Markov Switching Processes and Financial Applications

自汉密尔顿（1989）的开创性论文以来，制度转换模型在金融学的各个领域得到了广泛的应用。这些模型可以捕捉金融市场行为中经常观察到的突然变化。货币危机、股票市场泡沫或资产价格或汇率波动性的急剧变化都是这种现象的例子。金融回报的手段和波动性在不同制度之间可能会发生变化，几种资产回报之间的相关性也会发生变化。在这个项目中，我们打算在资产配置和资产定价中使用这些模型。我们还想开发易于实施的测试制度的数量。 例如，在资产配置中，资产收益的制度转换模型能够在熊市期间捕获更高的相关性结构，或者通过不同制度中的不同波动率捕获异方差性。我们的兴趣是将这类模型应用于一般投资者的有限时域问题，其中代理最优选择投资组合分配和（可能）消费与随机微分效用偏好。我们的目标是开发近似的分析解决方案的最优投资组合和消费在多制度经济。 在资产定价方面，Bonomo，Garcia，Meddahi et Tedongap（2011）已经建立了基本面中的长期风险模型，该模型采用了失望厌恶递归效用均衡的资产定价机制。马尔可夫结构导致了许多感兴趣的统计数据的封闭形式表达式，例如收益的均值和波动率，以及可预测性回归系数。我们的新贡献将扩展这种模型，以捕捉股权回报的期限结构。传统模型很难解释短期股权债权或股息条的平均回报率和夏普比率高于整体股票市场的事实（见货车Binsbergen和Koijen，2016）。 我们的第三条调查线旨在开发一个测试，以确定在一组给定的数据政权的数量。可用的测试（Garcia，1998; Carrasco等人，2014）适用于针对线性模型测试两种状态模型。将其扩大到更多的制度似乎非常困难。我们打算研究 Garcia和Perron（1996）中使用的两个简单的基于回归的检验的大小和功效特性。

Since the seminal paper of Hamilton (1989), regime switching models have been used widely in diverse fields of finance. These models can capture abrupt and sudden changes often observed in the behavior of financial markets. Currency crises, stock market bubbles, or sharp changes in the volatility of asset prices or exchange rates are examples of such phenomena. Means and volatilities of financial returns can change between regimes, as well as the correlations between returns of several assets. In this project we intend to use such models in asset allocation and asset pricing. We also want to develop easy to implement tests for the number of regimes. In asset allocation, regime switching models of asset returns are able, for example, to capture a higher correlation structure in bear periods or heteroscedasticity through distinct volatilities in different regimes. Our interest is to apply this class of models in a general investor's problem with finite horizon, in which the agent optimally chooses portfolio allocation and (possibly) consumption with stochastic differential utility preferences. The goal is to develop approximate analytical solutions for the optimal portfolio and consumption in a multiregime economy. In asset pricing, Bonomo, Garcia, Meddahi et Tedongap (2011) have modeled long-run risks in fundamentals with regimes to price assets in equilibrium with disappointment aversion recursive utility. The Markov structure leads to closed-form expressions for many statistics of interest such as means and volatilities of returns, and coefficients of predictability regressions. Our new contribution will extend such model to capture the term structure of equity returns. Traditional models have a hard time explaining the fact that short-term equity claims, or dividend strips, have higher average returns and Sharpe ratios than the aggregate stock market (see van Binsbergen and Koijen, 2016). Our third line of investigation aims at developing a test to determine the number of regimes in a given set of data. The available tests (Garcia, 1998; Carrasco et al., 2014) are applicable to testing a two-regime model against a linear model. Their extension to higher numbers of regimes appears very challenging. We intend to examine the size and power properties of two simple regression-based tests used in Garcia and Perron (1996).