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

Chapter 6 in Finance at Fields, 2012, pp 151-179 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractMotivated 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: Mathematical Finance; Financial Mathematics; Risk Management; Asset Pricing; Computational Finance; Derivatives; Option Pricing; Portfolio Optimization (search for similar items in EconPapers)
Date: 2012
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