## Wharton Research Scholars

#### Document Type

Working Paper

#### Date of this Version

4-2012

#### Abstract

This paper discusses the pricing of Contingent Convertible bonds (CoCos) with

stock price triggers. CoCos are a new kind of hybrid securities that aim to provide a capital bu er for banks in times of nancial distress. They are debt securities during periods of economic stability, but automatically convert into equity when a predetermined trigger is breached. Therefore, CoCos are attractive from a regulatory perspective, and several regulators have already shown an interest in using them to manage nancial crisis. The fair values of CoCos are driven by their structures, and the goal of this paper is to price CoCos with stock price triggers that have varying structures in terms of the trigger level, conversion ratios, and their maturity.

This paper presents rst the general form of the price and credit spread of CoCos without modeling stock price dynamics. Then, assuming the Black-Scholes model, we provide two explicit pricing formulas for CoCos. Because CoCos combine debt-like and equity-like features, they are priced using the credit derivatives (reduced form) and equity derivatives approaches. In addition to the analytical formulas presented herein, pricing by Monte Carlo simulation is also shown. In order to examine the suitability of the Black-Scholes assumptions, the formulas used in this study are applied to the CoCos issued by Credit Suisse. Because the market trigger, implied by the formulas, is associated with a constant accounting trigger, it is expected to be constant over time.

The comparative statics of the formulas show that the mathematical structures

of the formulas explain the economic structure of CoCos. However, we nd that the formula in the equity derivatives approach is more accurate than that in the credit derivatives approach because of its more realistic treatment of cash

ow. Its accuracy is con rmed by Monte Carlo simulation, as the estimated con dence interval includes the price evaluated using the equity derivatives approach. If the interest rate is equal to the dividend yield, we nd that the two analytical formulas provide the same price. The empirical analysis of the CoCos of Credit Suisse demonstrates that the Black-Scholes assumptions are empirically unreasonable for pricing CoCos, because the implied market trigger is volatile over time. Given that the constant volatility assumption of the Black-Scholes model is empirically unreasonable, this paper suggests the stochastic volatility model (Heston model) to be a suitable alternative for modeling stock price dynamics, because it produces a more realistic fat-tail distribution of stock returns. Thus, the pricing under the Heston model is expected to show a constant implied trigger over time.

#### Keywords

contigent convertible bonds, CoCos, finance

**Date Posted:** 18 July 2012