Local Variance Gamma and Explicit Calibration to Option Prices
AbstractIn 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1308.2326.
Date of creation: Aug 2013
Date of revision: Jan 2014
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-08-16 (All new papers)
- NEP-FMK-2013-08-16 (Financial Markets)
- NEP-SPO-2013-08-16 (Sports & Economics)
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- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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