Adjusting exponential Lévy models toward the simultaneous calibration of market prices for crash cliquets

Peter Carr and Ajay Khanna and Dilip B. Madan

Journal of Computational Finance

Abstract: ABSTRACT In this paper, option-calibrated exponential Lévy models are observed to typically;overprice crash cliquets.Typical model Lévy tails are then not crash-market consistent.;A general tail-thinning strategy is introduced that may be implemented on a class of;parametric Lévy models closed under exponential tilting. Implementation on the Carr-Geman-Madan-Yor (CGMY) model leads to the CGAKMY model with a thinning;function of (1 + Α | χ |)-Κ. It is observed that this model adjustment can be crashmarket;consistent.

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