In this paper, we assume that the log return of the underlying asset follows a semi-Markov process, then from the knowledge of the kernel we derive an explicit expression for the value of the option and for the bare risk in the case of the European call (put) option and, by means of a recursive...

In this paper, we present a model to describe the evolution of the yield spread by considering the rating evaluation as the determinant of credit spreads. The underlying rating migration process is assumed to be a non-homogeneous discrete time semi-Markov process. We calculate the total sum of...

This paper presents a duration dependent model for analyzing the evolution of credit ratings. It considers the backward recurrence process to tackle the time of permanence problem in the rating classes. In this way it is possible to manage the duration effects, which represent one of the most...

We propose a semi-Markov modulated interest rate model. We assume that the switching process is a semi-Markov process with finite state space and the modulated process is a diffusive process. Classical models such as those by Vasicek and CIR are generalized.