LOCAL VARIANCE GAMMA AND EXPLICIT CALIBRATION TO OPTION PRICES

Peter Carr, Sergey Nadtochiy

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)151-193
Number of pages43
JournalMathematical Finance
Volume27
Issue number1
DOIs
StatePublished - Jan 1 2017

Keywords

  • exact calibration
  • implied smile
  • local variance gamma

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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