First Passage Time Model Based on Lévy Process for Contingent Convertible Bond Pricing

Abstract

This paper develops a general Lévy framework to reduce the pricing problem of contingent convertible (CoCos) bonds to the problem of the first pass time of the triggering process. We consider two Lévy models driven by the derived Brownian motion and the spectrally negative Lévy process. These two Lévy models keep the form of the Lévy process unchanged under the measure transform, which avoids the difficulty that only rare forms of Lévy processes solved the first passage time problem. We use single and double Laplace transform in combination with numerical Fourier inversion to find closed form expressions for the price of CoCos bonds. The results show that the model driven by the spectrally negative Lévy process would provide a more accurate CoCos bonds price when taking into account the phenomenon of jumps in the financial market. Indeed, negative jumps play a much critical role in the pricing of CoCos bonds. This paper underlines the importance of the evaluation of the CoCos bonds by the Lévy process.