The Experts below are selected from a list of 15513 Experts worldwide ranked by ideXlab platform
Jinghai Shao - One of the best experts on this subject based on the ideXlab platform.
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Stability of Regime-Switching jump diffusion processes
Journal of Mathematical Analysis and Applications, 2020Co-Authors: Huijie Ji, Jinghai Shao, Fubao XiAbstract:Abstract This work studies the stability of Regime-Switching jump diffusion processes in a finite or a countably infinite state space. Some criteria with sufficient conditions for stability and instability are provided based on characterizing the stability property of the processes in any fixed state through constants under common measurements. Also, some variational formula of these constants are given. Moreover, some examples of nonlinear Regime-Switching jump diffusion processes are provided to show the usefulness and sharpness of these criteria.
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Variational formula for the stability of Regime-Switching diffusion processes
Science China-mathematics, 2018Co-Authors: Jinghai Shao, Lingdi WangAbstract:The asymptotical stability in probability is studied for diffusion processes and Regime-Switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coefficients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For Regime-Switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent Regime-Switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.
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Heavy tail and light tail of Cox-Ingersoll-Ross processes with Regime-Switching
arXiv: Probability, 2017Co-Authors: Jinghai ShaoAbstract:This work is denoted to studying the tail behavior of Cox-Ingersoll-Ross (CIR) processes with Regime-Switching. One essential difference shown in this work between CIR process with Regime-Switching and without Regime-Switching is that the stationary distribution for CIR process with Regime-Switching could be heavy-tailed. Our results provide a theoretical evidence of the existence of Regime-Switching for interest rates model based on its heavy-tailed empirical evidence. In this work, we first provide sharp criteria to justify the existence of stationary distribution for the CIR process with Regime-Switching, which is applied to study the long term returns of interest rates. Then under the existence of the stationary distribution, we provide a criterion to justify whether its stationary distribution is heavy-tailed or not.
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permanence and extinction of Regime Switching predator prey models
Siam Journal on Mathematical Analysis, 2016Co-Authors: Jinghai ShaoAbstract:In this work we study the permanence and extinction of a Regime-Switching predator-prey model with the Beddington--DeAngelis functional response. The Switching process is used to describe the random changes of corresponding parameters such as birth and death rates of a species in different environments. When a prey will die out in some fixed environments and will not in others, our criteria can justify whether it dies out in a random Switching environment. Our criteria are rather sharp, and they cover the known on-off type results on permanence of predator-prey models without Switching. Our method relies on the recent study of ergodicity of Regime-Switching diffusion processes.
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Approximation of Invariant Measures for Regime-Switching Diffusions
Potential Analysis, 2015Co-Authors: Jinghai Shao, Chenggui YuanAbstract:In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with Regime-Switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for Regime-Switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the “averaging condition” holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for Regime-Switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.
Minh Vo - One of the best experts on this subject based on the ideXlab platform.
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Regime Switching stochastic volatility evidence from the crude oil market
Energy Economics, 2009Co-Authors: Minh VoAbstract:This paper incorporates Regime-Switching into the stochastic volatility (SV) framework in an attempt to explain the behavior of crude oil prices in order to forecast their volatility. More specifically, it models the volatility of oil return as a stochastic volatility process whose mean is subject to shifts in Regime. The shift is governed by a two-state first-order Markov process. The Bayesian Markov Chain Monte Carlo method is used to estimate the models. The main findings are: first, there is clear evidence of Regime-Switching in the oil market. Ignoring it will lead to a false impression that the volatility is highly persistent and therefore highly predictable. Second, incorporating Regime-Switching into the SV framework significantly enhances the forecasting power of the SV model. Third, the Regime-Switching stochastic volatility model does a good job in capturing major events affecting the oil market.
Chenggui Yuan - One of the best experts on this subject based on the ideXlab platform.
