Internal Seminar: Umberto Cherubini

Title: "Long Term Risk: A Time Change Approach"

  • Date: 07 September 2022 from 13:00 to 14:00

  • Event location: Seminar Room - Piazza Scaravilli, 2 + Microsoft Teams Meeting

Abstract 

We study an asset pricing model in which a Stochastic Discount Factor (SDF) and a growth process have independent increments and are affected by a common stochastic clock. The stochastic clock is a strictly increasing process that may include a persistent component, that we call comonotonic, and represents sources of long run uncertainty, such as those induced by climate change issues. We find that long term log-returns are lower the higher the variance of the clock, and the more relevant its comonotonic component. The comonotonic component in the clock induces a separation of the SDF dynamics between persistent and transitory shocks similar to that assumed in the long term risk literature, with the difference that the system is non Markovian. We also provide an axiomatic definition of the compounding operation leading to an associative algebraic structure, with generator represented by the Laplace transform of the stochastic clock increments. The same generator characterizes the Archimedean copula function linking the SDF and the growth process.