Maximum Drawdown and Drawdown Duration of Spectrally Negative Levy Processes Decomposed at Extremes

TL;DR

This paper analyzes the maximum drawdown and duration of spectrally negative Levy processes by decomposing paths at extrema, providing detailed distributional characterizations of these financial risk measures.

Contribution

It introduces a novel path decomposition approach for spectrally negative Levy processes, enabling explicit distributional results for drawdowns and durations at extrema.

Findings

Derived distributions of supremum and drawdowns for decomposed processes

Characterized the law of drawdown durations in spectrally negative Levy processes

Provided analytical tools for risk assessment in financial models

Abstract

Path decomposition is performed to characterize the law of the pre/post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy process taken up to an independent exponential time T: As a result, mainly the distributions of the supremum of the post-infimum process and the maximum drawdown of the pre/postsupremum, post-infimum processes and the intermediate processes are obtained together with the law of drawdown durations.