樹狀結構評價法的延伸及其在訂價或有請求權與分析實證現象上的應用

Abstract

本論文包含兩個樹狀結構評價法在或有請求權訂價上的應用。第一個應用是最低保證提領附約和終生保證提領附約這兩種變額年金契約的訂價。其中，三維度樹狀結構被用來同時捕捉投資、利率、保單持有人死亡風險對契約價值所造成的影響。第二個應用是使用結構式信用風險模型評價公司有價證券。然而，現有的結構式信用風險模型因為過分地簡化債券發行公司的債權結構，導致模型無法確切呈現實證文獻所觀察到的現象。本論文提出一個可以真實考量公司債權結構的結構式模型，讓債權結構可以是由數張含不同條款、不同到期日、不同償債順序的債券所構成；發行公司對任何一張債券的償還能力，考量它對之前到期的債券的償還能力，使公司違約的觸發與其債權結構的特性緊密相關。這樣的改進讓結構式模型可同時捕捉到眾多的已實證現象，並給予合理的解釋，例如，優先償還債券存在封鎖公司償還其他債券的條款對此公司既有債券和新發行債券價格的影響。為了處理因債權結構中存在可贖(賣)回債券所可能發生的債權結構隨機改變，本文章提出一個新的數值方法 ― 森林結構。森林結構由數個樹狀結構有系統地用以捕捉所有可能的債權結構，例如某一債券提前贖回前、後的債權結構。此結構可以分析贖回延遲的現象與因贖回所產生的財富移轉效果的關聯性。

This study contains two applications on contingent claims’ valuation using the tree method. The first application is the evaluation of the variable annuity products associated with a guaranteed minimum withdral benefit (GMWB) and a guaranteed lifelong withdrawal benefit (GLWB). Specifically, a novel three-dimensional tree is established to capture how different policy provisions affect the evaluation of GMWB/GLWBs as investment, interest rate and mortality risks are considered simultaneously. The second application is the evaluation of corporate securities based on the structural model of credit risk. Although many different aspects of debt structures such as bond covenants and repayment schedules are empirically found to significantly influence values of bonds and equity, many theoretical structural models still oversimplify debt structures and fail to capture phenomena found in financial markets. To overcome such shortcoming, a carefully designed structural models that faithfully models typical complex debt structures containing multiple bonds with various covenants For example, the ability for an issuing firm to meet an obligation is modeled to rely on its ability to meet previous repayments, and the default trigger is shaped according to the characteristics of its debt structure such as the amount and schedule of bond repayments. Thus our framework reliably provides theoretical insight and concrete quantitative measurements consistent with extant empirical research such as the impact of payment blockage covenants on newly-issued and other outstanding bonds. We also develop the forest, a novel quantitative method to handle contingent changes in the debt structure due to premature bond redemptions. A forest consists of several trees that capture different debt structures, for instance those before or after a bond redemption. This method can be used to investigate how the presence of wealth transfer among the remaining claim holders due to a bond redemption influences the firm’s call policy, or further reconcile conflicts among previous empirical studies on call delay phenomena.