A market model for stochastic smile: a conditional density approach

The purpose of this paper is to introduce a new approach that allows to construct no-arbitrage market models of for implied volatility surfaces (in other words, stochastic smile models). That is to say, the idea presented here allows us to model prices of liquidly traded vanilla options as separate stochastic quantities. The main reason why market models of implied volatilities need to be constructed is that they can capture the stochastic nature of an implied volatility surface. More to the point, market models have a potential of improved pricing of forward volatility depending products, such as compound options. Besides, this framework allows to match the initial vanilla market by construction and hedge with simple call and put options in a natural way. The modelling approach presented in this paper relies on taking a deterministic smile model as a backbone around which a stochastic smile model can be constructed without violating no-arbitrage constraints

Model theory of special subvarieties and Schanuel-type conjectures

We use the language and tools available in model theory to redefine and clarify the rather involved notion of a {\em special subvariety} known from the theory of Shimura varieties (mixed and pure)

The Uniform Schanuel Conjecture Over the Real Numbers

We prove that Schanuel's conjecture for the reals is equivalent to a uniform version of itself

Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic

We show that algebraic analogues of universal group covers, surjective group homomorphisms from a $\mathbb{Q}$-vector space to $F^{\times}$ with "standard kernel", are determined up to isomorphism of the algebraic structure by the characteristic and transcendence degree of $F$ and, in positive characteristic, the restriction of the cover to finite fields. This extends the main result of "Covers of the Multiplicative Group of an Algebraically Closed Field of Characteristic Zero" (B. Zilber, JLMS 2007), and our proof fills a hole in the proof given there.Comment: Version accepted by the Bull. London Math. So