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Pricing correlation options: from the P. Carr and D. Madan approach to the new method based on the Fourier transform

100%
Orzechowski A.
Economics and Business Review
|
2018
|
vol. 4(18)
|
issue 1
16-28
EN
Pricing of options plays an important role in the financial industry. Investors knowing how to price derivative contracts quickly and accurately can beat the market. On the other hand market participants constructing their investment strategies with the use of options based on techniques that do not assure the highest computational speed and efficiency are doomed to failure. The aim of the article is to extend the existing methodology of pricing correlation options based on the Fourier transform. The article starts with a presentation of Carr and Madan’s concept (Carr & Madan, 1999). Then other methods of pricing options with the use of the Fourier transform are summarized. Finally, a new approach to pricing derivative contracts is derived and then applied to the correlation options.
2
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WYCENA ASYMETRYCZNYCH OPCJI LOGARYTMICZNYCH ZA POMOCĄ TRANSFORMATY FOURIERA

75%
Orzechowski A.
Metody Ilościowe w Badaniach Ekonomicznych
|
2018
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vol. 19
|
issue 3
238-250
PL
Celem artykułu jest wycena europejskich opcji logarytmicznych o asymetrycznym profilu wypłaty. W ramach podejmo­wanej problematyki zaproponowane zostały trzy podejścia pozwalające określić wartość modelową analizowanych instrumentów pochodnych przy utrzymaniu założeń właściwych modelowi F. Blacka i M. Scholesa, tj. podejście martyngałowe, F. Blacka i M. Scholesa oraz bazujące na transformacie Fouriera. Ponadto, dokonano analizy szybkości i dokładności obliczeniowej uwzględnionych podejść do wyceny analizowanych derywatów.
EN
"The aim of the article is to price European logarithmic options via Fourier transform. As a part of the subject metter, three approaches were proposed to determine theoretical value of the analyzed derivatives in the F. Black and M. Scholes setting, i.e. the martingale approach, F. Black and M. Scholes approach and the approach based on the Fourier transform. In addition, an analysis of the computational speed and accuracy of the valuations was carried out."
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