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    题名: CEV股價過程下之可轉換公司債評價
    Valuation Convertible Bonds with CEV stock process
    作者: 鄧宜皓
    Teng, Yi-Hao
    贡献者: 陳威光
    Chen, Wei‑Kuang
    鄧宜皓
    Teng, Yi-Hao
    关键词: CEV股價動態
    可轉換公司債評價
    縮減式信用模型
    CRR二元樹
    CEV
    Convertible bond pricing
    Reduced form
    CRR binomial tree
    日期: 2014
    上传时间: 2022-09-02 14:49:47 (UTC+8)
    摘要: 本文以CEV ( Constant Elasticity of Variance ) 做為股價動態過程，擷取CEV具備的波動度群集 (cluster) 特性以及與股價動態交互產生的槓桿效應 (leverage effect) 的特色，拓展至可轉換公司債的評價。並嘗試解決縮減式模型描述違約過程中的不足，于設定違約模型時參數校正以及經濟意義上取得平衡。

    本研究的框架以Das and Sundaram (2007) 發表的 “An Integrated Model for Hybrid Securities” 為主體，建立利率、股價動態、違約結構的可轉換公司債評價模型。並以CRR二元樹做為數值分析法，模擬可轉換公司債的價格，並建立違約機率的期間結構。本文發現CEV股動動態在標的股價低迷或連續下跌時，能夠較精準的反應違約機率大幅跳升的變動，並在報價上保持更高的敏感性；而GBM (Geometric Brownian Motion) 幾何布朗寧股價動態下於股價看多，或是連續上漲時，對於違約機率的捕捉有較理想的表現。此外，CEV的彈性係數亦對可轉換公司債的價格存在偏態的現象，且市場對於轉換公司債違約風險的看法，可能存在低估傾向。
    This research applies Constant Elasticity of Variance (CEV) to describe the dynamic process of stock price, instead of the original Geometric Brownian motion (GBM) process, using features of the CEV model of volatility cluster and the leverage effect, and further expanding to the structure of the convertible bond valuation principle. In the meantime, the research improves the default process in the Reduced form credit model, eventually reaching a balance between parameter calibration and enhancing economic intuition.

    Based on "An Integrated Model for Hybrid the Securities" published by Das and Sundaram (2007), this research builds up a model channeling interest rate, stock price, and default rate, combined with CRR binomial-tree lattice as major methodology method to simulate convertible bond price and default rate term structure. This paper finds that the CEV process performs well when the underlying stock is at a low level or consecutive price plunging, and also maintains sensitivity to pricing estimation. On the other hand, the GBM stock process has accurate performance when the stock price is in a period of bullish. In addition, the practical evidence noticed that the elasticity coefficient of CEV contains skewness to the price of convertible corporate bonds, and the market may underestimate the default risks of the convertible bond.
    參考文獻: 1. 羅紹玫 (2010)。“考慮信用風險之可轉債評價：股價遵循CEV過程”
    2. 劉昶輝, (2009)。“考慮信用風險之可轉債評價研究”
    3. 李存修 (2006)。“轉換公司債訂價模式之研究”
    4. 葉隆賢 (2004)。”轉換債重設條款之評價”
    5. 張世東 (2003)。“海外可轉換公司債的評價— 考慮平均重設條款、信用風險及利率期間結構”
    6. Loncarski, Horst and Veld (2009).“The Rise and Demise of the Convertible Arbitrage Strategy”
    7. RiskMetrics Group, J.P. Morgan & Co. (2007)."CreditMetrics Technical Document"
    8. Das S.R., and R.K. Sundaram (2007).“An Integrated Model for Hybrid Securities”, Management Science, 53, 1439–1451.
    9. Chamber, D. and Q. Lu (2007).“A Tree Model for Pricing Convertible Bond with Equity, Interest Rate, and Default Risk”, Journal of Derivatives, 14, 4, 25–46.
    10. Hull, Nelken and White (2005).“Merton’s model, credit risk and volatility skews”
    11. Finger and Stamicar (2005).“Incorporating equity derivatives into the CreditGrades model”
    12. Tomer (2005).“An effective Binomial Tree Algorithm for the CEV model”
    13. Duffie, Saita and Wang (2005) . “Multiperiod Corporate Default Probabilities”
    14. Ayache, E., P.A. Forsyth, and K.R. Vetzal (2003).“Valuation of Convertible Bonds with Credit Risk”, Journal of Derivatives, 11, 1, 9–29.
    15. Carayannopoulos, P. and M. Kalimipalli (2003).“Convertible Bonds and Pricing Biases", Journal of Fixed Income, 13, 3, 64–73.
    16. Finger, C.C., Finkelstein, V., Pan, G., Lardy, J., Ta, T. and Tierney, J. (2002)."Credit Grades. Technical Document, Riskmetrics Group, New York."
    17. Davydov and Linetsky (2001).“Pricing and Hedging Path-Dependent Options Under the CEV Process”
    18. Boyle and Tian (1999).“Pricing Lookback and Barrier Options under the CEV process”
    19. Tsiveriotis, K. and C. Fernandes (1998).“Valuing Convertible Bonds with Credit Risk”, Journal of Fixed Income, 8, 3, 95–102.
    20. Altman and Kishore (1996).“Almost everything you want to know about recoveries on defaulted bonds”
    21. Nyborg, K. G. (1996).“The Use and Pricing of Convertible Bonds”, Applied Mathematical Finance, 3, 167–190.
    22. Jarrow and Turnbull (1995).“Pricing Derivatives on Financial Securities Subject to Credit Risk”
    23. Derman, E. (1994).“Valuing Convertible Bonds as Derivatives”, Technical report, Goldman Sachs.
    24. Goldman Sachs. (1994) ."Valuating Convertible Bonds as Derivatives”
    25. Nelson, D. and K. Ramaswamy (1990).“Simple Binomial Processes as Diffusion Approximations in Financial Models,” The Review of Financial Studies, 3, 3, 393-430.
    26. McConnell J. J. and E. S. Schwartz (1986).“LYON Taming”, Journal of Finance, 41, 561–576.
    27. Beckers, S. (1980).“The constant elasticity of variance model and its implications for option pricing”, Journal of Finance, 35, 661–673.
    28. Brennan, M. J. and E.S. Schwartz (1980)."Analyzing Convertible Securities", Journal of Financial and Quantitative Analysis, XV, 4, 907–929.
    29. Schmalensee R. and R. R. Trippi (1978).“Common stock volatility expectations implied by option premia.” Journal of Finance, 33, 129–147.
    30. Brennan, M. J. and E.S. Schwartz (1977)."Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion", Journal of Finance, 32, 1699–1715.
    31. Ingersoll, J. (1977).“An Examination of Corporate Call Policies on Convertible Securities”, Journal of Finance, 32, 463– 478.
    32. Cox, J. (1975).“Notes on option pricing I: constant elasticity of variance diffusions”, Working Paper, Stanford University.
    33. Merton (1973).“On the Pricing of Corporate Debt：The Risk Structure of Interest Rates”
    描述: 碩士
    國立政治大學
    金融學系
    97352027
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0097352027
    数据类型: thesis
    DOI: 10.6814/NCCU202201322
    显示于类别:[金融學系] 學位論文

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