First-to-Default Swaps: A Tool for Bespoke Credit Exposure and Correlation Trading

An Introduction to First-to-Default Swaps

First-to-default (FTD) swaps are a type of credit derivative that provides protection against the first default in a basket of reference entities. They are a effective tool for managing credit risk and for expressing views on credit correlation. FTD swaps are more complex than single-name CDS, but they can offer significant advantages in terms of cost and flexibility.

The Mechanics of an FTD Swap

An FTD swap is a contract between two parties, a protection buyer and a protection seller. The protection buyer pays a periodic fee to the protection seller, and in return, the protection seller agrees to make a payment to the protection buyer if any of the reference entities in the basket defaults. The contract terminates after the first default.

The Role of Correlation

The pricing of an FTD swap is highly dependent on the correlation of default among the reference entities in the basket. Correlation measures the likelihood that multiple entities will default at the same time.

• High Correlation: If the correlation is high, it is more likely that multiple entities will default at the same time. This is beneficial for the protection seller, as it is less likely that they will have to make a payment. As a result, the premium on an FTD swap will be lower in a high-correlation environment.
• Low Correlation: If the correlation is low, it is more likely that defaults will be idiosyncratic and spread out over time. This is beneficial for the protection buyer, as it is more likely that they will receive a payment. As a result, the premium on an FTD swap will be higher in a low-correlation environment.

Applications of FTD Swaps

FTD swaps have a wide range of applications for both investors and hedgers.

• Hedging: An FTD swap can be used to hedge the credit risk of a portfolio of bonds. For example, an investor who holds a portfolio of five corporate bonds can buy an FTD swap on those five names. This will protect the investor against the first default in the portfolio.
• Speculation: An FTD swap can also be used to speculate on the credit quality of a basket of reference entities. For example, a trader who believes that the credit quality of a particular sector is likely to deteriorate can buy an FTD swap on a basket of names from that sector.
• Correlation Trading: FTD swaps are a key instrument for trading credit correlation. A trader who believes that credit correlation is likely to increase can sell an FTD swap, and a trader who believes that credit correlation is likely to decrease can buy an FTD swap.

Pricing and Valuation

The pricing of an FTD swap is more complex than the pricing of a single-name CDS. It requires a model that can capture the joint default probability of the reference entities in the basket. The most common approach is to use a copula function, which is a mathematical function that describes the dependence between multiple random variables.

The key inputs into an FTD swap pricing model are:

• The CDS spreads of the individual reference entities
• The recovery rates of the individual reference entities
• The correlation of default among the reference entities

Conclusion

FTD swaps are a effective and versatile tool for managing credit risk and for trading credit correlation. They are more complex than single-name CDS, but they can offer significant advantages in terms of cost and flexibility. For those who have the expertise, FTD swaps can be an invaluable addition to the credit trading toolkit.