Markov Switching Processes and Financial Applications

自Hamilton（1989）的开创性论文发表以来，制度转换模型已广泛应用于金融的各个领域。这些模型可以捕捉到金融市场行为中经常观察到的突然变化。货币危机、股市泡沫或资产价格或汇率波动的急剧变化都是这种现象的例子。金融回报的均值和波动性在不同制度之间会发生变化，多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。我们还希望开发易于实施的制度数量测试。例如，在资产配置中，资产收益的制度转换模型能够通过不同制度下的不同波动性捕获熊市期间较高的相关性结构或异方差。我们的兴趣是将这类模型应用于具有有限视界的一般投资者问题，其中代理最优地选择具有随机微分效用偏好的投资组合分配和（可能的）消费。目标是为多制度经济中的最优投资组合和消费提供近似解析解。在资产定价方面，Bonomo、Garcia、Meddahi和Tedongap（2011）利用失望厌恶递归效用对资产进行均衡定价，对基本面中的长期风险进行了建模。马尔可夫结构导致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性，以及可预测性回归的系数。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总体股票市场的事实（见van Binsbergen和Koijen， 2016）。我们的第三条研究路线旨在开发一种测试，以确定给定数据集中的制度数量。现有的测试（Garcia, 1998; Carrasco et al., 2014）适用于对线性模型进行双体系模型的测试。将它们扩展到更多的政权似乎非常具有挑战性。我们打算检验Garcia和Perron（1996）使用的两个简单的基于回归的测试的大小和功率特性。

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 thesize and power properties of two simple regression-based tests used in Garcia and Perron (1996).