Regime-switching Process Research Articles

American Option Valuation Under the Framework of CGMY Model with Regime-Switching Process

American Option Valuation Under the Framework of CGMY Model with Regime-Switching Process

Fintech industry risk: does investor attention matter?

ABSTRACT The Fintech industry risk challenges the stability of China’s financial system. This paper makes the first attempt to capture the dynamics of the Fintech industry risk, represented by Fintech stock volatility, from the investor attention perspective. The novelty of this paper is that we fully consider the regime changes in the Fintech industry risk by adopting the AR-MS-GARCH-MIDAS with the Markov regime-switching process incorporated in the short-run volatility component, long-run volatility component, or both. We find that (1) Fintech industry risk is subject to structural breaks, (2) higher investor attention tends to alleviate the Fintech stock volatility, while the negative impact strengthens when the industry is in volatile condition, (3) investor attention contributes to improving the accuracy of the Fintech stock volatility forecasting, (4) considering the structural breaks of investor attention is important in volatility forecasting. We enrich the literature on the Fintech industry risk regulation, stock volatility forecasting, and the attention allocation theory.

Oil price shocks and macroeconomic dynamics in resource-rich emerging economies under regime shifts

How do global oil price fluctuations affect macroeconomic activity and monetary policy in resource-rich emerging economies? This paper tackles this question by developing a unified emerging market/rest-of-the-world DSGE framework featuring Ricardian and Non-Ricardian households, an oil-producing sector, a fuel subsidy programme, and a regime-switching process. The model is estimated using Bayesian methods, allowing us to be agnostic regarding regime shifts in the monetary policy rule and oil price volatility. Using data for Nigeria, we find substantial empirical support for the regime-switching behaviour and discuss how macroeconomic implications of oil price shocks may vary depending on the nature of the shock, monetary policy responses, and the fuel subsidy policy in place. Apart from providing important insights into the monetary policy transmission mechanism, the paper offers a novel, flexible, and functional model for future policy analysis, especially in resource-rich emerging countries.

Feller property of regime-switching jump diffusion processes with hybrid jumps

The transition kernel of an ℝ n -valued diffusion or jump diffusion process {X t } is known to satisfy the Feller property if {X t } is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X t } is the solution of an SDE whose coefficients depend on a state-dependent regime-switching process {θ t }. In this paper it is shown that pathwise uniqueness and the Feller property are satisfied under mild conditions for a regime-switching jump diffusion process {X t , θ t } with hybrid jumps, i.e. jumps in {X t } that occur simultaneously with {θ t } switching.

Stochastic DDM with regime–switching process

This paper introduces a stochastic dividend discount model with regime–switching and conditional heteroscedasticity. We obtain formulas, corresponding to a default probability and $ \ell $-th moment of a random stock price of a company. Next, we connect option pricing, hedging, and equity–linked life insurance products to the stochastic dividend discount model. Also, the paper provides maximum likelihood estimators of parameters of the stochastic dividend discount model. Finally, we present numerical results for the equity–linked life insurance products in the case of Walmart.

Modeling Long Memory and Regime Switching with an MRS-FIEGARCH Model: A Simulation Study

Recent research suggests that long memory can be caused by regime switching and is easily confused with it. However, if the causes of confusion were properly controlled, they could be distinguished. Motivated by this idea, our study aims to distinguish between the long memory and regime switching of financial volatility. We firstly modeled the long memory and regime switching of volatility using the Fractionally Integrated Exponential GARCH (FIEGARCH) and Markov Regime-Switching EGARCH (MRS-EGARCH) frameworks, respectively, and performed a simulation study on their finite-sample properties when innovations followed a non-normal distribution. Subsequently, we demonstrated the confusion between the FIEGARCH and MRS-EGARCH processes using simulations. A recent study theoretically proved that the time-varying smoothing probability series can induce the presence of significant long memory in the regime-switching process. To control for its effect, the two-stage two-state FIEGARCH and MRS-FIEGARCH frameworks are proposed. The Monte Carlo studies showed that both frameworks can effectively distinguish between the pure FIEGARCH and pure MRS-EGARCH processes. When the MRS-FIEGARCH model was further employed to fit series generated with the MRS-FIEGARCH process, it outperformed the ordinary FIEGARCH model. Finally, an empirical study of NASDAQ index return was conducted to demonstrate that our MRS-FIEGARCH model can provide potentially more reliable long-memory estimates, identify the volatility states and outperform both the FIEGARCH and MRS-EGARCH models.

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.

Stochastic modeling and adaptive forecasting for parking space availability with drivers’ time-varying arrival/departure behavior

Parking space availability is valuable information to travelers. This paper aims at modeling drivers’ behavioral changes in arrivals/departures over time of day and developing an adaptive forecasting approach for parking space availability. We propose a stochastic model that consists of two inter-connected Markov processes. First, the lower level of the model focuses on the parking behavior within a short time period, based on conventional M/M/C/C queueing theory with the assumption of fixed arrival and parking rates. Next, to account for the behavioral changes in drivers’ arrivals/departures over a longer time period (e.g. time of day), we incorporate a Markov regime switching process to describe the regime switching mechanism of the arrival/departure behavior. The integrated model leads to an adaptive forecasting formula with time-varying forecasting coefficients adaptively adjusted based on the arrival/departure regimes. We investigate two real traffic applications to illustrate the developed stochastic model and to test the performance of the adaptive forecasting method using out-of-sample data.

