5 papers
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…
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…
Finite Element Method for HJB in Option Pricing with Stock Borrowing Fees
Rakhymzhan Kazbek, Aidana Abdukarimova
In mathematical finance, many derivatives from markets with frictions can be formulated as optimal control problems in the HJB framework. Analytical optimal control can result in h…
Isogeometric Analysis for the Pricing of Financial Derivatives with Nonlinear Models: Convertible Bonds and Options
Rakhymzhan Kazbek, Yogi Erlangga, Yerlan Amanbek +1
Computational efficiency is essential for enhancing the accuracy and practicality of pricing complex financial derivatives. In this paper, we discuss Isogeometric Analysis (IGA) fo…
Valuation of the Convertible Bonds under Penalty TF model using Finite Element Method
Rakhymzhan Kazbek, Yogi Erlangga, Yerlan Amanbek +1
In this paper, the TF system of two-coupled Black-Scholes equations for pricing the convertible bonds is solved numerically by using the P1 and P2 finite elements with the inequali…