Interest rate swaps : why do they exist and how should they be priced?

Abstract

This thesis applies the contingent claims analysis to investigate the reasons for the development and the pricing of interest rate swaps. I show that an interest rate swap transaction involves an exchange of credit risk between two firms and is not an arbitrage of market imperfections or inefficiencies as suggested by existing literature. The difference in credit risks gives firms comparative advantages by borrowing in different credit markets. Two firms can reduce their borrowing costs through interest rate swaps by trading their comparative advantages. This exchange of credit risks helps to complete the securities markets by expanding the opportunities for risk allocation, that is, by creating opportunities which are not yet provided by existing securities. Hence, an interest rate swap is not a redundant security and its contributions to reduce firms' borrowing costs and to complete the securities markets provide stronger reasons for its continuing development. The credit risks of interest rate swaps are not dealt with property by existing literature that either replicate an interest rate swap by using either a series of forwards or futures or by the exchange of a fixed rate bond for a floating rate note. I show that the contingent claims analysis on the payoffs of firms' liabilities and interest rate swaps can better deal with the credit risk of an interest rate swap.

In this thesis I make the following contributions to the research of interest rate swaps:

1) I show that quality spread differentials exist under the Black-Scholes-Merton option pricing models that assume perfect and efficient market conditions. The model shows that financial leverage and volatility of earnings asset values are the two major factors in determining the quality spread differential. The quality spread differential allows two firms to lower their borrowing costs through interest rate swaps.

2) Relaxing the standard assumptions of Black-Scholes-Merton models by including the coupon paying debts and allowing the default free interest rate to be variable, I develop a simulation model to price the default risky corporate fixed and floating rate debts. The results of the model show that quality spread differentials exist.

3) With the application of the Arrow-Debreu security analysis, I show that interest rate swaps help to complete the market under the debt and swap priority rules. By contrast, interest rate swaps under the cross default rule cannot complete the market.

4) I write option-like equations for the payoffs of interest rate swaps under different settlement rules based on the state contingent payoff analysis. The equations reflect the credit risks of both participating firms and serve as a foundation for the pricing of interest rate swaps.

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