This chapter discusses, including mathematical descriptions, trading strategies relating to convertible bonds. A convertible bond is a hybrid security with an embedded option to convert the bond to a preset number of the issuer’s stock when the stock price reaches a preset level. The chapter discusses a convertible arbitrage strategy which involves buying a convertible bond and Delta-hedging it with the underlying stock, and also a convertible trading strategy involving two convertible bonds of the same issuer and based on the difference between the option-adjusted spreads of these convertible bonds. The chapter describes an iterative mathematical procedure for computing the option-adjusted spread, which involves parallel shifting the input Treasury curve when computing the value of the embedded conversion option.
KeywordsConvertible bond Hybrid security Embedded option Convertible arbitrage Delta Gamma Underlying stock Option-adjusted spread (OAS) Parallel shift Treasury curve Conversion option Conversion price Conversion ratio Fair value Hedge ratio
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