本論文包含兩大主題，主要探討投資人在不同訊息集合下，如何訂價信用型衍生性商品與公司債信用價差。本論文有效地結合信用風險兩大主流評價模型– 精簡模型（reduced form model）與結構模型（structural form model），亦即採用精簡模型為基礎，再適度結合結構模型中之直觀經濟意義，來評價相關的商品。論文前後兩部分分別考慮投資人面臨的兩種情境，論文第一部份考慮投資人面對窗飾之財務報表，在不完全資訊下，如何從市場交易資訊中，估測公司真實財務體質，以評價該公司之信用型衍生性商品。由實際數值模擬所展現的結果顯示，這些由不完全資訊所產生的額外信用價差，在長到期日的衍生性商品下，是相當顯著的。
本論文第二部分本文主要探討投資人若具有擴大的訊息集合，亦即其訊息集合中具有某種預期性或內線型訊息，則評價一公司債的信用價差會具有何種期間結構。本部分論文中，我們展示如何將內線訊息加入傳統的隨機架構之中，並探討投資人在不真實財務報表下，信念更新與對內線消息的預期效果。在本文模型下， 確實改進傳統結構模型的重大缺點，即短到期日下，信用價差明顯過小的問題。The thesis includes two articles. These two articles focus on the
same issue--how to pricing credit derivatives and credit spreads
under different information sets. These two articles all employ
reduced models as a base framework, and combine intuitions from
structural models to consider the pricing problems. But they
consider different situations an investor may face, the first
article focus on the situation when investors only possess a
firm's noisy financial report (incomplete information). We develop
methods to infer the company's real financial constitution from
market trading data. The second article considers the situation
when an investor's information set is enlarged to include
anticipative information. Conditioning on the extended information
set, we show how to incorporate the insider information into the
original model, and thus give us a better estimation of the firm's
survival probability.Contents
1. Introduction ………………………………………………………..… 1
2. Pricing Credit Derivatives under Incomplete Information ……….. 3
2.1 Introduction …………………………………………………….. 3
2.2 Preliminaries …………………………………………………… 9
2.3 State Variables of Default Risk ………………………………… 13
2.4 Credit Derivatives ……………………………………………… 18
2.5 Learning Process ……………………………………………….. 21
2.6 Numerical Results ……………………………………………… 25
2.7 Conclusion ……………………………………………………… 43
3. Term Structure of Credit Spreads with Anticipation Effects …….. 45
3.1 Introduction …………………………………………………….. 45
3.2 The General Framework ……………………………………….. 48
3.3 Anticipations from Derivative Markets ……………………….. 50
3.4 Learning Effects on Market Information ……………………… 59
3.5 Numerical Results ……………………………………………... 61
3.6 Conclusion …………………………………………………….. 69
4. Conclusion …………………………………………………………. 71
Appendix ………………………………………………………………... 72
References ………………………………………………………………. 74
Figures
Figure 1: Default Probability I ……………………………..……..… 27
Figure 2: Default Probability I …………………………….…..…….. 28
Figure 3: Zero Recovery Defaultable Bond Price I………..…....…….. 31
Figure 4: Zero Recovery Defaultable Bond Price II………..…….…….. 32
Figure 5: Default Digital Put Option Price I ………………..………….. 34
Figure 6: Default Digital Put Option Price II ………………..…..…….. 35
Figure 7: Survival Probability under Incomplete Information ..……….. 39
Figure 8: Zero Recovery Defaultable Bond Price under Incomplete
Information ..………………………………………………. 40
Figure 9: Default Digital Put Option Price under Incomplete
Information ..………………………………………….….. 41
Figure 10: Credit spreads under information of terminal asset value
V_T ..………………………………..………………….….. 63
Figure 11: Conditional survival probabilities under information of
terminal asset value V_T ..…………..………………….….. 64
Figure 12: Credit spreads under extended information of terminal
asset value points distribution I ….…..………………….….. 65
Figure 13: Conditional survival probabilities under extended information
of terminal asset value points distribution I .…………….….. 66
Figure 14: Credit spreads under extended information of terminal
asset value points distribution II ….…..………………….….. 67
Figure 15: Conditional survival probabilities under extended information
of terminal asset value points distribution II .…………….….. 68
Tables
Table 1: Parameters Used in Numerical Analysis ……………..………… 26
Table 2: Parameter Impact Analysis ………………………….…..…….... 30
Table 3: Default Put Option Prices ………………..………..…....…….... 36
Table 4: Credit Default Swap Spreads ……………………..…….…….... 37
Table 5: Parameter Impact Analysis on V^DP and CDS Spreads ………. 37
Table 6: Default Put Option Prices under Incomplete Information ….….. 42
Table 7: CDS Spreads under Incomplete Information ..………………….. 4
