The Impact of Skew on the Pricing of Coco Bonds

Posted: 1 Apr 2014

See all articles by Jan De Spiegeleer

Jan De Spiegeleer

RiskConcile

Monika B. Forys

KU Leuven - Department of Mathematics

Ine Marquet

KU Leuven - Department of Mathematics

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: March 31, 2014

Abstract

This paper presents a Heston-based pricing model for contingent convertible bonds (CoCos). The main finding is that skew in the implied volatility surface has a significant impact on the CoCo price. Hence stochastic volatility models, like the Heston model, which incorporate smile and skew are appropriate in the context of pricing CoCos.

The financial crisis of 2007-2008 triggered an avalanche of financial worries for financial institutions around the globe. After the collapse of Lehman Brothers, governments intervened and bailed out banks using tax-payer’s money. Preventing such bail-outs in the future and designing a more stable banking sector in general, requires both higher capital levels and regulatory capital of a higher quality. Bank debt needed therefore to be made absorbing. This is where CoCos come in. The Lloyds Banking Group introduced the first CoCo bonds as early as December 2009. Since then a lot of other banks followed Lloyds and the market of CoCos, currently around $70bn, is expanding very rapidly.

CoCos are hybrid financial instruments that convert into equity or suffer a write-down of the face value upon the appearance of a trigger event, often in terms of the bank’s CET1 level in combination with a regulatory trigger. The valuation of CoCos boils down to the quantification of the trigger probability and the expected loss suffered by the investors if such a trigger event eventually takes place. There are at least two schools of thought regarding valuation of CoCos. Structural models can be put at work or investors can rely on market implied models. The latter category uses market data (share prices, CDS levels and implied volatility, ...) in order to calculate the theoretical price of a CoCo bond. In De Spiegeleer & Schoutens (2012a), the pricing of CoCo notes has been worked out in a market implied Black-Scholes context.

In this paper we move away from the assumption of a constant volatility which is the back-bone of Black-Scholes based valuation and put the Heston model at work and study CoCos in a stochastic volatility context. The existence of a semi closed-form formula for European options pricing under the Heston model allows for a fast calibration of the model. In our approach we combined market quotes of listed option prices with CDS data. As a case study, the procedure was applied on the Tier 2 10NC CoCo issued by Barclays in 2012.

Suggested Citation

De Spiegeleer, Jan and Forys, Monika B. and Marquet, Ine and Schoutens, Wim, The Impact of Skew on the Pricing of Coco Bonds (March 31, 2014). Available at SSRN: https://ssrn.com/abstract=2418150 or http://dx.doi.org/10.2139/ssrn.2418150

Jan De Spiegeleer

RiskConcile ( email )

Kapeldreef 60
Leuven, 3000
Belgium
492227143 (Phone)

HOME PAGE: http://www.riskconcile.com

Monika B. Forys

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium
+3216322276 (Phone)

HOME PAGE: http://www.kuleuven.be/wieiswie/nl/person/00074950

Ine Marquet

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

Wim Schoutens (Contact Author)

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

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