Risk-sensitive credit portfolio optimization under partial information and contagion risk

This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we connect the control problem to a quadratic BSDE with jumps, in which the driver term is nonstandard and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and proving uniform a priori estimates, we obtain the existence of a solution to the BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

The Pricing Model of Pension Benefit Guaranty Corporation Insurance with Regime-Switching Processes

This paper aims to evaluate Pension Benefit Guaranty Corporation (PBGC) insurance values through regime-switching models. We separate periods of the economy with faster growth from those with slower growth to observe long-term trends in the economy. We derive a fair PBGC insurance pricing formula under distress termination and intervention termination using regime-switching processes. We set parameters by estimating the S&P 500 index and one-year treasury bills via expectation maximization particle swarm optimization (EM-PSO)-Gradient, which is an extension of the EM-Gradient method. Then, we conduct sensitivity analysis to investigate the impact of model parameters on insurance values. According to the maximum likelihood estimation results, the Akaike information criterion (AIC) and Bayesian information criterion (BIC) estimators show that the regime-switching process has better goodness of fit than the geometric Brownian motion. Scenario analysis also supports the adequacy of our pricing formula.

The dynamics of money velocity

ABSTRACT The dynamic of money velocity has changed gradually, influencing how macroeconomic shocks affect money velocity. This paper examines the response of money velocity to the external shocks in a system of equations, where money velocity, real output growth, money growth volatility, expected inflation, and risk premium are jointly determined. The regime-switching behaviour of money velocity is then examined through a Bayesian threshold approach. The main finding suggests that money velocity drops significantly after negative output and expected inflation shocks, followed by a sudden increase. In addition, the regime-switching process distinguishes the deterministic and stochastic behaviour of money velocity.

Optimal Trading Algorithms under Regime Switching

In this article, the author is concerned with the problem of efficiently trading a large position in the marketplace when the stock price dynamic follows a regime-switching process. If the execution of a large order is not done properly, this will certainly lead to large losses. Given that the execution of a large position may take several trading days, it is therefore reasonable to assume that the market microstructure may change during the execution of the order. To address this possibility, the author assumes that the stock price follows a regime-switching model. This article is particularly interested in trading algorithms that track market benchmarks such as the volume-weighted average price (VWAP) and the minimum execution shortfall. The author proposes trading algorithms that break the execution order into small pieces and execute them over a predetermined period of time so as to minimize the overall execution shortfall or exceed the overall market VWAP. The underlying problem is formulated as a discrete-time stochastic optimal control problem with resource constraints. The value function and optimal trading strategies are derived in closed form. Numerical simulations with market data are reported to illustrate the pertinence of the approach.

Optimal portfolio and consumption for a Markovian regime-switching jump-diffusion process

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases. doi:10.1017/S1446181121000122

Sovereign contagion risk measure across financial markets in the eurozone: a bivariate copulas and Markov Regime Switching ARMA based approaches

This paper analyzes sovereign risk contagion across financial markets in the eurozone during and after the European debt crisis. A particular focus is made on the causal impact of pre-Brexit and Covid-19 pandemic on the dependence between European markets. We use data set from 28 February 2008 to 11 March 2021 and combine copulas and MRS-ARMA techniques to measure dependence across financial markets and assessing asymmetric dependence structure and regime switching process. We develop a dynamic Kendall’s tau correlation and provide evidence of time-varying dependence structure between several pairwise markets. The dependence structure shows a sharp rise on 23 June 2016, day of the referendum on Brexit. Results indicates that Covid-19 pandemic has intensified dependence and sovereign risk spillovers between sovereign CDS European markets. Significant time-varying characteristics of dynamic dependence structures suggests that fund managers and investors should consider in their investment strategies to manage systemic risk and high-risk investment. The identification of dependence structure regime between global financial markets would enhance response to major crises by investors and policy makers.

Numerical Method for a System of PIDEs Arising in American Contingent Claims under FMLS Model with Jump Diffusion and Regime-Switching Process

This paper investigates a numerical method for solving fractional partial integro-differential equations (FPIDEs) arising in American Contingent Claims, which follow finite moment log-stable process (FMLS) with jump diffusion and regime switching. Mathematically, the prices of American Contingent Claims satisfy a system of d problems with free-boundary values, where d is the number of regimes of the market. In addition, an optimal exercise boundary is needed to setup with each regime. Therefore, a fully implicit scheme based on the penalty term is arranged. In the end, numerical examples are carried out to verify the obtained theoretical results, and the impacts of state variables in our model on the optimal exercise boundary of American Contingent Claims are analyzed.

