NUMERICAL PRICING OF CoCo BONDS WITH PARISIAN TRIGGER FEATURE USING THE FORTET METHOD

Abstract

Unlike conventional convertible bonds, contingent convertible (CoCo) bonds are converted into equity shares of the issuing bank subject to certain trigger mechanisms (accounting and/or regulatory trigger) when the issuing bank is under financial nonviable state. We consider pricing of these CoCo bonds using the contingent claims approach, where the state variables are the stock price and Tier 1 capital ratio. We use the Parisian feature to model the regulatory trigger where equity conversion is triggered when the capital ratio stays under the nonviable state consecutively for a certain period of time. The accounting trigger is modeled using the one-touch barrier feature associated with the capital ratio. The Parisian trigger feature adds one extra path dependent state variable in the pricing model of a CoCo bond. We design effective numerical algorithms for pricing the CoCo bonds using the extended Fortet method that avoid adding one extra state variable for the Parisian feature of regulatory trigger. Pricing properties of the CoCo bonds under both regulatory trigger and accounting trigger are explored.