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The Quadratic Local Variance Gamma Model: an arbitrage-free interpolation of class $\mathcal{C}^3$ for option prices

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  • Fabien Le Floc'h

Abstract

This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function. The formulation encompasses the piecewise linear Bachelier and piecewise linear Black local variance gamma models. The quadratic local variance function results in an arbitrage-free interpolation of class $\mathcal{C}^3$. The increased smoothness over the piecewise-constant and piecewise-linear representation allows to reduce the number of knots when interpolating raw market quotes, thus providing an interesting alternative to regularization while reducing the computational cost.

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  • Fabien Le Floc'h, 2023. "The Quadratic Local Variance Gamma Model: an arbitrage-free interpolation of class $\mathcal{C}^3$ for option prices," Papers 2305.13791, arXiv.org.
    • Handle: RePEc:arx:papers:2305.13791
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    File URL: http://arxiv.org/pdf/2305.13791
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