Tangent models as a mathematical framework for dynamic calibration

Rene A. Carmona, Sergey Nadtochiy

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Motivated by the desire to integrate repeated calibration procedures into a single dynamic market model, we introduce the notion of a "tangent model" in an abstract set up, and we show that this new mathematical paradigm accommodates all the recent attempts to study consistency and absence of arbitrage in market models. For the sake of illustration, we concentrate on the case when market quotes provide the prices of European call options for a specific set of strikes and maturities. While reviewing our recent results on dynamic local volatility and tangent Lévy models, we present a theory of tangent models unifying these two approaches and construct a new class of tangent Lévy models, which allows the underlying to have both continuous and pure jump components.

Original languageEnglish (US)
Pages (from-to)107-135
Number of pages29
JournalInternational Journal of Theoretical and Applied Finance
Volume14
Issue number1
DOIs
StatePublished - Feb 1 2011

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics, Econometrics and Finance(all)

Keywords

  • HeathJarrowMorton approach
  • Market models
  • implied volatility
  • local volatility
  • tangent Lévy models

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