Risk Premiums in the Term Structure of Interest Rates

本論文探討隱含在利率期間結構的風險貼水問題。ㄧ般而言，影響這個風險貼水的因子很多，例如：流動性風險、信用風險、市場風險、作業風險、及法律風險等。這些風險當中，流動性風險與信用風險是最常被討論者，本論文分三個章節來探討這兩類的風險如何影響利率期間結構的風險貼水，及評價。其中，本論文的第二章探討流動性風險對利率交換利差的影響，第三章與第四章則探討有違約可能的金融商品的信用風險，並探討其風險貼水問題。 第二章“利率交換之利差期間結構模型—吻合殖利率曲線與分析解”，拓展Grinblatt (2001) 以流動性做為IRS利差期間結構決定因子的均衡理論模型，使之更一般化與吻合現今市場上的殖利率曲線，並將Grinblatt (2001)的模型納為一特例。根據本文建構的IRS利差期間結構模型做實證，可以矯正Grinblatt (2001)理論與實證不一致的問題。本文樣本內的實證結果與Grinblatt (2001)者相似，即模型配適樣本內的市場上實際之IRS利差資料非常好。再者，本文樣本外的實證結果顯示：模型對預測樣本外的IRS利差之趨勢，具備不錯的預測能力；但是，對於預測IRS利差的準確度上則是不足的。 第三章: “可調整信用風險貼水之一般化馬可夫鏈模型”，以擴大狀態空間的設定將公司信用評等改變的資訊納入模型中，進而求出更一般化的信用風險貼水調整函數。例如：假設公司信用評等分為A、B、C三個等級，其中A表示最好的信用評等狀況，B為中等的信用評等，C為差的信用評等狀況，目前債信評等為B的公司，它可能是由C B、B B或是A B，雖然這些公司目前的評等都是B，但是它們是從不同的等級改變到目前的B等級，給投資人是截然不同的信用風險感受。模型 釮 B、B B或是A B這三種公司的風險貼水調整函數應該不同，如此將信用評等改變的資訊納入模型中可賦予信用商品評價模型具備更一般化的結構。 第四章:“評價信用衍生性商品的一般化隨機倒帳機率之馬可夫鏈模型”， 指出Kodera模型會使得非倒帳狀態的推移機率之和有大於1的情況產生的缺點，並且介紹一個不同信用等級之信用價差波動性都不同的隨機變數矩陣，在此較一般化的模型下探討非倒帳狀態的推移機率之和有大於1的問題。This dissertation investigates the risk premiums that are involved in the term structure of interest rates. Many factors may influence the risk premiums, including liquidity risk, credit risk, market risk, operation risk and legal risk. Among these risks, liquidity risk and credit risk are frequently discussed. This dissertation explores how the two risks influence the risk premiums in the term structure of interest rates. This dissertation comprises three chapters to discuss the term structure of interest rates. Particularly, it explores how the liquidity risk and credit risk affect the risk premium and how to evaluate it. Pricing the interest rate swap spreads induced by the liquidity risk is discussed in chapter two. In chapters three and four discuss two models for valuing credit derivatives. Chapter two in this dissertation, “Term Structure of Interest Rate Swap Spreads--Consistent with Current Term Structure of Interest Rates and Analytical Solution,” follows Grinblatt’s idea that attributes the IRS spreads to the liquidity risk and overcomes the drawback for the inconsistency between the theory and empirical studies of Grinblatt (2001). This study assumes that the short rate and liquidity follow the Hull-White (1990b) model and computes the term structure of swap spreads, which can be exactly consistent with today’s term structure. The empirical results of this paper are comparable to those of Grinblatt (2001), and the model fits quite well the sample of actual IRS spreads. In addition, the empirical results conducted for out-samples indicate that this model has the capacity to accurately forecast the future trend of out-sample IRS spreads. However, the accuracy of the predictions of future IRS spreads for out-samples remains inadequate. The chapter three in this dissertation, “A Generalized Markov Model for the risk premium adjustment” expands the state space to incorporate the credit rating changes into the model, and thus a more generalized risk premium adjustment function is achieved. For example, suppose credit rating for a firm is divided into three grades A, B and C, where A represents the highest credit class, B the second highest, and C the lowest credit class. If the credit rating of firms that are currently rated B, they may probably derive from C B, B B or A B. Despite the firms are rated B, it must be noted that they have turned to B from different grades, and that will give investors different feelings of the credit risk. In the model given, the risk premium adjustment function for the three different firms C B, B B or A B should be different. Therefore, if the information of the credit rating changes is incorporated into the model, it will be a more generalized structure for pricing the credit derivatives. The chapter four in this dissertation, “A Generalized Markov Chain Model with Stochastic Default Rate for Valuation of Credit Spreads”, introduces a general stochastic matrix to discuss the shortcomings in Kodera’s model.目 錄 口試委員會審定書…………………………………………………………………..i 誌謝…………………………………………………………………………………..ii 中文摘要……………………………………………………………………………..iii 英文摘要……………………………………………………………………………...v 第一章 緒論………………………………………………………………………..1 第二章 利率交換之利差期間結構模型—吻合殖利率曲線與分析解…………..8 第一節 前言……………………………………………………………… … 8 第二節 吻合市場殖利率曲線之IRS利差期間結構模型…… …………… 9 第三節 實證分析……………………………………………………………. 16 第四節 結論…………………………………………………………………..25 第三章 可調整信用風險貼水之一般化馬可夫鏈模型…………………………..27 第一節 前言…….…………………………………………………………….27 第二節 模型設定………………………………… ………………………….28 第三節 本模型之風險貼水調整項…………………………………………..36 第四節 數值例子……………………………………………………………..38 第五節 結論…………………………………………………………………..42 第四章 一般化隨機倒帳機率之馬可夫鏈模型評價信用衍生性商品…………..43 第一節 前言…………………………………………………………………..43 第二節 模型設定與分析……………………………………………………..44 第三節 結論…………………………………………………………………..50 第五章 結論與後續研究方向………………………………………………………52 參考文獻………………………………………………………………..……………55 附錄…………………………………………………………………………………. 6