臺灣博碩士論文加值系統

信用連結債券 (CSN) 是一種浮動收益債券與信用違約互換相結合的 信用衍生產品，Acharya，Das 和 Sundaram 提出可計算在不同信用評等之下 CSN 價格的定價模型。此模型使用的是固定信用評等轉移矩陣。其中信用評等轉移矩陣裡的元素代表的是不同信用評等之間的轉移機率。然而，在市場中信用評等的轉移機率並非定值。這篇論文主要探討的是轉移機率的不確定性對於 CSN 價格造成的差異及影響，進而提出一個基於非固定信用評等轉移矩陣來定價的模型。Acharya 等人提出之模型的複雜度為指數時間。這篇論文使用蒙地卡羅演算法來降低其時間複雜度。

A credit-sensitive note (CSN) is a corporate coupon bond linked to the credit rating of the corporation. Acharya, Das and Sundaram present a model to price CSNs of different rating classes. Their model uses a fixed credit rating transition matrix whose elements are the probabilities of rating transitions. However, the transition probabilities should not be constant. Uncertainty in the transition probabilities will change CSN’s prices. To study the difference, the thesis proposes an approach to incorporate a non-constant credit rating transition matrix into Acharya et al.’s model. The time complexity of Acharya et al.’s model is exponential. The thesis proposes a method to reduce the time complexity with Monte Carlo simulation.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Credit Rating and Its Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Our approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Basic Concepts and Terminologies . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 Stochastic Process and Martingale . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 Risk-Free Rate and Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.3 Arbitrage-Free Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Structures of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 2: The ADS Model and Its Extension . . . . . . . . . . . . . . . . . . . . . 7
2.1 Equations and Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Lattice Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 A Corrected Algorithm for the ADS Model . . . . . . . . . . . . . . . . . . . . 12
2.4 The Role of a Dynamic Credit Rating Transition Matrix . . . . . . . . . . 16
Chapter 3: Our New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 The Dirichlet Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Introduction to the Dirichlet Distribution . . . . . . . . . . . . . . . . . . . . . 19
3.1.2 The Concentration Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 Introduction to Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 4: Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 Comparison of Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Time Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 5: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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