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Approximation of Invariant Measures for Regime-Switching Diffusions
Potential Analysis, 2015Co-Authors: Jinghai Shao, Chenggui YuanAbstract:In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with Regime-Switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for Regime-Switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the “averaging condition” holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for Regime-Switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.
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Almost sure asymptotic stability for Regime-Switching diffusions
SCIENTIA SINICA Mathematica, 2015Co-Authors: Junhao Hu, Chenggui YuanAbstract:In this paper, we discuss long-time behavior of sample paths for a wide range of Regime-Switching diffusions. Almost sure asymptotic stability is concerned (i) for Regime-Switching diffusions with finite state spaces by the Perron-Frobenius theorem, and, with regard to the case of reversible Markov chain, via the principal eigenvalue approach; (ii) for Regime-Switching diffusions with countable state spaces by means of a finite partition trick and an M -Matrix theory. Moreover, we apply our theory to study the stabilization for linear Switching models. Several examples are given to demonstrate our theory.
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Almost Sure Asymptotic Stability for Regime-Switching Diffusions
arXiv: Probability, 2014Co-Authors: Junhao Hu, Chenggui YuanAbstract:In this paper, we discuss long-time behavior of sample paths for a wide range of Regime-Switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for Regime-Switching diffusions with finite state spaces by the Perron-Frobenius theorem, and, with regard to the case of reversible Markov chain, via the principal eigenvalue approach; (ii) for Regime-Switching diffusions with countable state spaces by means of a finite partition trick and an M-Matrix theory. We then apply our theory to study the stabilization for linear Switching models. Several examples are given to demonstrate our theory.
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Approximation of Invariant Measures for Regime-Switching Diffusions
arXiv: Probability, 2014Co-Authors: Jinghai Shao, Chenggui YuanAbstract:In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with a range of Regime-Switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for Regime-Switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the "averaging condition" holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for Regime-Switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.
Sovan Mitra - One of the best experts on this subject based on the ideXlab platform.
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Regime Switching volatility calibration by the Baum-Welch method
Journal of Computational and Applied Mathematics, 2010Co-Authors: Sovan Mitra, Paresh DateAbstract:Regime Switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of Regime Switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate Regime Switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating and comparing the performance of the Baum-Welch and the Hamilton filter to S&P 500 and Nikkei 225 data, examining their performance in and out of sample.
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Regime Switching stochastic volatility option pricing
International Journal of Financial Markets and Derivatives, 2010Co-Authors: Sovan MitraAbstract:Stochastic volatility option pricing has become popular in financial mathematics due to its theoretical and empirical consistencies. However, stochastic volatility models generally suffer from analytical and calibration intractability, except for Regime Switching stochastic volatility. However, Regime Switching models neither model volatility nor price options over short time periods accurately, hence they are of limited use. This paper proposes a general method of pricing Regime Switching options over short time periods. We achieve this by relating Fouque's perturbation based option pricing method to Regime Switching models. We conduct numerical experiments to validate our method using empirical S&P 500 index option prices and compare our results to Black-Scholes and Fouque's standard option pricing method. We demonstrate our pricing method which provides lower relative error compared to the Fouque's standard option pricing method and Black-Scholes pricing. In addition, this paper can be seen as an extension to Fouque's standard option pricing method.
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Regime Switching Volatility Calibration by the Baum-Welch Method
arXiv: Statistical Finance, 2009Co-Authors: Sovan MitraAbstract:Regime Switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of Regime Switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate Regime Switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating the Baum-Welch filter to S&P 500 data and validate its performance in and out of sample.
Mary R Hardy - One of the best experts on this subject based on the ideXlab platform.
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a Regime Switching model of long term stock returns
The North American Actuarial Journal, 2001Co-Authors: Mary R HardyAbstract:In this paper I first define the Regime-Switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the Regime-Switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the Regime-Switching model is derived. Prices of European options using the Regime-Switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the Regime-Switching lognormal model results with those using the more traditional lognormal stock return model.
