Modelling spread risk via time-change approach

The thesis considers two stochastic models for managing spread risk: i) the Duffie-Singleton model; ii) a model developed in the context of electricity spot price modelling, properly adapted to model spread risk, obtained by changing the Duffie-Singleton model with compound Poisson’s jumps with exponentially distributed jump size and a subordinated process as a random clock. The latter has a mean reverting jump component that leads to mean reversion in the level of credit spread in addition to the smooth mean reversion force. In order to calibrate the models the particle filtering technique is used, which allows for the estimate of real-world and risk-neutral probability distributions from time series of credit spread observations.