Journal of Computational Finance

Risk.net

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

Peter Carr, Ajay Khanna and Dilip B. Madan

  • Near money exponentially extrapolated jump arrival rates too high for crash cliquets. 
  • Completely monotone dampers are employed for tail thinning. 
  • Single name crash cliquets priced by exposure to index crashes.

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 |). It is observed that this model adjustment can be crashmarket consistent.

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