Saddlepoint Approximation Methods in Financial Engineering by Yue Kuen Kwok & Wendong Zheng

Author:Yue Kuen Kwok & Wendong Zheng
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

It is well known that the density function can be obtained by the Fourier inversion method once the characteristic function is available. Yet, the numerical Fourier inversion procedure tends to lose information about the potential infinitely many small jumps of the Lévy process, due to the truncation made to facilitate the numerical integration. Fortunately, there is no such truncation needed in saddlepoint approximation. This may make the identification of extremely small jumps possible in the density function.

Using (3.16), the cgf of is given by

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