The default of a security written on some underlying is often modelled as the first time the value of the underlying falls below a certain level. Pricing such securities therefore requires knowledge about the law of first passage times. Today underlying securities are often modelled by jump diffusion processes. For such models it is usually impossible to find closed form expressions for first passage time densities. Pricing defaultable securities can only be realized numerically. A naive approach is the simulation of discretized trajectories. This method is biased and very time consuming. The thesis presents more efficient algorithms for pricing defaultable securities, which introduce smaller or no bias. All except one are based on Brownian bridge techniques. This is motivated by the fact that in between jumps a jump diffusion behaves like a pure diffusion. Under the assumption that volatility and drift of the pure diffusion are constant, Brownian bridge techniques are applicable. The alternative algorithm requires much weaker assumptions. The volatility and drift of the pure diffusion part can be stochastic and time dependent. They merely need to satisfy sufficient smoothness properties. The method is heavily based on rejection sampling techniques. All algorithms are implemented for different model parameters and compared in terms of accuracy and speed.      «

The default of a security written on some underlying is often modelled as the first time the value of the underlying falls below a certain level. Pricing such securities therefore requires knowledge about the law of first passage times. Today underlying securities are often modelled by jump diffusion processes. For such models it is usually impossible to find closed form expressions for first passage time densities. Pricing defaultable securities can only be realized numerically. A naive approac...     »