Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
Adjusting exponential Lévy models toward the simultaneous calibration of market prices for crash cliquets
Peter Carr, Ajay Khanna and Dilip B. Madan
Need to know
- 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
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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