Pricing Credit Derivatives in a Wiener-Hopf Framework

We present fast and accurate pricing techniques for credit-derivative contracts when discrete monitoring is applied and the underlying evolves according to an exponential Lévy process. Our pricing approaches are based on the Wiener–Hopf factorization, and their computational cost is independent of the number of monitoring dates. Numerical results are presented in order to validate the pricing algorithm. Moreover, an analysis on the sensitivity of the probability of default and the credit spread term structures with respect to the process parameters is considered

Pricing Credit Derivatives in a Wiener-Hopf Framework

We present fast and accurate pricing techniques for credit-derivative contracts when discrete monitoring is applied and the underlying evolves according to an exponential Lévy process. Our pricing approaches are based on the Wiener–Hopf factorization, and their computational cost is independent of the number of monitoring dates. Numerical results are presented in order to validate the pricing algorithm. Moreover, an analysis on the sensitivity of the probability of default and the credit spread term structures with respect to the process parameters is considered

Modelling healthcare systems with phase-type distributions

Phase-type distribution, Coxian distribution, Markov chain, Patient flow, Healthcare modelling,

Invariance principles for non-uniform random mappings and trees

In the context of uniform random mappings of an n-element set to itself, Aldous and Pitman (1994) established a functional invariance principle, showing that many n!1 limit distributions can be described as distributions of suitable functions of reflecting Brownian bridge. To study non-uniform cases, in this paper we formulate a sampling invariance principle in terms of iterates of a fixed number of random elements. We show that the sampling invariance principle implies many, but not all, of the distributional limits implied by the functional invariance principle. We give direct verifications of the sampling invariance principle in two successive generalizations of the uniform case, to p-mappings (where elements are mapped to i.i.d. non-uniform elements) and P-mappings (where elements are mapped according to a Markov matrix). We compare with parallel results in the simpler setting of random trees