7 papers
DSINC beyond Heston: the 3/2 and other non-affine stochastic-volatility models
Andrey Itkin
This paper extends the damped-sinc (DSINC) method for American options beyond the affine Heston class to general one-factor stochastic-volatility models. We show that the collapse…
Diagonal Frog meets ADI: trading matrix exponentials for rational maps in the Fokker--Planck equation
Andrey Itkin, Rakhymzhan Kazbek
A companion paper \cite{ItkinDF2026} introduced the Diagonal Frog (DF) positivity-preserving schemes for anisotropic Fokker--Planck equations, advancing each directional substep by…
Flux-Corrected Diagonal Frog: second order and positivity at all time steps
Andrey Itkin
By Godunov's theorem, linear second-order finite-difference schemes for the Fokker-Planck equation cannot preserve positivity. The Diagonal Frog (DF) framework previously bypassed…
Valuing American options and Flexible Forwards contracts in time-dependent models
Leif Andersen, Andrey Itkin, Rakhymzhan Kazbek
A flexible forward (FF) is a customized FX hedging instrument that guarantees a fixed exchange rate while letting the holder choose the delivery date within a pre-agreed window. It…
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
Andrey Itkin
The Fokker-Planck equation is fundamental to statistical mechanics, yet in settings with multiple state variables, anisotropic (cross-) diffusion, and jumps, conventional discretiz…
Semi-analytical pricing of American options with hybrid dividends via integral equations and the GIT method
Andrey Itkin
This paper introduces a semi-analytical method for pricing American options on assets (stocks, ETFs) that pay discrete and/or continuous dividends. The problem is notoriously compl…
American options valuation in time-dependent jump-diffusion models via integral equations and characteristic functions
Andrey Itkin
Despite significant advancements in machine learning for derivative pricing, the efficient and accurate valuation of American options remains a persistent challenge due to complex…