Markov Switching Processes and Financial Applications

自 Hamilton（1989）发表开创性论文以来，政权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性的急剧变化都是此类现象的例子。财务回报的平均值和波动性以及多种资产回报之间的相关性可能会在不同制度之间发生变化。在这个项目中我们打算在资产配置和资产定价中使用这样的模型。我们还希望开发易于实施的针对多个政权的测试。 例如，在资产配置中，资产回报的制度切换模型能够通过不同制度中的不同波动性来捕获熊市期间更高的相关性结构或异方差性。我们的兴趣是将此类模型应用于有限范围内的一般投资者问题，其中代理以随机差异效用偏好最优地选择投资组合配置和（可能）消费。目标是为多体制经济中的最优投资组合和消费开发近似分析解决方案。 在资产定价中，Bonomo、Garcia、Meddahi 和 Tedongap（2011）利用基本面的长期风险模型，对资产进行定价，使其与失望厌恶递归效用保持平衡。马尔可夫结构导致许多感兴趣的统计数据的封闭式表达式，例如回报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该模型以捕获股权回报的期限结构。传统模型很难解释短期股权索赔或股息剥离的平均回报率和夏普比率高于股市总体的事实（参见 van Binsbergen 和 Koijen，2016 年）。 我们的第三条研究线旨在开发一种测试来确定给定数据集中的政权数量。可用的测试（Garcia，1998；Carrasco 等人，2014）适用于针对线性模型测试两种机制模型。将它们扩展到更多的政权似乎非常具有挑战性。我们打算研究 Garcia 和 Perron (1996) 使用的两个简单的基于回归的检验的大小和功效属性。

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).