Ghost Calibration and Pricing Barrier Options and CDS in Spectrally One-Sided L'evy Models: The Parabolic Laplace Inversion Method

Abstract

Recently, the advantages of conformal deformations of the contours of integration in pricing formulas were demonstrated in the context of wide classes of L'evy models and the Heston model. In the present paper we construct efficient conformal deformations of the contours of integration in the pricing formulas for barrier options and CDS in the setting of spectrally one-sided L'evy models, taking advantage of Rogers's trick (J. Appl. Prob. 2000) that greatly simplifies calculation of the Wiener-Hopf factors. We extend the trick to wide classes of L'evy processes of infinite variation with zero diffusion component. In the resulting formulas (both in the finite variation and the infinite variation cases), we make quasi-parabolic deformations as in S. Boyarchenko and Levendorskiu (IJTAF 2013), which greatly increase the rate of convergence of the integrals. We demonstrate that the proposed method is more accurate than the standard realization of Laplace inversion in many cases. We also exhibit examples in which the standard realization is so unstable that it cannot be used for any choice of the error control parameters.

This may lead to a ghost calibration: a situation where a parameter set of a model is declared to be a "good fit" to the data only because the errors of calibration and of the numerical method used for pricing (almost) cancel each other out.