Local Variance Gamma and Explicit Calibration to Option Prices

Peter Carr and Sergey Nadtochiy

Papers from arXiv.org

Abstract: In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for calibrating a pure jump Markov martingale model to match the market prices of European options of multiple strikes and maturities. This algorithm only requires solutions of several one-dimensional root-search problems, as well as application of elementary functions. We show how to construct a time-homogeneous process which meets a single smile, and a piecewise time-homogeneous process which can meet multiple smiles.

Date: 2013-08, Revised 2014-01
New Economics Papers: this item is included in nep-fmk and nep-spo
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Citations: View citations in EconPapers (7)

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Journal Article: LOCAL VARIANCE GAMMA AND EXPLICIT CALIBRATION TO OPTION PRICES (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1308.2326

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