Dynamic Currency Hedging with Non-Gaussianity and Ambiguity

43 Pages Posted: 19 Aug 2021 Last revised: 6 Feb 2023

See all articles by Pawel Polak

Pawel Polak

Stony Brook University-Department of Applied Mathematics and Statistics; Institute for Advanced Computational Science

Urban Ulrych

École Polytechnique Fédérale de Lausanne (EPFL); University of Zurich - Department of Banking and Finance; Swiss Finance Institute

Date Written: August 10, 2021

Abstract

This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need of additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios in gross terms and net of transaction costs.

Keywords: Currency Hedging, Non-Gaussianity, Ambiguity, Filtered Historical Simulation, Expected Shortfall, Currency Risk Management.

JEL Classification: C53, C58, F31, G11, G15

Suggested Citation

Polak, Pawel and Ulrych, Urban, Dynamic Currency Hedging with Non-Gaussianity and Ambiguity (August 10, 2021). Swiss Finance Institute Research Paper No. 21-60, Available at SSRN: https://ssrn.com/abstract=3906716 or http://dx.doi.org/10.2139/ssrn.3906716

Pawel Polak

Stony Brook University-Department of Applied Mathematics and Statistics ( email )

Stony Brook University
Stony Brook, NY 11794
United States

Institute for Advanced Computational Science ( email )

100 Nicolls Rd
Mailstop 5250
Stony Brook, NY 11794
United States

HOME PAGE: http://https://sites.google.com/view/pawelpolak/

Urban Ulrych (Contact Author)

École Polytechnique Fédérale de Lausanne (EPFL) ( email )

Switzerland

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

Plattenstr 32
Zurich, 8032
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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