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研究生:劉志清
研究生(外文):Liu-chin Chimg
論文名稱:可轉換債券之定價與拆解
論文名稱(外文):CB Asset Swap
指導教授:張傳章張傳章引用關係張森林張森林引用關係
指導教授(外文):Chuang-Chang ChangSan-Lin Chung
學位類別:碩士
校院名稱:國立中央大學
系所名稱:財務金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:54
中文關鍵詞:馬可夫鏈定價蒙第卡羅可轉換公司債
外文關鍵詞:Credit DerivativesCB Asset Swap
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論文摘要
目前市場上有許多關於可轉換公司債的資產交換,其中牽涉到利率交換的交易,其中風險溢酬的給定還沒有良好的方式作定價。
公司債的發行必須依據公司的破產風險給予不同的風險溢酬,風險溢酬的來源也就必須根據公司的破產機率決定。可轉換公司的定價與拆解,亦需依據公司債的利率評價,才符合風險與報酬的關係。
本論文的研究目的在於運用馬可夫鏈估計出各種不同評等公司之破產機率,並依據此破產機率算出合理的風險溢酬,再結合蒙地卡羅的股價模型與Vasicek 利率模型,運用Longstuff與Schwartz發展出來之最小平方法,算出可轉換公司債的價格。由於我們已經算出可轉換公司債的價格,依據可轉換公司債的價格,我們亦算出一個可轉換公司債的買權(Call on CB),另外還有純債券的部分,我們可以將債券部位以公司債的方式賣出。
透過評等公司如Standard and Poor’s與Moody’s的歷史資料,我們可取得transition matrix,依據transition matrix,我們可以估計各種評等的破產機率。運用此破產機率,我們可以評價各種信用衍生性金融商品。
另外,我們在第五章還探討了可轉換公司債中,發行者買回權與轉換價格重設對可轉債價格的影響,還有回復率對可轉債的敏感度分析。我們得到的結論是:發行者買回權對可轉債會有負面的影響,但是對評等越差的公司,影響越小。重設轉換價格對可轉債會有正面的影響,對評等越差的公司,影響程度越大。而回復率對可轉債也有正面的影響,評等越差的公司,對回復率越敏感。最後,關於破產風險與風險溢酬的關係,在第四章我們有詳細的探討。
Abstract
A CB Asset SWAP is now very popular in the market and it involves the IRS. In the pricing process, there does not exist a proper credit spread for the credit premium. We show in the paper a way to forecast the credit spread with the use of a Markov chain.
When issuing a corporate bond, one can determine the default premium according to the default probability; hence, we could say that the premium mainly comes from default risk. In the evaluation and stripping process of a CB, one should use the corporate interest rate to price the CB. In this way, the relationship between the risk and the premium will be reasonable.
This paper applies the Markov chain to predict the default probability among different ratings and from with the default probability we can estimate a credit spread. We also use the Monte Carlo simulation and the Vasicek model to evaluate CB prices. Longstuff and Schwartz modify the Monte Carlo approach with a least-square method to evaluate the American option price. We apply a modified method to evaluate the CB price, and from this, we are able to evaluate the call on a CB. We strip the CB into a call on the CB and a pure corporate bond and then sell it to an option investor and a fixed-income investor.
With historical data like transition matrix coming from S&P or Moody’s, we are able to estimate a CB’s the default probability and according to the default, we can evaluate all kinds of credit derivatives.
Moreover, we also analyze the effect of options which are embed in CBs. The options are the issuer’s call option and the reset right and conversion right. We also analyze the sensitivity of the recovery rate and find that the issuer’s call option has a negative impact on the a CB’s value, and the effect is decreasing as the rating falls. The reset right has a positive effect on a CB’s value and its derivatives, with the effect increasing as the rating decreases. The recovery rate has a positive effect on a CB’s value, whereby for a lower rated, it is more sensitive for the recovery rate. We also show the relationship between default probability and default-risk premium in section 4.
Contents
1. INTRODUCTION1
2. CB ASSET SWAP TRANSACTION STRUCTURE2
2.1 MOTIVATION OF STRIPPING CONVERTIBLE BOND2
2.2 CONTRACT DESCRIPTION2
2.3 STRIPPING STRUCTURE5
3. LITERATURE REVIEW10
4. PRICING CONVERTIBLE BOND AND CALL OPTION ON CBS WITH DEFAULT RISK ENDOGENOUSLY12
4.1 MODELING CREDIT SPREAD12
4.1.1 Markov Process12
4.1.2 Two state Model – Default / No Default14
4.2 CONVERTIBLE BOND MODEL16
4.3 NUMERICAL EXAMPLE18
4.4.1 Restrictions26
4.4.2 Parameters27
4.4.3 Results29
5. SENSITIVITY ANALYSIS30
5.1 EFFECT OF RESTRICTION30
5.2 EFFECT OF RESET34
5.3 EFFECT OF ISSUER’S CALL OPTION36
5.4 EFFECT OF RECOVERY RATE38
5.5 CREDIT SPREAD ANALYSIS42
6. CONCLUSIONS44
REFERENCES45
Reference1.Andgelo Arvanitis, Jonathon Gregory, and Jean-Paul Laurent(Spring 1999):” Building Models for Credit Spreads,” The Journal of Derivatives,27-43.2.Brennan, M, and E. Schwartz. “Analyzing Convertible Bonds.” Journal of Financial and Quantitative Analysis, 15 ( 1980 ), pp. 907-929.3.Bernard Kolman. Introductory Linear Algebra with Applications Macmillan.1993, Fifth Edition.4.Duffie. D., and K. Singleton. “Modeling Term Structure of Defaultable Bonds.” Review of Financial Studies, 12 ( 1999 ), pp. 687-720.5.Ingersoll, J. E., Jr. “ A Contingent-Claims Valuation of Convertible Securities.” Journal of Financial Economics, 4 (1977 ), pp.289-382.6.Jarrow, R.A, and S.A. Turnbull. “Pricing Derivatives on Financial Securities Subject to Credit Risk.” Journal of Finance, March 1995.7.Jarrow, R. A., and Lando, and S. M. Turnbull (1997):”A Markov Model for the Term Structure of Credit Risk Spreads,” Review of Financial Studies, 10(2),481-523.8.John C. Hull and Alan White (Fall 2000):” Valuing Credit Default Swaps I: No Counterparty Default Risk,” The Journal of Derivatives, 29-40.9.Longstuff, F.A., and E.S. Schwartz. “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt.” Journal of Finance, 50 ( 1995 ), pp 789-819.10.Longstaff, F. A., and E. S. Schwartz (2001):” Valuing American Options by Simulation: A Simple Lease-Squares Approach,” The Review of Financial Studies,14(1),113-147.11.O. A. Vasicek:” An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics,5 (1997),177-88.12.S. L. Chang, S. W. Lai, S.Y. Lin, G. Shyy (2002) “CB Asset Swaps and CB Options: Structure and Pricing.”
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