Three essays on the pricing of fixed income securities with credit risk

This thesis studies the impacts of credit risk, or the risk of default, on the pricing of fixed income securities. It consists of three essays. The first essay extends the classical corporate debt pricing model in Merton (1974) to incorporate stochastic volatility (SV) in the underlying firm asset value and derive a closed-form solution for the price of corporate bond. Simulation results show that the SV specification for firm asset value greatly increases the resulting credit spread levels. Therefore, the SV model addresses one major deficiency of the Merton-type models: namely, at short maturities the Merton model is unable to generate credit spreads high enough to be compatible with those observed in the market. In the second essay, we develop a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. Our empirical results show that the model is successful at fitting actual corporate bond credit spreads. In addition, key properties of actual credit spreads are better captured by the model. Finally, the third essay proposes a model of interest rate swap spreads. The model accommodates both the default risk inherent in swap contracts and the liquidity difference between the swap and Treasury markets. The default risk and liquidity components of swap spreads are found to behave very differently: first, the default risk component is positively related to the riskless interest rate, whereas the liquidity component is negatively correlated with the riskless interest rate; second, although default risk accounts for the largest share of the levels of swap spreads, the liquidity component is much more volatile; and finally, while the default risk component has been historically positive, the liquidity component was negative for much of the 1990s and has become positive since the financial market turmoil in 1998.