Tomáš Vlček

Tomáš Vlček is a Senior Associate in the Mathematical Finance Division at the Institute for Advanced Dynamic Uncertainty, specialising in credit derivatives pricing, counterparty credit risk, and valuation adjustments. He holds a PhD in Probability and Mathematical Statistics from the University of Edinburgh (School of Mathematics), where his doctoral research developed a continuous-time Markov chain framework for credit rating migration with regime-dependent transition intensities. His thesis established the connection between the generator matrix of the credit quality process and the term structure of credit spreads, deriving closed-form and semi-analytical pricing formulas for credit default swaps, nth-to-default basket products, and synthetic CDO tranches under correlated migration dynamics. A central result of the thesis characterised the sensitivity of CDS spreads to off-diagonal elements of the intensity matrix — a result with direct application to hedge construction and credit factor decomposition in multi-name portfolios.

Following his doctorate, Vlček moved into the valuation adjustments literature, focusing on the rigorous mathematical formulation of the full XVA stack — credit valuation adjustment (CVA), debit valuation adjustment (DVA), funding valuation adjustment (FVA), and capital valuation adjustment (KVA). His research reformulated these quantities as solutions to backward stochastic differential equations (BSDEs) driven by the joint default processes of the two counterparties and by the bilateral collateral flow, showing that CVA, DVA, and FVA can be unified under a single non-linear BSDE whose driver encodes credit quality, funding costs, and regulatory capital consumption simultaneously. He developed variance-reduced Monte Carlo schemes for numerical solution of this BSDE system, with particular attention to the wrong-way risk setting in which the counterparty's default intensity is positively correlated with the mark-to-market exposure.

At IADU, Vlček applies these frameworks to credit portfolio analytics, structured credit instrument valuation, and the design of credit risk transfer mechanisms for institutional clients. His current research addresses the interface between XVA mathematics and optimal capital allocation under Basel IV constraints — a problem that involves solving a high-dimensional stochastic control system in which the state space spans both market risk factors and discrete credit quality states. He also maintains active research on credit contagion in large financial networks, using mean field approximations of interacting default intensities to characterise systemic credit risk at scale.