Pricing Discrete Barrier Options and Credit Default Swaps Under Levy Processes

We consider discretely monitored barrier options under Levy models, including single and double barrier options and first touch digitals, as well as CDS and defaultable bonds. At each step of backward induction, we use piece-wise polynomial interpolation and an efficient version of the Fourier transform techniques, which allows for efficient control of errors. We derive accurate recommendations for the choice of parameters of the numerical scheme, and produce numerical examples showing that oversimplified prescriptions in other methods can result in large errors