Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps

Swiss Finance Institute Research Paper No. 19-76

Forthcoming, Mathematical Finance

50 Pages Posted: 2 Jan 2020 Last revised: 12 Jan 2021

See all articles by Walter Farkas

Walter Farkas

University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zürich

Ludovic Mathys

University of Zurich - Department of Banking and Finance

Nikola Vasiljevic

University of Zurich, Department of Banking and Finance

Date Written: December 27, 2019

Abstract

The present article deals with intra-horizon risk in models with jumps. Our general understanding of intra-horizon risk is along the lines of the approach taken in [BRSW04], [Ro08], [BMK09], [BP10], and [LV20]. In particular, we believe that quantifying market risk by strictly relying on point-in-time measures cannot be deemed a satisfactory approach in general. Instead, we argue that complementing this approach by studying measures of risk that capture the magnitude of losses potentially incurred at any time of a trading horizon is necessary when dealing with (m)any financial position(s). To address this issue, we propose an intra-horizon analogue of the expected shortfall for general profit and loss processes and discuss its key properties. Our intra-horizon expected shortfall is well-defined for (m)any popular class(es) of Lévy processes encountered when modeling market dynamics and constitutes a coherent measure of risk, as introduced in [CDK04]. On the computational side, we provide a simple method to derive the intra-horizon risk inherent to popular Lévy dynamics. Our general technique relies on results for maturity-randomized first-passage probabilities and allows for a derivation of diffusion and single jump risk contributions. These theoretical results are complemented with an empirical analysis, where popular Lévy dynamics are calibrated to the S&P 500 index and the Brent crude oil data, and an analysis of the resulting intra-horizon risk is presented.

Keywords: Intra-Horizon Risk, Value at Risk, Expected Shortfall, Levy Processes, Hyper-Exponential Distribution, Risk Decomposition

JEL Classification: C32, C63, G01, G51

Suggested Citation

Farkas, Walter and Mathys, Ludovic and Vasiljevic, Nikola, Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps (December 27, 2019). Swiss Finance Institute Research Paper No. 19-76, Forthcoming, Mathematical Finance, Available at SSRN: https://ssrn.com/abstract=3510202 or http://dx.doi.org/10.2139/ssrn.3510202

Walter Farkas (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

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Zürich, 8001
Switzerland
+41-44-634 3953 (Phone)
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HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

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ETH Zürich ( email )

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Ludovic Mathys

University of Zurich - Department of Banking and Finance ( email )

Plattenstr 32
Zurich, 8032
Switzerland

Nikola Vasiljevic

University of Zurich, Department of Banking and Finance ( email )

Plattenstrasse 14
Zurich, CH-8032
Switzerland

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