The Regime-switching Models And The Application In Long-term Risk Management

The outbreak of subprime mortgage crisis leads the world to reconsider about the financial derivatives trading and the importance of risk management. The innovation of financial products may be useful for reconstructing risk distribution, diversifying the risk and hedging the risk. At the meantime, it will help financial institution to break through the limitation of liquidity, to reduce financing cost, and then, to bring us a dynamic market. However, if market participants pay more attention to profit maximization, without noticing or foreseeing the long-term trend or changes of economic and financial environment, the leverage of derivatives will enlarge the risks and bring them to worldwide.Based on the necessity of long-term risk management, we focus on a popular nonlinear time series model, Markov regime-switching model. It is very flexible and widely used in analyzing long-run dynamics of macro economy, like GNP data, to capture those unexpected but recurrent phenomena. Recently, it's recommended by the investors, such as insurance company, which make long-term investments, to calculate reserve. But it has not been systematically studied by domestic researchers.The frame and innovation are described in six chapters in this paper.In Chapter 1, the development and the importance of risk management are briefly summarized, and the researches of regime-switching models are reviewed. Then, the frame of the whole paper is introduced.In Chapter 2, the basic theory of regime-switching type models is described. The methods to set a concrete model, estimate parameters and analyze estimation residuals are systematically presented. At last, two specific extensions of regime-switching model are listed.Chapter 3 is the application of regime-switching model to a new field. The model is used to measure the credit risk implied by credit default swap index. We assume that the spread of CDS index locates in one of the two states, which are spread tighten-volatility decrease state and spread widen-volatility increase state. The results show that CDS index does sensitively respond to big events in financial market. Therefore, when pricing and hedging the equity tranche of standard CDO, the regime shifts of underlying CDS index and the long-run risk of economic cycle and business cycle should be considered, especially when the credit risk increases sharply in crisis period.In Chapter 4, the research goes back to focus on stock market. Firstly, the capability of regime-switching model to represent the characteristics of asset return distribution, including high kurtosis, heavy tail and skewness, is studied and compared to other models. The result suggests that the regime-switching model forecasts the probability of downward stock market, especially the large crash, better than other models. Secondly, a change point detecting algorithm is proposed due to the sensitivity of regime-switching parameters to new information. Then the stock market is dived into bear market phase and bull market phase. The segmented regime-switching model is estimated in the whole series segmented by estimated change points. We can find that the segmented estimations are consistent with real market scene.In Chapter 5, the constrained regime-switching model is proposed for the first time to imbed mean-reversion without underestimating the high-order moments and the tail risk. Meanwhile, the parameter estimations of CRSLN model are more robust than other two regime-switching type models. Then the stock index path modeled by the CRSLN model is used to pricing stock index option, although it is only a primary design.The last chapter is the conclusion of the whole thesis, the shortcomings and future improvements are pointed out.