TITLE:
Some Explicitly Solvable SABR and Multiscale SABR Models: Option Pricing and Calibration
AUTHORS:
Lorella Fatone, Francesca Mariani, Maria Cristina Recchioni, Francesco Zirilli
KEYWORDS:
Multiscale Stochastic Volatility Models; Option Pricing; Calibration Problem; FX Data
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.3 No.1,
February
26,
2013
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.