Convertible Bond Arbitrage and the Term Structure of Volatility

A mark-to-market approach for convertible bonds is proposed where the volatility from the bond optionality is implied from the traded credit spread and bond price. By linking the convertible bond implied volatility to the listed equity option implied volatility surface, the set of available tenors is significantly extended. The resulting volatility term structure classifies rich versus cheap bonds. Convertible bond arbitrage trades, where the trader buys the bond and hedges a combination of the underlying assets, are subsequently identified. Each bond’s relative cheapness translates to its arbitrage potential as a long volatility position, as shown through case studies