Pathwise Moderate Deviations for Option Pricing
25 Pages Posted: 21 Jun 2018
Date Written: March 21, 2018
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised variances. In passing, we highlight some intuitive relationships between moderate deviations rate functions and their large deviations counterparts; these turn out to be useful for numerical purposes, as large deviations rate functions are often difficult to compute.
Keywords: moderate deviations, weak convergence, multiscale diffusions, option pricing
JEL Classification: 60F10, 91G99, 91B25
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