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Some Explicitly Solvable SABR and Multiscale SABR Models: Option Pricing and Calibration

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DOI: 10.4236/jmf.2013.31002    5,964 Downloads   11,162 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Fatone, F. Mariani, M. Recchioni and F. Zirilli, "Some Explicitly Solvable SABR and Multiscale SABR Models: Option Pricing and Calibration," Journal of Mathematical Finance, Vol. 3 No. 1, 2013, pp. 10-32. doi: 10.4236/jmf.2013.31002.

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