NUMERICAL ANALYSIS ON LOCAL RISK-MINIMIZATION FOR EXPONENTIAL LÉVY MODELS

Takuji Arai (), Yuto Imai () and Ryoichi Suzuki ()
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Takuji Arai: Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
Yuto Imai: Department of Mathematics, Waseda University, 3-4-1 Okubo, Shinjyuku-ku, Tokyo 169-8555, Japan
Ryoichi Suzuki: Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 02, 1-27

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.

Keywords: Local risk minimization; fast Fourier transform; exponential Lévy processes; Merton jump-diffusion processes; variance gamma processes (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219024916500084

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