TANGENT MODELS AS A MATHEMATICAL FRAMEWORK FOR DYNAMIC CALIBRATION

René Carmona () and Sergey Nadtochiy ()
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René Carmona: Bendheim Center for Finance, ORFE, Princeton University, Princeton, NJ 08544, USA
Sergey Nadtochiy: Bendheim Center for Finance, ORFE, Princeton University, Princeton, NJ 08544, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 01, 107-135

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.

Keywords: Market models; Heath–Jarrow–Morton approach; implied volatility; local volatility; tangent Lévy models (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219024911006280

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