A Markov Regime Switching Model for Ultra-Short-Term Wind Power Prediction Based on Toeplitz Inverse Covariance Clustering

The rapid development of wind energy has brought a lot of uncertainty to the power system. The accurate ultra-short-term wind power prediction is the key issue to ensure the stable and economical operation of the power system. It is also the foundation of the intraday and real-time electricity market. However, most researches use one prediction model for all the scenarios which cannot take the time-variant and non-stationary property of wind power time series into consideration. In this paper, a Markov regime switching method is proposed to predict the ultra-short-term wind power of multiple wind farms. In the regime switching model, the time series is divided into several regimes that represent different hidden patterns and one specific prediction model can be designed for each regime. The Toeplitz inverse covariance clustering (TICC) is utilized to divide the wind power time series into several hidden regimes and each regime describes one special spatiotemporal relationship among wind farms. To represent the operation state of the wind farms, a graph autoencoder neural network is designed to transform the high-dimensional measurement variable into a low-dimensional space which is more appropriate for the TICC method. The spatiotemporal pattern evolution of wind power time series can be described in the regime switching process. Markov chain Monte Carlo (MCMC) is used to generate the time series of several possible regime numbers. The Kullback-Leibler (KL) divergence criterion is used to determine the optimal number. Then, the spatiotemporal graph convolutional network is adopted to predict the wind power for each regime. Finally, our Markov regime switching method based on TICC is compared with the classical one-state prediction model and other Markov regime switching models. Tests on wind farms located in Northeast China verified the effectiveness of the proposed method.

Risk spillovers and hedge strategies between global crude oil markets and stock markets: Do regime switching processes combining long memory and asymmetry matter?

This paper investigates risk spillovers and hedge strategies between global crude oil markets and stock markets. In the paper, we propose a multivariate long memory and asymmetry GARCH framework that integrates state-dependent regime switching in the mean process with multivariate long memory and asymmetry GARCH in the variance process. Our results first show that there are linear risk spillovers running from the US stock markets to the WTI oil market in the short term. However, the linear risk spillover effect running from the oil market to the US stock market can only exist in the long term. In addition, there is a bidirectional linear risk spillover effect between the European stock markets and the Brent oil market in the short and long terms. Furthermore, there is no linear risk spillover effect between the Dubai oil market and the Chinese stock market. Second, the nonlinear risk spillovers running from the WTI oil market to the US stock market can be found in the tranquil regime. Moreover, there is also a nonlinear risk spillover effect running from the European stock markets to the Brent oil market in the tranquil regime. In addition, the nonlinear risk spillover effect running from the Brent oil markets to the European stock market can be found in the crisis regime. Furthermore, there is bidirectional nonlinear Granger causality between the Dubai crude oil market and the Chinese stock market in the tranquil regime. Finally, dynamic hedge effectiveness shows that the regime switching process combined with long memory and asymmetry behavior seems to be a plausible and feasible way to conduct hedge strategies between the global crude oil markets and stock markets.

On a class of non-zero-sum stochastic differential dividend games with regime switching

This paper investigates a class of non-zero-sum stochastic differential game problems between two insurance companies. The surplus process of each company is modeled by a Brownian motion where drift and volatility depend on the continuous-time Markov regime switching process. Both companies have the option of paying dividends. The objective is to maximize the expected discount utility of surplus relative to a reference point for each insurer, the gains brought by the insurer’s own dividend payout, and the losses incurred by the dividend payment of the competitor. The gains and losses are proportional to the amount of corresponding dividend payment. To find the optimal dividend policy, we relate this singular control problem to a stopping game. Further, we prove the link based on the verification theorem and show that value functions of the non-zero-sum stochastic differential problem can be derived by integrating value functions of a stopping game. Finally, we apply our results to the case with two regimes and the case without regime switching. Numerical examples are also provided.

Statistical filtering algorithms based on the maximum cross section method for stochastic systems with regime switching

New statistical algorithms are formed to estimate the state vector of stochastic systems with regime switching. These algorithms are based on the particle method, i.e., on numerical methods for solving stochastic differential equations, methods for modeling conditional Markov processes with a finite set of states, and methods for calculating weights. An important part of proposed algorithms is the use of the maximum cross section method and its modification, which allows the exact simulation of the regime switching process. This paper continues the authors’ research in the field of statistical methods and algorithms of the analysis and filtering for continuous-time stochastic systems.

Stabilization of bilateral teleoperators with asymmetric stochastic delay

Abstract In this paper we consider the problem of position tracking and error boundedness for a master–slave teleoperation system when the communication channel is characterized by a time-varying stochastic delay. In particular, we assume the delay to be a time-varying Markov regime switching process. Our solution is based on a suitable proportional–derivative (PD) like controller. Exploiting a Lyapunov–Krasovskii functional approach, we are able to show that the velocity and position errors remain bounded, provided specific inequality is satisfied. Moreover, zero steady-state position error is achieved when the human operator and the environment do not interact with the system. In order to be able to exploit Lyapunov–Krasovskii approach we need to lift the underlying process to an infinite-dimensional process taking values in a suitable Banach space so that, in the new space, the process is a Markov process. Our conditions for guaranteeing boundedness and the zero steady-state position tracking error are the natural generalization of the deterministic counterparts available in the literature, i.e. when considering the trivial case of a single-state Markov process previous results are recovered. Simulation results show the effectiveness of the proposed approach.