Tangent models as a mathematical framework for dynamic calibration

Rene A. Carmona, Sergey Nadtochiy

Research output: Chapter in Book/Report/Conference proceedingChapter

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)
Title of host publicationFinance at fields
PublisherWorld Scientific Publishing Co.
Pages151-180
Number of pages30
ISBN (Electronic)9789814407892
ISBN (Print)9789814407885
DOIs
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • Business, Management and Accounting(all)
  • Economics, Econometrics and Finance(all)
  • Mathematics(all)

Keywords

  • Heath-Jarrow-Morton approach
  • Implied volatility
  • Local volatility
  • Market models
  • Tangent Lévy models

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  • Cite this

    Carmona, R. A., & Nadtochiy, S. (2012). Tangent models as a mathematical framework for dynamic calibration. In Finance at fields (pp. 151-180). World Scientific Publishing Co.. https://doi.org/10.1142/9789814407892_0006