A Complete Model for Pricing CoCo Bonds

Abstract

Contingent convertible (CoCo) bonds comprise a specialized market segment of the contingent capital market, an instrument that offers a valuation challenge to investment professionals. In this article, we develop new pricing models for these bonds that provide a methodology useful to both equity and fixed-income investors. We develop models in terms of the free boundary value problem where the spatial variable is the underlying stock price. These models allow the calculation of delta and gamma, as well as any kind of interest rate measure (i.e., duration and convexity) including the callability feature. Moreover, we revise the closed-form solution of a well-known model suggested for CoCo bond pricing such that it meets all practical needs. We use this explicit solution for testing the accuracy of their numerical methods. Two approaches are used based on the assumption about the dynamics of the underlying stock price. The first approach is based on the primary assumptions about the market used in the development of the Black-Scholes option pricing model; the second approach involves credit risk modeling by means of jump-to-default stock price dynamics.

TOPICS: Project finance, fixed income and structured finance, derivatives, quantitative methods, credit risk management

Key Findings

• • Two improved models for pricing contingent convertible (CoCo) bonds are developed using (1) a framework entirely based on the assumptions of the Black-Scholes option-pricing model and (2) a framework involving credit risk modeling by means of jump-to-default stock price dynamics.

• • The numerical models allow for not only CoCo bond pricing for a given interest rate term structure but also for the calculation of delta, gamma, and any kind of duration and convexity for CoCo bonds including the callability feature.

• • Unlike other proposed CoCo bond pricing models that have been oriented to one investor group, the models presented in this article are useful for both equity investors and fixed income investors.