Modeling bonds and bond options in the presence of default risk.

Summary The purpose of this thesis is to propose a model of bonds and bond options in the presence of default risk in the most realistic framework possible. The first chapter presents the main models that account for the valuation of debt issued by private firms, subject to default risk. We find that it is difficult, within a realistic framework, to obtain a simple and easy-to-implement analytical formula to calculate the value of securities subject to default risk. The second chapter proposes an extension of the Merton (1974) model. We present a bond valuation model of risky zero-coupon bonds based on both the Cox, Ingersoll, and Ross (1985) single-factor rate model and the explicit finite difference method improved by Hull and White (1990). The third chapter focuses on the valuation of coupon bonds in the presence of default risk. The default event is modeled as the first date when the value of the firm's assets falls below the value of its liabilities. In line with practice, default is declared not only for the coupon bond, but also for all other debts of the firm. In case of default, the bondholder receives a fraction of the value that the bond would have had in case of non-default. We show that the level of spreads deduced by our model corresponds to that observed in practice. Through an empirical study on the French bond market, we show that our model estimates the price of private sector coupon bonds in a satisfactory manner. In the fourth chapter, we adapt the model constructed in the previous chapter to the valuation of European and American bond options in the presence of default risk. We distinguish three categories of options: (I) options issued by third parties with no default risk on risky bonds, (II) options issued by third parties subject to default risk on bonds with no default risk, and (III) options in the presence of two sources of default risk, the first relating to the option writer and the second to the underlying.