the banking sector as a whole, or of an individual bank’s whole loan portfolio, and the macro-economic factors affecting it (without grouping them by type of loan). Thus, an analysis of the credit risk of the whole loan portfolio (measured by all non-performing loans) is insufficient. Therefore, the aim of this research is to identify the macroeconomic determinants of the consumer loan credit risk and quantitatively assess their impact in Central and Eastern European countries. After the analysis of scientific literature in the field of credit risk determinants, a detailed classification of factors influencing banking credit risk is proposed. The distinguishing feature of the classification is that the factors influencing credit risk are classified at five different levels; twelve groups of general macroeconomic conditions variables were selected as the potential factors of NPLs. This classification can be useful to better understand and investigate the factors influencing banking credit risk for the whole loan portfolio (in the same way as the factors that affect the credit risk of different types of loans, e.g., consumer loans). Using the methods of constant, fixed and random-effects panel analysis, simple OLS, least squares with breakpoints regression analysis and Markov regime-switching models, the impact of the macroeconomic variables from twelve separate groups is evaluated. The data from 11 CEE countries are used, and the period from 2008 to 2020 is covered. The results of this assessment reveal that in the group of CEE countries, such variables as GDP and labour market variables appeared to have contributed to the increase in the share of non-performing consumer loans, while inflation and real estate market variables were related to the decrease in consumer NPLs; at the same time, the impact of variables form other groups appeared to be mixed-nature or insignificant. The results of this research are useful in that they allow the identification of the most important determinants of consumer loan credit risk and thus allow making assumptions about NPL changes due to the changing macroeconomic situation. In the case of Lithuania, this kind of study (assessment of macroeconomic determinants of consumer loan credit risk) was conducted for the first time. Consumer loan credit risk assessment is especially relevant in an increasing interest rate environment, and deeper analysis can help banks and other financial institutions to manage credit risk. On the other hand, a better understanding of the main influencing factors of the macroeconomic environment can help central banks and other official institutions take appropriate monetary and fiscal policy decisions to ensure a good credit transmission channel for sustainable economic growth.

Environmental degradation, energy use, and globalization in Ghana: New empirical evidence from regime switching and neural network autoregression models

This study investigates the nexus between environmental degradation, energy use, and globalization using Markov-switching (MS) models which previous studies on Ghana have not considered. We utilize this method because of its ability to detect possible non-linear relationships. The Neural Network Autoregression (NNAR [p, k]) model is also employed to predict carbon-dioxide (CO2) emissions for the country over the next decade. In doing so, secondary time-series data on CO2 releases, per capita gross domestic product (GDP), energy use, and KOF (Konjunkturforschungsstelle) globalization indexes spanning the period 1971–2016 are employed. The results from all three MS estimations show no support for the existence of the Environmental Kuznets Curve (EKC) in Ghana. The results further demonstrate that energy use and an overall globalization index result in more CO2 emissions causing deterioration of the environment. Economic globalization is also revealed to harm the environment whereas social and political globalization have different effects in different regimes. The forecast results from the NNAR (14, 8) estimation also indicate that Ghana will have an upward trajectory of CO2 discharge for the next decade. The implication of the findings is that there is an urgent need for strengthening and/or revising environmental policies in the country with greater focus on mitigation strategies in line with the Paris Agreement and Kyoto Protocol. These measures are likely to curb CO2 emissions as the economy expands. Recommendations and areas for further research to improve the environmental quality in Ghana are also provided for policy consideration.

WITHDRAWN: Risk-Return Trade-off in International Stock Returns: Skewness and Business Cycles

The fundamental risk-return relation is examined with a flexible regime switching model combining the impact of skewness and business cycle regimes in stock returns. Key methodological and empirical findings point out the need for a highly nonlinear and non-Gaussian model to get a reliable picture on the risk-return relationship. With an international dataset of major countries to global financial markets, the empirical results show that accounting especially for skewness patterns leads to the expected positive risk-return relation, which is importantly also maintained over different business cycle conditions.

Asymptotic properties of the maximum likelihood estimator in regime-switching models with time-varying transition probabilities

Summary Time-varying transition probability (TVTP) regime-switching models extend the constant regime transition probability in Markov-switching models to include information from observations. We show consistency and asymptotic normality of the maximum likelihood estimator (MLE) in general TVTP regime-switching models where the conditional distribution of $Y_t$ depends on lagged regimes. Consistency of the MLE is also shown under misspecification. The assumptions are verified in regime-switching autoregressive models with widely applied TVTP specifications. A simulation study examines the finite-sample distributions of the MLE and compares the asymptotic variance estimates constructed from the Hessian matrix and the outer product of the score. The simulation results favour the latter. As an empirical example, we compare three leading economic indicators in terms of describing U.S. industrial production.

Intensity and Direction of Volatility Spillover Effect in Carbon–Energy Markets: A Regime-Switching Approach

This paper advances a volatility-regime-switching mechanism to investigate the intensity and direction of the volatility spillover effect in carbon–energy markets. Switching between a low-volatility (LV) and high-volatility (HV) regime, our mechanism involves a four-state system (i.e., LV-LV, HV-LV, LV-HV and HV-HV). Our findings are listed as follows: First, the highest EUA–WTI correlation occurs when both are in an HV regime (i.e., HV-HV), revealing the intensity of the volatility spillover effect. Second, when EUA and WTI are experiencing an opposite volatility regime (one in LV and the other in HV), a higher EUA–WTI correlation is observed when WTI is in an HV regime. This result implies that the direction of the volatility spillover effect is from the energy market to the carbon market. Third, the regime-switching model involving the non-uniform volatility–correlation relations outperforms the conventional GARCH and DCC models in volatility forecasting and portfolio construction.