A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes

Abstract

This work aims to forecast (over 1, 5, and 15 years) the extremes, the expected value, and the volatility of natural disasters occurrences. To achieve this objective, we adopt a generalized two‐factor square‐root model linking together occurrences and volatility through stochastic correlation (Brownian motion). We use a generalized Pareto distribution (GPD) to forecast the maximum number of occurrences as a measure of value at risk (VaR). The results are checked in terms of accuracy, compared versus some baseline models (i.e., the Poisson process and the extreme value model) and backtested.

Modelling the Bitcoin prices and media attention to Bitcoin via the jump‐type processes

“…Note that here we essentially use the assumption that two Brownian motions used in (9) are independent. The case of correlated Brownian motions is considered in some applied papers, for example, in Orlando 26 it is used for modelling the occurrences of natural catastrophes.…”

Resilience and Complex Dynamics — Safeguarding Local Stability Against Global Instability

“…20 For a stochastic model on the expected value and the volatility of natural disasters occurrences see Orlando and Bufalo (2022a;.…”