Theoretical Foundations for Quantitative Finance

Jumping VaR: Order Statistics Volatility Estimator for Jumps Classification and Market Risk Modeling

“…We mainly consider this paper and Mancini et al (2011) as a starting point for our contribution. Additional details on this estimator can be found in Spadafora et al (2017). While several authors have focused their research on jump-diffusion models to describe the asset return dynamics, it is worth noting that Carr et al (2002) and Geman (2002) have pointed out that pure jump Lévy processes can be used to model asset returns in a more realistic way, substituting the continuous part with infinite small jumps due to the infinite activity jump component of the Lévy process.…”