Sensitivity of the near - to - maturity European options: comparison of the Carr - Madan approach with a new method based on the Fourier transform
Sensitivity of the near - to - maturity European options: comparison of the Carr - Madan approach with a new method based on the Fourier transform

Summary/Abstract: Purpose – analysis of the sensitivity of the valuation of the near - to - maturity European options (performed via the Fourier transform) on the parameter alpha and other risk factors. Design/methodology/approach – research is based on the analysis of the sensitivity of the differences between the prices of the European options in the Black - Scholes framework with the theoretical values of the contracts generated by two methods based on the Fourier transform on the changes of different factors. Findings – the Black - Scholes model is better than other approaches based on the Fourier transform. Despite this, in the case of some models, e.g. stochastic volatility models, methods based on the Fourier transform, e.g. the Carr - Madan method or a new method proposed in the article, must be applied. Originality/value – an analysis of the sensitivity of the valuation of the near - to - maturity European options to different factors using two methods based on the Fourier transform (including one discovered by the author of the article).

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