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Quantitative Finance > Computational Finance

Title: An Expanded Local Variance Gamma model

Abstract: The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the option price which plays a role of Dupire's equation for the standard local volatility model. It is shown how calibration of multiple smiles (the whole local volatility surface) can be done in such a case. Further, assuming the local variance to be a piecewise linear function of strike and piecewise constant function of time this ODE is solved in closed form in terms of Bessel and hypergeometric functions. Calibration of the model to market smiles does not require solving any optimization problem and, in contrast, can be done term-by-term by solving a system of non-linear algebraic equations for each maturity, which is ultra-fast.
Comments: 35 pages, 7 figures, 4 tables
Subjects: Computational Finance (q-fin.CP); Mathematical Finance (q-fin.MF); Pricing of Securities (q-fin.PR)
Cite as: arXiv:1802.09611 [q-fin.CP]
  (or arXiv:1802.09611v1 [q-fin.CP] for this version)

Submission history

From: Andrey Itkin [view email]
[v1] Mon, 26 Feb 2018 21:16:57 GMT (234kb,D)