無 / Existing literature has shown that force of mortality has amazing resemblance of interest rate. It is then tempting to extend existing model of interest rate model context to mortality modeling. We apply the model in Diebold and Li (2006) and other models that belong to family of yield rate model originally proposed by Nelson and Siegel (1987) to forecast (force of) mortality term structure. The fitting performance of extended Nelson-Siegel model is comparable to the benchmark Lee-Carter model. While forecasting performance is no better than Lee-Carter model in younger ages, it is at the same level in elder ages. The forecasting performance increases for 5-year ahead forecast is better than 1-year ahead comparing to Lee-Carter forecast. In the end, the forecast outperforms Lee-Carter model when age dimension is trimmed to age 20-100.

本篇論文將厚尾分配（Heavy-Tailed Distribution）應用在財務及保險精算上。本研究主要有三個部分：第一部份是用厚尾分配來重新建構Lee-Carter模型（1992），發現改良後的Lee-Carter模型其配適與預測效果都較準確。第二部分是將厚尾分配建構於具有世代因子（Cohort Factor）的Renshaw and Haberman模型（2006）中，其配適及預測效果皆有顯著改善，此外，針對英格蘭及威爾斯（England and Wales）訂價長壽交換（Longevity Swaps），結果顯示此模型可以支付較少的長壽交換之保費以及避免低估損失準備金。第三部分是財務上的應用，利用Schmidt等人（2006）提出的多元仿射廣義雙曲線分配（Multivariate Affine Generalized Hyperbolic Distributions; MAGH）於Boyle等人（2003）提出的低偏差網狀法（Low Discrepancy Mesh; LDM）來定價多維度的百慕達選擇權。理論上，LDM法的數值會高於Longstaff and Schwartz（2001）提出的最小平方法（Least Square Method; LSM）的數值，而數值分析結果皆一致顯示此性質，藉由此特性，我們可知道多維度之百慕達選擇權的真值落於此範圍之間。 / The thesis focus on the application of heavy-tailed distributions in finance and actuarial science. We provide three applications in this thesis. The first application is that we refine the Lee-Carter model (1992) with heavy-tailed distributions. The results show that the Lee-Carter model with heavy-tailed distributions provide better fitting and prediction. The second application is that we also model the error term of Renshaw and Haberman model (2006) using heavy-tailed distributions and provide an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model. Using the RH model with non-Gaussian innovations can pay lower premiums of longevity swaps and avoid the underestimation of loss reserves for England and Wales. The third application is that we use multivariate affine generalized hyperbolic (MAGH) distributions introduced by Schmidt et al. (2006) and low discrepancy mesh (LDM) method introduced by Boyle et al. (2003), to show how to price multidimensional Bermudan derivatives. In addition, the LDM estimates are higher than the corresponding estimates from the Least Square Method (LSM) of Longstaff and Schwartz (2001). This is consistent with the property that the LDM estimate is high bias while the LSM estimate is low bias. This property also ensures that the true option value will lie between these two bounds.