A Generalized Fourier Transform Approach to Risk Measures

Journal of Statistical Mechanics (2010) P01005, Erratum: J. Stat. Mech. (2012) E05001

Posted: 6 Jun 2012

See all articles by Giacomo Bormetti

Giacomo Bormetti

University of Bologna - Department of Mathematics

Valentina Cazzola

affiliation not provided to SSRN

Giacomo Livan

Abdus Salam International Centre for Theoretical Physics (ICTP)

Guido Montagna

University of Pavia and INFN, Pavia Unit

Oreste Nicrosini

Istituto Nazionale di Fisica Nucleare Sezione di Pavia

Date Written: June 5, 2012

Abstract

We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework in which to efficiently compute the most popular risk measures, value-at-risk and expected shortfall (also known as conditional value-at-risk). The only ingredient required by our approach is the knowledge of the characteristic function describing the financial data in use. This allows us to extend risk analysis to those non-Gaussian models defined in the Fourier space, such as Lévy noise driven processes and stochastic volatility models. We test our analytical results on data sets coming from various financial indexes, finding that our predictions outperform those provided by the standard log-normal dynamics and are in remarkable agreement with those of the benchmark historical approach.

Keywords: Models of financial markets, Value-at-Risk, CVaR, Bootstrap

JEL Classification: C15, C22, G10

Suggested Citation

Bormetti, Giacomo and Cazzola, Valentina and Livan, Giacomo and Montagna, Guido and Nicrosini, Oreste, A Generalized Fourier Transform Approach to Risk Measures (June 5, 2012). Journal of Statistical Mechanics (2010) P01005, Erratum: J. Stat. Mech. (2012) E05001, Available at SSRN: https://ssrn.com/abstract=2078160

Giacomo Bormetti (Contact Author)

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Valentina Cazzola

affiliation not provided to SSRN ( email )

Giacomo Livan

Abdus Salam International Centre for Theoretical Physics (ICTP) ( email )

Strada Costiera 11
34100 Trieste
United States

Guido Montagna

University of Pavia and INFN, Pavia Unit ( email )

via A. Bassi 6
Pavia, Pavia 27100
Italy

Oreste Nicrosini

Istituto Nazionale di Fisica Nucleare Sezione di Pavia ( email )

via A. Bassi 6
Pavia, Pavia 27100
Italy

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