運用最小平方蒙地卡羅法評價可轉債

Pricing Convertible Bond by Least Square Monte Carlo Simulation

蔡燿均(Yao-Chun Tsai)

指導教授 ： 林允永

淡江大學/商管學院/財務金融學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00384

摘要

可轉換公司債是一種非常複雜的金融商品，除了需考慮股價波動度、股價、無風險利率和信用貼水等因素外，還需考慮到可轉換公司債具有美式選擇權的特性。

常見的數值方法中最小平方蒙地卡羅法較容易評價複雜且多因子的金融商品，因此本論文運用此數值方法，並以GARCH當作股價波動參數評價可轉債，在同時考慮利率、股價波動度與信用貼水的情況下，看是否能夠準確的估計可轉債。

本論文評價可轉債有兩種方式，一種只運用一因子評價可轉債，另一種是個別探討債券與選擇權部位，在不耗費的時間成本的前提下，運用實際案例找出何種理論價較能準確的估計可轉債市價，並針對較準確的訂價方式探討造成其價差的原因為何。實證結果顯示可轉債拆解訂價會顯著優於一因子訂價，而造成拆解訂價價差的原因可能有流動性、參數估計錯誤、理論價波動較市場高、條款簡化等原因。

關鍵字

可轉換公司債 ； 最小平方蒙地卡羅法 ； 可轉換公司債拆解 ； 廣義自迴歸條件異方差模型

並列摘要

Convertible bond is a very complex financial instrument. It needs not only to consider stock volatility, risk free rate, issuer’s credit risk but also implies American option’s nature.
Least square monte carlo simulation approach is used to pricing complicated and multi-factor financial instrument. As a result, this research used this numerical procedure with GARCH to estimate stock volatility parameters for pricing convertible bonds. With stock volatility, risk free rate, issuer’s credit risk, our research tries to value convertible more accurately.
In this research, under the less time cost, we have two different ways to price convertible bonds. One is with one factor model and another is with compound option and bond. After pricing convertible bonds with actual case, we will find out which model is more accurate and discuss what reason let the spread occur.
The empirical result show that compound option and bond’s approach is more accurate than one factor model. Trading volume, estimated parameters, sensitive model and clauses assumption will extend the spread.

並列關鍵字

Convertible Bond ； Least Square Monte Carlo Simulation ； Compound Option and Bond ； GARCH

參考文獻

李奇樺（2009），可轉換公司債資產交換評價，淡江大學財務金融學系碩士在職專班碩士論文。

Black, F., and M. Scholes, (1973), “The Pricing of Options and Corporate Liabilities,“ Journal of Political Economy.Vol 81,pp.637-659.

Brennan, M.J. and E.S. Schwartz., (1977), “Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion,” Journal of Finance. Vol. 32, pp.1699-1715.

Ingersoll, J.E., (1977), “A Contingent-Claims Valuation of Convertible Securities,” Journal of Financial Economics. Vol. 4, pp. 289-322.

Jennings, E.H., (1974), “An Estimate of Convertible Bond Premiums,” Journal of Finance and Quantitative Analysis. Vol. 9, pp.33-56.