TAILIEUCHUNG - Decomposing and Valuing the Callable Convertible Bonds: A New Method Based on Exotic Options *

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for the Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are obtained by using the analytic formulae for those simpler securities decomposed from CCB. This method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses, soft call condition clauses and dividend payment are analyzed respectively. These give a lot of new insights into the valuation and analysis of CCB and much help to replicate. | Decomposing and Valuing the Callable Convertible Bonds A New Method Based on Exotic Options Qi-yuan Zhou Chong-feng Wu Yun Feng Financial Engineering Research Center Shanghai Jiao Tong University 200052 Shanghai City China Abstract In the framework of Black-Scholes-Merton option pricing models by employing exotic options instead of plain options or warrants this paper presents an equivalent decomposition method for the Callable Convertible Bonds CCB . Furthermore the analytic valuation formulae for CCB are obtained by using the analytic formulae for those simpler securities decomposed from CCB. This method is validated by comparing with Monte Carlo simulation. Besides the effects of call clauses coupon clauses soft call condition clauses and dividend payment are analyzed respectively. These give a lot of new insights into the valuation and analysis of CCB and much help to replicate and hedge CCB. Key words Callable convertible bonds Equivalent decomposition Up-and-out calls American binary calls Derivative pricing Funding for this work was provided by the National Science Fund of China. We would like to acknowledge helpful comments by Guofu Zhou in Washington University and Zongwu Cai in University of North Carolina at Charlotte. Of course all errors remain our own. t Corresponding author e-mail zsi@. Professor and the vice dean of Antai College of Economics and Management in Shanghai Jiao Tong University Associate professor in Shanghai Jiao Tong University 1 1. Introduction Convertible bonds have been playing a major role in the financing of companies because of their appealing hybrid feature that provides investors with both the downside protection of ordinary bonds and the upside return of equities. In practice there are many kinds of the convertible bonds with diversified additional clauses such as call clauses put clauses reset clauses screw clauses and negative pledge clauses and so on. Although convertible bonds in the developed derivative markets

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