Empirical study in Value-at-Risk -via Analysis on Stochastic Volatility Stochastic Jump Intensity Model
- 王亚南院－学位论文 
近年来，金融学尤其是资产定价领域和实证金融领域的长足发展积累了众多优秀的研究成果，而风险管理领域也在不断吸收消化这些新思想、新技术的过程中进化。在风险管理领域，风险价值(Value-at-Risk)一直占据着重要地位，学术界对于VaR计算模型和方法的改进和开发从未停止。目前，蒙特卡洛模拟方法是学术界公认的计算VaR最有效的方法，由此改进VaR计算的出发点转移到不断改进刻画资产价格波动的模型上。 在这样的背景下，本文所做的是关于VaR的实证研究，目的是试图找到两个问题的答案：第一、这些复杂的跳跃过程模型能否在风险管理方面得到应用；第二，来自于期权市场的信息是否有助于提高VaR的计算精度。 本文的研究对象主要是Santa-Clara and Yan（2010）提出的SVSJ模型。SVSJ模型的特殊之处在于它不仅使用了股票市场的信息，还使用了期权市场的信息。期权的价格中包含了市场对于未来市场风险的期望，期权价格信息也许可以帮助我们更好地刻画资产价格波动以及预测市场风险。 我们的估计结果指出SVSJ的扩散波动率和跳跃密度很好地反应了市场的真实状况，对样本区间内的市场波动率和风险溢价的刻画符合市场的观测，尤其是在2008年金融危机时，SVSJ模型对股市跳跃行为的刻画有很好的表现。 SVSJ模型在计算风险价值VaR中的表现在整体上仍差于传统模型。我们找到了其中的原因，主要是由于SVSJ在资产价格波动较小的样本区间内表现很差，而这是由于模型本身设定的缘故。进一步的实证研究验证了SVSJ模型在市场剧烈波动时期（如金融危机）的表现超越了传统模型，在一定程度上说明了时变的跳跃密度的模型设定对于刻画金融危机时期的资产价格波动是非常重要的。Following the increase in financial uncertainty in the 1990’s, resulting in the famous financial disasters, there has been intensive research from financial institutions, regulators and academics to better develop sophisticated models for market risk estimation. The most well known risk measure is Value-at-Risk(VaR), which refers to a portfolio’s worst outcome that is expected to occur over a predetermined period and at a given confidence level. VaR is an estimation of the tails of the empirical distribution. Many applications presume that asset returns are normally distributed, while it is widely documented that they exhibit skewness and excess kurtosis, resulting in an underestimation or overestimation of the true VaR. Considering the calculation method, Monte Carlo Simulation is known as the most accurate VaR calculation method while traditional VaR calculation perspective is from the asset itself. The paper intends to do an empirical study about VaR calculation and tries to find the answers to two questions: First, can the models considering the jump behavior actually increase the accuracy of VaR calculation? Second, can models considering information from other markets actually make sense in the risk management area? The SVSJ model of Stochastic Volatility and Stochastic Jump Intensity with estimates reported by Pedro Santa-Clara and Shu Yan(2010) is introduced to imply time series of diffusive volatility and jump intensity from S&P 500index options. Compared with traditional model, SVSJ model contains the information from both option market and stock market. In other words, the option price contains the expectation of future market risk, thus the diffusive volatility and jump intensity which is implied from the S&P 500 index and option market can significantly predict subsequent market returns. Our findings suggest that SVSJ model can be used to predict accurate value at risk especially during the market crash for SVSJ model capture the ex ante risk assessed by investors. In empirical studies, we use the method of Monte Carlo simulation to calculate VaR through SVSJ model, SV model and GARCH(1,1) model based on weekly data between Jan. 1996 and Dec. 2009. The result shows that compared with traditional models such as GARCH(1,1) model and SV model, the accuracy of VaR calculation through SVSJ model is worse than the traditional model in the whole sample period. However, we analyze the problem and find the reason leading to the situation. Thus, we divide the sample period into four parts and illustrate the result of two sample periods during which the S&P 500 index jumps frequently. Our new findings are that in the market crash period, the jump behavior happens frequently in the stock market. In this period, SVSJ model is better than SV model and GARCH(1,1) model in VaR calculation. In some degree it shows that time-changed jump intensity is important in model specification considering market crash periods.