Essays on pricing of derivatives with interest rate, credit, and equity risks

Date of Completion

January 2007


Economics, Finance




There are three essays in this dissertation. In the first essay titled "Extending the LYONs pricing Model", we extend the McConnell and Schwartz (1986) model for pricing liquid yield option notes (LYONs). LYONs are zero-coupon, callable, putable and convertible bonds. The McConnell and Schwartz model assumes that the LYONs can be converted into common stock unconditionally, and no interest is paid on these bonds. However, for many LYONs trading today, their convertibility into common stock is conditional upon the issuer's stock price crossing certain prescribed thresholds. Also, many LYONs pay interest, contingent upon the price of the LYON again crossing certain prescribed thresholds. The McConnell and Schwartz pricing model does not address these issues. We extend their model to take into account the issues of conditional convertibility and contingent interest, and also treat default risk differently.^ In the second essay titled "Pricing Securities with Multiple Risks: An Empirical Study", we test the empirical performance of the Das and Sundaram (2006) model. This model is for the pricing of securities faced with equity, interest rate and credit risks. After showing how various inputs to the model can be estimated, we first apply the model to a sample of non-convertible bonds in the American and the European markets.^ Then we show how the Das and Sundaram model can be extended to price convertible bonds which have a peculiar conversion feature; these bonds are convertible not into the stock of the bond issuer, but into the stock of a different company. We also test the empirical performance of this extended model.^ In the third essay titled "An Empirical Comparison of Two Simple Models for Valuing Risky Debt", we compare the empirical performance of the Longstaff and Schwartz (1995) model and the Das and Sundaram (2006) model. The Das and Sundaram model is for valuing both convertible debt and non-convertible debt, whereas the Longstaff and Swchartz model is for valuing only non-convertible debt. The interesting feature of the Longstaff and Schwartz model is that it provides a closed-form solution. We test the relative performance of these two models on a sample of non-convertible bonds.^