Numerical analysis on local risk-minimization for exponential lévy models

Takuji Arai, Yuto Imai, Ryoichi Suzuki

Research output: Contribution to journalArticle

4 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 languageEnglish
Article number1650008
JournalInternational Journal of Theoretical and Applied Finance
Volume19
Issue number2
DOIs
Publication statusPublished - 2016 Mar 1

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Local risk-minimization
Numerical analysis
Call option
Fast Fourier transform
Variance gamma
Hedging
Jump-diffusion model
Incomplete markets
Contingent claims

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

Cite this

Numerical analysis on local risk-minimization for exponential lévy models. / Arai, Takuji; Imai, Yuto; Suzuki, Ryoichi.

In: International Journal of Theoretical and Applied Finance, Vol. 19, No. 2, 1650008, 01.03.2016.

Research output: Contribution to journalArticle

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