Numerical analysis on local risk-minimization for exponential lévy models

Takuji Arai; Yuto Imai; Ryoichi Suzuki

doi:10.1142/S0219024916500084

Numerical analysis on local risk-minimization for exponential lévy models

Takuji Arai, Yuto Imai, Ryoichi Suzuki

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

Original language	English
Article number	1650008
Journal	International Journal of Theoretical and Applied Finance
Volume	19
Issue number	2
DOIs	https://doi.org/10.1142/S0219024916500084
Publication status	Published - 2016 Mar 1

Keywords

exponential Lévy processes
fast Fourier transform
Local risk minimization
Merton jump-diffusion processes
variance gamma processes

ASJC Scopus subject areas

Economics, Econometrics and Finance(all)
Finance

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10.1142/S0219024916500084

Cite this

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abstract = "We illustrate how to compute local risk minimization (LRM) of call options for exponential L{\'e}vy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential L{\'e}vy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.",

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AU - Imai, Yuto

AU - Suzuki, Ryoichi

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N2 - We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

AB - We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

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Numerical analysis on local risk-minimization for exponential lévy models

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Keywords

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