Wycena asymetrycznych opcji potęgowych – nowe podejście oparte na transformacie Fouriera
Pricing Asymmetric Power Options – New Method Based on the Fourier Transform

Summary/Abstract: The purpose of this article is to compare three ways of evaluating asymmetric power options in the Black-Scholes framework: martingale approach and two concepts based on the Fourier transform (including one derived by the author of the article). The methodology of the conducted research is based on comparing computational efficiency of every approach to pricing asymmetric power options. As a part of the subject matter, speed and accuracy of three methods of pricing options is analyzed. Based on the obtained results, it can be concluded that both Fourier-based approaches generate theoretical prices of the options slower than in the martingale method. Moreover, Fourier-based methods are error-prone. In spite of this, they can not be considered to be unequivocally worse than the martingale approach, as they offer possibility of pricing options, including asymmetric power options, in models that best reflect the real market conditions, i.e, the stochastic volatility models. The greatest value of the submitted paper is a possibility of applying the author’smethod of pricing asymmetric power options and analysis of its speed and computational accuracy.

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