Essays on the Interest Rate Model Specification, Estimation and Valuation of Defaultable Securities

The first chapter compares two different panel-data estimation methods, the Kalman filter and the Chen and Scott methods, on the Cox, Ingersoll, and Ross (CIR, 1985) term structure model through Monte Carlo simulation. Both methods utilize all information available but have different assumptions on the structure of the variancecovariance matrix of the measurement errors, C. My main findings are that the Kalman filter method with a diagonal C assumption has the best performance with large samples and with both monthly and weekly data. For the small sample case, the Kalman filter with a non-diagonal C assumption dominates. The second chapter presents a re-examination of Chan, Karolyi, Longstaff, and Sanders (CKLS, 1992) based on a panel-data approach. It is assumed that all zerocoupon yields are observed with measurement errors but imposing linear restrictions on the errors. I find that by redefining the regime period, there is strong evidence of a structural break between the 1979-1 982 period. Furthermore, I find evidence that interest rate volatility is not as sensitive to level of the interest rates as stated in the CKLS paper. Finally, I find that the Brennan and Schwartz (1980) model is superior to others when the 1979-1982 period is included in the data, whereas the Cox, lngersoll and Ross (CIR, 1985) model is the best for data excluding the 1979-1982 period. This last finding suggests that the decision to allow or not to allow for a structural break can have a statistically and economically significant impact on the short-rate volatility estimation and model selection. The third chapter studies the valuation of defaultable, callable bonds and credit default swaps when both interest rates and default intensity are stochastic. The model I adopt in the paper follows the framework of Duffie and Singleton (1 999) and I determine the prices of these two defaultable securities numerically. I allow for non-zero correlation between the market and the credit risk risks and examine the effect of this correlation on valuation and term structures of callable bonds and on default spreads. In addition, for defaultable, callable bonds, I examine the effects of different assumptions regarding recovery rate and the notice period on the valuation of callable bonds.