Parisian barrier option applied to convertible bonds

Erwan Curien, Nicolas Koumchatzky and Quentin Serres, of the Sophis research team, demonstrate the influence, pricing and hedging of the ‘20 out of 30’ soft call feature on the price and greeks of convertible bonds

Introduction

Parisian barrier options are products that grew in the market at the end of the 1990s. Compared to the standard barrier option, the barrier is activated only if the spot crosses the barrier for a given proportion of days in a given time lag – usually 20 days out of the last 30. This feature is now very common in the convertible bond (CB) market. Indeed, most CBs now have a soft call clause – an option for the issuer to call back the CB if the spot crosses a given level, thus allowing