本計畫計畫從兩個大方向來改進投資組合風險值測量。首先，運用 Gram‐Charlier 展開式為基礎，所選用之概似分佈則是一些多維偏度函數，包括： 常態、T 以及Laplace 分佈。第二個方向則從四個子題來發展。第一子題從隨機 波動模型來突破，除了延續Jun and Meyer(2006)之架構，更引進最新發展之模型。 第二子題則結合重要性採樣與傅立業時間序列分析等技術。第三子題則考慮尾端 資料通常違反指數衰退形式之假設，嘗試利用跳躍─擴散、Lévy 過程，以及隨機 波動加上跳躍等模型來突破。第四子題則是引進隱藏馬可夫鏈模型，以捕捉尾端 極直資料之複雜非線性結構。 This project plans to join the efforts and study PVaR in the two specified directions. For the former direction, modified Gram‐Charlier expansion is employed to capture the multivariate return distribution and PVaR is estimated according to its specific quantile levels. The selected multivariate skew models as approximating distributions include normal, Student‐t, and Laplace. For the latter direction, four topics are planned. First, various stochastic volatility models summarized in Jun and Meyer(2006) are tried and newly proposed innovative models are put to test. The second is based on the new method which combines modified importance sampling and Fourier time series analysis. The third and fourth topics consider and examine the significant properties on the tail behaviors, while some previous literatures seldom study or even arbitrarily neglected for model simplification. For example, jumps and possible regime‐switching phenomenon are confirmed in the tails and they are violations to the popular power‐decaying assumption. The third topic is projected to be studied via jump‐diffusion models, Lévy processes, and stochastic volatility models with jump. The fourth topic can be examined via hidden Markov process for the highly nonlinear structure among the tail extremes are hardly well captured by known models.
