Piergiacomo Sabino (Uniper Golbal Commodities)

We analyze a method to produce pairs of non independent Poisson processes (M(t);N(t)) from positively correlated, self-decomposable, exponential renewals. In particular we provide the family of copulas pairing the renewals, along with the closed form for the joint distribution of the pair (M(t);N(t)). If indeed the pairs of correlated, exponential random variables (Xk; Yk) used as renewals in our processes are interpreted as random times with a random delay, the proposed model can help describing their co-movement and can answer some common questions arising in the financial context: - Once a financial institution defaults how long should one wait for a dependent institution to default too? - A market receives a news interpreted as a shock: how long should one wait to see the propagation of that shock onto a dependent market? - If different companies are interlinked, what is the impact on insurance risk? These outcomes turn out to be instrumental to produce a new explicit algorithm applied in the option pricing, as well as in the credit and insurance risk modeling.