In this final instalment of the series we’re going to take a look at Robert Merton’s 1974 ‘Distance-to-Default’ method for predicting financial distress. Merton is the often forgotten third player in the Black-Scholes formula (properly called the Black-Scholes-Merton model) and won the 1997 Nobel Prize in Economics accordingly. His work in expanding the mathematical understanding of the options price model inspired to him to apply the technique to other financial problems including the prediction of company defaults. It is one of the most popular approaches to default probability estimation and has the advantage of being insensitive to the leverage ratio. It can therefore be applied more readily to banks and other highly leveraged firms where the other models can’t. For that reason alone we thought it was worth looking at in more depth.

### Merton’s DD

Having developed the Black-Scholes model for pricing options at a time when option trading was in its infancy, Merton cast around for other purposes the basic approach could be used for. He found that by characterising a company’s equity as an option on its assets (we’ll try and explain this a bit later) he could accurately assess the credit risk of a company. Put –call parity (the relationship between the price to long or short the stock) was then used to value the long option which is treated as a proxy for the firm’s credit risk. To try and simplify this a bit we’ll go through it step by step below. For any newcomers to the field of options and option pricing, you can find a good summary here.

• Firstly, the model assumes that a company has an amount of debt that will become payable at a fixed time in the future T (calculated through a combination of short-term and long-term debt obligations to assume all the debt matures at the same time);
• A company is deemed to have defaulted if the value of its assets falls below the face value of the debt promised at time T;
• By introducing the options pricing formula, we can calculate the expected asset value at time T and compare it to the debt value. The equity of the company is characterised as a European call option on the assets (a long position on the theoretical right to buy the equity at a price equal to the face value of the debt at time T) and should the option suggest…

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