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

Peter Carr; Ajay Khanna; Dilip B. Madan

doi:10.21314/JCF.2016.309

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

Peter Carr, Ajay Khanna, Dilip B. Madan

Finance and Risk Engineering

Research output: Contribution to journal › Article › peer-review

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 + A|x|)^−K. It is observed that this model adjustment can be crashmarket consistent.

Original language	English (US)
Pages (from-to)	89-111
Number of pages	23
Journal	Journal of Computational Finance
Volume	20
Issue number	1
DOIs	https://doi.org/10.21314/JCF.2016.309
State	Published - Sep 2016

Keywords

Beta exposure pricing
CGMY model
Completely monotone function
Gap risk pricing
Gauss Laguerre quadrature
Negative binomial process

ASJC Scopus subject areas

Finance
Computer Science Applications
Applied Mathematics

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10.21314/JCF.2016.309

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title = "Adjusting exponential l{\'e}vy models toward the simultaneous calibration of market prices for crash cliquets",

abstract = "In this paper, option-calibrated exponential L{\'e}vy models are observed to typically overprice crash cliquets. Typical model L{\'e}vy tails are then not crash-market consistent. A general tail-thinning strategy is introduced that may be implemented on a class of parametric L{\'e}vy 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 + A|x|)−K. It is observed that this model adjustment can be crashmarket consistent.",

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

Abstract

Keywords

ASJC Scopus subject areas

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