Rafail Theodorakis

Rafail Theodorakis completed his doctorate at the Mathematics Institute of the University of Warwick, where his dissertation developed high-order finite difference schemes for parabolic PDEs arising in computational finance under stochastic volatility. The central challenge addressed was the degeneracy of the pricing operator at the boundary of the variance process — where standard finite difference stencils lose accuracy and positivity — and the work introduced a family of weighted upwind schemes that maintain second-order accuracy in the interior while handling the degenerate boundary condition through a careful treatment of the near-boundary region. The dissertation benchmarked these schemes against finite element and ADI splitting methods for the Heston model and a class of rough volatility PDEs, demonstrating accuracy and stability advantages in the low-volatility regime where many standard approaches fail. The analysis covered both European and American option problems, with the American case addressed through a penalty approximation whose convergence to the linear complementarity problem was established rigorously.

Following his doctorate, Theodorakis developed multilevel Monte Carlo methods for derivative pricing under stochastic volatility models with jumps, constructing telescoping estimators that achieve the canonical MLMC complexity result — mean square error of order ε² at cost of order ε² log(ε)² — for a class of discontinuous payoffs and non-smooth coefficients that lie outside the scope of the original Giles analysis. A companion programme examined sparse grid methods for high-dimensional Black-Scholes equations with early exercise features, using sparse tensor product constructions to mitigate the curse of dimensionality for basket option pricing problems in dimensions up to twelve, and establishing a priori error estimates under mixed regularity assumptions.

At IADU, Theodorakis contributes numerical methods to the Institute's computational finance programme. His work focuses on the implementation and verification of finite difference, finite element, and Monte Carlo pricing algorithms for derivative instruments relevant to sovereign and institutional clients — including interest rate swaptions, sovereign credit default swap options, and energy derivatives — and on the adaptation of high-order PDE discretisations to the degenerate operators that arise in stochastic volatility and jump-diffusion models used across IADU's quantitative research.