Local variance gamma and explicit calibration to option prices

Peter Carr, Sergey Nadtochiy

Research output: Contribution to journalArticle

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)
JournalMathematical Finance
DOIs
StateAccepted/In press - 2015

Fingerprint

maturity
Calibration
market price
strike
currency
European Options
Elementary Functions
commodity
Currency
Search Problems
Equity
equity
Martingale
Jump
market
Roots
Maturity
Option prices
Variance gamma
Model

Keywords

  • Exact calibration
  • Implied smile
  • Local variance gamma

ASJC Scopus subject areas

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

Cite this

Local variance gamma and explicit calibration to option prices. / Carr, Peter; Nadtochiy, Sergey.

In: Mathematical Finance, 2015.

Research output: Contribution to journalArticle

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