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

TL;DR

This paper introduces a novel order statistics-based estimator for disentangling volatility and jumps in financial data, improving market risk forecasting and outperforming traditional methods in empirical tests.

Contribution

It presents a new integrated variance estimator within jump-diffusion models and an iterative algorithm for better volatility and jump detection in market risk modeling.

Findings

Outperforms standard historical simulation in VaR forecasting

Successfully disentangles volatility from jumps in simulated and empirical data

Provides a practical iterative algorithm for real-time volatility and jump estimation

Abstract

This paper proposes a new integrated variance estimator based on order statistics within the framework of jump-diffusion models. Its ability to disentangle the integrated variance from the total process quadratic variation is confirmed by both simulated and empirical tests. For practical purposes, we introduce an iterative algorithm to estimate the time-varying volatility and the occurred jumps of log-return time series. Such estimates enable the definition of a new market risk model for the Value at Risk forecasting. We show empirically that this procedure outperforms the standard historical simulation method applying standard back-testing approach.