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Some Explicitly Solvable SABR and Multiscale SABR Models: Option Pricing and Calibration
Department of Mathematics and Information Technology, University of Camerino, Camerino, Italy
Department of Economics, University of Verona, Verona, Italy
Department of Management, University Politecnica Marche, Ancona, Italy
Department of Mathematics, “G. Castelnuovo”, University of Rome “La Sapienza”, Rome, Italy
- 1 Department of Mathematics and Information Technology, University of Camerino, Camerino, Italy
- 2 Department of Economics, University of Verona, Verona, Italy
- 3 Department of Management, University Politecnica Marche, Ancona, Italy
- 4 Department of Mathematics, “G. Castelnuovo”, University of Rome “La Sapienza”, Rome, Italy
Journal of Mathematical Finance·Volume 03 (2013)·Pages 10–32·Published 26 February 2013·DOI10.4236/jmf.2013.31002
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Abstract
A multiscale SABR model that describes the dynamics of forward prices/rates is presented. New closed form formulae for the transition probability density functions of the normal and lognormal SABR and multiscale SABR models and for the prices of the corresponding European call and put options are deduced. The technique used to obtain these formulae is rather general and can be used to study other stochastic volatility models. A calibration problem for these models is formulated and solved. Numerical experiments with real data are presented.
KeywordsMultiscale Stochastic Volatility ModelsOption PricingCalibration ProblemFX Data
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