基于历史模拟法和M-C方法的VaR算法改进

发布时间：2018-04-06 04:07

本文选题：蒙特卡洛　切入点：VaR　出处：《复旦大学》2013年硕士论文

【摘要】：对风险的常见理解包括：风险是损失的可能性；风险是损失的几率；风险是实际结果与预期结果的偏差；风险是未来结果的变异程度等等。但是从经济行为和活动本质上来说风险是指未来收益的不确定性。也就是说我们未来的状况可能变得更好好,也可以是我们未来的情形恶化。标准历史模拟法的原理：将各个风险因子在过去某一事件上的变化或分布准确的刻画出来,作为这些风险因子在未来的变化分布或者变化情形,在此基础上,通过建立风险因子与自查组合价值之间的映射表达式来模拟出自查组合在未来的损益根部状况,进而计算出给定置信度下的VAR.显然,标准历史模拟法不需要假设市场风险因子服从某种概率分布,而是直接用风险因子过去的变化分布表示未来的变化分布,所以,标准历史模拟法不需要进行参数估计,因而是一种非参数全值估计法本质上来说,历史模拟法求VaR是基于未来是对历史的简单重现这一假设,但是时间加权历史模拟法针对标准历史模拟法不切实际的等概率假设,提出了给风险因子不同时期的历史数据赋予不同权重时间加权历史模拟法对离当前越近的历史数据赋予的权重越大,一次来反映这样一个具有普遍性的事实：风险因子已经发生的离现在越近的行为在未来再次重复发生的可能性就越大,或者说,风险因子离现在越近的变化情景可为预测其未来的变化分布提供越多的信息 t分布和GARCH模型的蒙特卡罗模拟法上一章对上证指数收益率进行的正态性检验的结果表明市场的收益率并不服从正态分布,存在尖峰厚尾现象.因此,在正态假设下计算VaR值会产生较大的误差,特别是在较高置信度的情况下误差更严重.我们在一般的蒙特卡罗模拟法中加入GARCH族模型后,虽然失败天数有所减少,但是在95%的置信水平上,基于GARCH模型的失败天数仍然处于非拒绝区域的边缘。
[Abstract]:The common understanding of risk includes: risk is the possibility of loss, risk is the probability of loss, risk is the deviation between actual result and expected result, risk is the degree of variation of future result, and so on.But in terms of economic behavior and activity, risk is the uncertainty of future income.In other words, our future situation may be better or worse.The principle of the standard historical simulation method: to accurately depict the changes or distributions of each risk factor in a certain event in the past, as the distribution or change of these risk factors in the future, and on this basis,By establishing the mapping expression between the risk factor and the value of the self-checked portfolio, we can simulate the future profit and loss of the self-checking portfolio, and then calculate the VARs under the given confidence level.Obviously, the standard historical simulation method does not need to assume that the market risk factor is based on a certain probability distribution, but directly uses the past variation distribution of the risk factor to represent the future change distribution. Therefore, the standard historical simulation method does not need to carry out parameter estimation.So it is a nonparametric total value estimation method.In essence, the historical simulation method for VaR is based on the assumption that the future is a simple recurrence of history, but the time-weighted historical simulation method is based on the impractical equiprobability hypothesis of the standard historical simulation method.It is proposed that historical data of different periods of risk factors be given different weights.The time-weighted historical simulation gives greater weight to historical data that is closer to the present.Reflecting at one time the universal fact that the closer the risk factor has taken place to the present, the more likely it is to repeat it in the future, or, in other words,The closer a risk factor is to the present, the more information can be provided to predict its future distribution.T distribution and Monte Carlo simulation of GARCH model in the last chapter, the results of normal test on the return rate of Shanghai stock market show that the return rate of the market does not follow normal distribution, and there exists the phenomenon of peak and thick tail.Therefore, the calculation of VaR value under normal assumption will result in a large error, especially in the case of higher confidence.After adding the GARCH family model to the general Monte Carlo simulation, the failure days are reduced, but at the 95% confidence level, the failure days based on the GARCH model are still on the edge of the non-rejection region.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830;F224

【相似文献】