Local Variance Gamma and Explicit Calibration to Option Prices

43 Pages Posted: 15 Jan 2017

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Sergey Nadtochiy

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: January 2017

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 analyze a special class of pure jump Markov martingale models and provide an algorithm for calibrating such models to match the market prices of European options with multiple strikes and maturities. This algorithm matches option prices exactly and only requires solving several one‐dimensional root‐search problems and applying 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.

Keywords: exact calibration, implied smile, local variance gamma

Suggested Citation

Carr, Peter P. and Nadtochiy, Sergey, Local Variance Gamma and Explicit Calibration to Option Prices (January 2017). Mathematical Finance, Vol. 27, Issue 1, pp. 151-193, 2017. Available at SSRN: https://ssrn.com/abstract=2899169 or http://dx.doi.org/10.1111/mafi.12086

Peter P. Carr (Contact Author)

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Sergey Nadtochiy

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

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