Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging
problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may …

So far, path-dependent volatility models have drawn little attention from both practitioners
and academics compared to local volatility and stochastic volatility models. This is unfair: in …

We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the
Hörmander's condition. We prove an intrinsic Taylor formula with global and local bounds for …

A new analytical approximation tool, derived from the classical PDE theory, is introduced in
order to build approximate transition densities of diffusions. The tool is useful for …

We give a complete and self-contained proof of the existence of a strong solution to the free
boundary and optimal stopping problems for pricing American path-dependent options. The …

Установлена полиномиальная субриманова дифференцируемость широких классов
гёльдеровых в субримановом смысле отображений таких, как классы гладких …

We develop approximate formulae expressed in terms of elementary functions for the
density, the price and the Greeks of path dependent options of Asian style, in a general local …

The polynomial sub-Riemannian differentiability is established for the large classes of
Hölder mappings in the sub-Riemannian sense, namely, the classes of smooth mappings …

Dupire's functional Itô calculus provides an alternative approach to the classical Malliavin
calculus for the computation of sensitivities, also called Greeks, of path-dependent …

We study the obstacle problem for a class of degenerate parabolic operators with
continuous coefficients. This problem arises in the Black–Scholes framework when …