Coco Bonds Pricing With Credit and Equity Calibrated First-Passage Firm Value Models

Abstract

Since the beginning of the credit and liquidity crisis, financial institutions have been considering creating a convertible-bond type contract focusing on capital. Under the terms of this contract, a bond is converted into equity if the authorities deem the institution to be under-capitalized. This paper discusses this contingent capital (CoCo) bond instrument and presents a pricing methodology based on firm value models that calibrate exactly the credit term structure of the issuer either through credit default swaps or corporate bonds data. Decorrelation between the capital conversion trigger and credit quality is introduced. The equity value for the issuer is derived in closed form with a barrier option type formula. A stress test of model parameters is illustrated to account for potential model risk and the obtained prices are compared to the price obtained from a market source. Finally, a brief overview of how the instrument valuation performs compared to pure corporate bonds and a discussion involving the CDS bond basis are presented.

Examples of Wrong-Way Risk in CVA Induced by Devaluations on Default

“…In addition to those works, we refer to [8] for the deduction of results on the pricing formulas for one-touch barriers in AT1P and to [9] for an application of AT1P to Contingent Conversion (CoCo) bond pricing, where a technique to calibrate AT1P to the spot stock price, the entity Tier-1 Capital Ratio, and the CDS spreads is introduced.…”

Enhanced equity-credit modelling for contingent convertibles

“…The structural approach starts with the modelling of a bank's balance sheet dynamics that allows one to analyse the impact of the issuance of CoCos on the capital structure (Albul et al 2010, Pennacchi 2011, Glasserman and Nouri 2012, Brigo et al 2015. On the other hand, Cheridito and Xu (2015) apply the reduced form approach to price CoCo bonds.…”

“…In this model framework, the CoCo bond is seen to consist of a straight bond component while the equity component is only a residual. A criticism of the reduced form approach is that it completely ignores the contractual feature of an accounting trigger and neglects the interaction between stock price and capital ratio (Brigo et al 2015).…”

“…This framework of joint modelling is particularly important for pricing CoCos since the conversion value depends on the joint distribution of the first passage time of the capital ratio hitting the trigger threshold and the stock price at conversion. Since we model the bivariate process of capital ratio and stock price for pricing CoCos directly, the parametrization procedure is easier than a bottom-up structural model that requires a judicious choice of the proxy conversion epoch linked to other balance sheet quantities (Pennacchi 2011, Brigo et al 2015. We demonstrate that the equity derivative approach proposed by Spiegeleer and Schoutens (2012) can be recast under our bivariate framework when the stock price and capital ratio are perfectly correlated, and explain the justification for the equity derivative approach that replicates the CoCo components using barrier options.…”

Pricing CoCos with a Market Trigger

“…It is also quite appealing, since it allows to consider the whole capital structure of the company, to study the effect of CoCo debt in the equity value and to obtain the optimal conversion barrier for the shareholders. See for instance [6,28] or [2]. In this latter paper they also consider other triggers aiming at providing a proxy for regulatory triggers.…”