本論文涵蓋兩篇於財務模型風險管理的文章，每一篇各代表論文內容的一章。
第一章提出使用即期利率做為利率期間結構狀態變數之替代變數的三因子模型。同時進行即期利率模型於樣本內解釋能力與樣本外預測能力，並比較修正的Macaulay存續期間和即期利率存續期間對債券投資組合避險等多項實證研究。其結果顯示此最適化三因子(即期利率)模型不僅對利率期間結構的未預期變動之解釋能力優於由EGM (1990)所提出的二因子即期利率模型，更說明此模型於運用即期利率存續期間避險時能捕捉利率期間的曲率變化等特性。此三因子即期利率存續期間避險的優異結果隱含著於債券投資組合風險管理時可將狀態變數的個數控制於三因子的可行性。
第二章則探討於一般化自我相關條件異質變異-跳躍(GARCH-Jump)狀況下的選擇權評價。一般化自我相關條件異質變異-跳躍(GARCH-Jump)模型已被證明較能描述標的資產價格分佈存在著偏態、波動群聚與極端報酬等特性。對於一般化自我相關條件異質變異-跳躍(GARCH-Jump)模型的選擇權評價，本文除比較於文獻當中被公認為最有效率的兩種蒙地卡羅模擬(Monte Carlo simulation, MC)—近似蒙地卡羅模擬(quasi-Monte Carlo simulation, QMC)與實證martingale模擬(Empirical Martingale simulation, EMS)以外，同時也考慮將此兩種模擬方法整合應用的比較。選擇權評價結果顯示EMS於變異數縮減的表現上顯著優於QMC模擬。除外可能由於QMC與EMS兩種方法之間的相互干擾，其整合應用並沒能得到進一步的變異數縮減。經由對跳躍強度的敏感度分析，本研究發現QMC模擬是較適合於處理單純一般化自我相關條件異質變異過程。但隨著跳躍成分的存在，EMS的表現是顯著優於QMC模擬。由於EMS執行上的方便性與優異的表現，當考慮一般化自我相關條件異質變異-跳躍(GARCH-Jump)狀況下的選擇權評價，本研究較為推薦EMS的方法。

The dissertation consists of two essays on risk management in financial models, each being one chapter of this dissertation.
The first chapter proposes a three-factor model using spot rates as proxies for the state variables of the term structure of interest rates. Several empirical works are performed on the tests of the in-sample explanatory power and the out-of-sample prediction ability of spot-rate models, and on comparison between the modified Macaulay duration and spot-rate duration hedging for bond portfolios. The results not only show that the optimal three-spot-rate model outperforms the optimal two-spot-rate model proposed by Elton et al. (1990) with respect to explanation ability of unexpected changes in the term structure of interest rates, but also illustrate the importance of capturing the curvature characteristic of the term structure of interest rates for spot-rate duration hedging methods. Moreover, the impressive performance of three-spot-rate durations hedging implies that it is feasible to reduce the dimensions of state variables to three for the purposes of risk exposure prediction and risk management of bond portfolios.
The second chapter investigates the valuation of options under the GARCH-Jump process, which has been demonstrated to provide a better description for underlying asset prices exhibiting the characteristics of non-zero skewness, volatility clustering, and extreme returns. For pricing GARCH-Jump options, we compare the performance of two of the most efficient Monte Carlo simulation (MC) methods recognized in the literature—the quasi-Monte Carlo simulation (QMC) and the empirical martingale simulation (EMS). Moreover, the integrated approach of these two methods is considered for comparison as well. The results indicate that the EMS performs significantly better than the QMC on variance reduction. In addition, integrating the QMC with the EMS cannot bring further improvement over the EMS due to possible interference between these two methods. Via the sensitivity analysis for the jump intensity, it is first found in the literature that the QMC method is well suited to dealing with the pure GARCH process, but with the existence of the jump component, the EMS method exhibits substantial superiority over the QMC method. Given its better performance and simpler implementation, the EMS method is the recommended method for pricing options under the GARCH-Jump process.

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