Financial mathematics

Deep Smoothing of the Implied Volatility Surface

We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial …

Dependent Defaults and Losses with Factor Copula Models

We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high dimensional models remain parsimonious with pair copula constructions, and nest many …