Bank Default Risk – An Alternative Approach [DRAFT]

The following is the draft introduction of the paper I'm working on. I will be posting updates as I keep working through the data and start rolling out the sections proper. I would very much appreciate any feedback/suggestions.

1.    INTRODUCTION

Traditional accounting-ratio based forecasting models of debt default (e.g. Altman z-Score and its progeny) have been empirically proven to be better predictors of credit events by corporate borrowers than the alternative structural models (e.g. Merton’s model).

However, ratio-based models are not appropriate to assess the credit risk of banks, since the Altman methodology specifically excludes regulated companies and financial institutions from its training set.

In this paper we test the hypothesis of whether structural models can satisfactorily predict a bank’s credit risk.

Merton’s model assumes that a company has a certain amount of zero-coupon debt that will become due at a future time T. The company defaults if the value of its assets is less than the promised debt repayment at time T. The equity of the company is, therefore, a European call option on the assets of the company with maturity T and a strike price equal to the face value of the debt.

As inputs, Merton’s model requires the current value of the company’s assets, the volatility of the company’s assets, the outstanding debt and the debt maturity. One popular way of implementing his model estimates the current value of the company’s assets and the volatility of the assets from the market value of company’s equity and the equity’s instantaneous volatility. A debt maturity is chosen and debt payments are mapped on to a single payment on the debt maturity.

           In this paper we develop a new way of implementing Merton’s model, specifically for bank debt. This is based on the use of the implied volatilities of options on the bank’s stock to estimate model parameters.

Under Merton’s model an option on the equity of a company is a compound option on the company’s assets. Geske (1979), who provides a valuation formula for compound options, also shows that Merton’s model is consistent with the type of volatility skew observed in equity markets. In this paper we carry Geske’s analysis one stage further to show that the credit spread in Merton’s model can be calculated from the implied volatilities of two equity options. The options we choose are two-month at-the-money and out-of-the money puts.

To test our implementation of Merton’s model and compare it with the more traditional implementation we use credit default swaps (CDS) data. Most previous researchers have used bond data to test implementations of Merton’s model. Using CDS spreads is an attractive alternative. Bond prices have the disadvantage that they are often indications rather than firm quotes. Also, the credit spread calculated from a bond depends on the bond’s liquidity and involves an assumption about the benchmark risk-free rate.

The rest of this paper is organized as follows. Section 2 develops the theory that underlies our implementation of Merton’s model. Section 3 describes the date we use. In section 4 we compare bank credit spreads implied by Merton’s model with CDS spreads for both our implementation of Merton’s model and the traditional implementation. In Section 5 we present some results on the theoretical relationships between implied volatilities and bank credit spreads under Merton’s model and test whether these relationships hold. In Section 6 we develop a relatively simple model, based on Merton’s (1976) jump-diffusion model, for relating credit risk to implied volatilities and use it as a benchmark to test whether the more elaborate structure underlying our implementation of Merton (1974) provides a better explanation of observed bank credit spreads. Section 7 concludes.