Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided Lévy 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 Lévy 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 Lévy models, taking advantage of Rogers’s trick [J. Appl. Prob., 2000, 37, 1173–1180] that greatly simplifies calculation of the Wiener-Hopf factors. We extend the trick to wide classes of Lévy 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 Boyarchenko and Levendorskiĭ [Int. J. Theor. Appl. Finance, 2013, 16 (3), 1350011], which greatly increase the rate of convergence of the integrals. We demonstrate that in many cases the proposed method is more accurate than the standard realization of Laplace inversion. 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.

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