On the drawdown of completely asymmetric Lévy processes

By Aleksandar Mijatovic, Martijn Pistorius. 2011

92 citations recorded by the source corpus.

The drawdown process Y of a completely asymmetric Levy process X is equal to X reflected at its running supremum X¯: Y=X¯−X. In this paper we explicitly express in terms of the scale function and the Levy measure of X the law of the sextuple of the first-passage time of Y over the level a>0, the time G¯τa of the last supremum of X prior to τa, the infimum X¯τa and supremum X¯τa of X at τa and the undershoot a−Yτa− and overshoot Yτa−a of Y at τa. As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential Levy model.

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/120e2306a32dcf876e8b866797a50e674ac705f4

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In Finance

1. Bin Li
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In Management Science and Operations Research

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2. Hongzhong Zhang
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Citations in the corpus

• ON A CONVEX MEASURE OF DRAWDOWN RISK (2014, unknown): “Drawdowns of spectrally negative Lévy processes were analyzed in Mijatovic and Pistorius (2012).”
• On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, methodology): “Moreover, by a similar approximation argument, one can solve for the joint distribution of equation (3.6) but with the law of Yτa , which then recovers the sextuple law in Theorem 1 of Mijatović and Pistorius [29] (the running minimum at τa can also be easily incorporated).”