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The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
Cox-Ingersoll-Ross (CIR) processes are extensively used in state-of-the-art models for the approximative pricing of financial derivatives. In particular, CIR processes are day after day employed to model instantaneous variances (squared…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes…
In this research, we proposed a Mean Convection Finite Difference Method (MCFDM) for European options pricing. The Black-Scholes model, which describes the dynamics of a financial asset, was first transformed into a convection-diffusion…
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
The alternating direction implicit (ADI) methods are computationally efficient and numerically effective tools for computing low-rank solutions of large-scale linear matrix equations. It is known in the literature that the low-rank ADI…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…
We provide a complete representation of the interest rate in the extended CIR model. Since it was proved in Maghsoodi (1996) that the representation of the CIR process as a sum of squares of independent Ornstein-Uhlenbeck processes is…
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough…
We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static…
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation…
This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a…
Computational efficiency is essential for enhancing the accuracy and practicality of pricing complex financial derivatives. In this paper, we discuss Isogeometric Analysis (IGA) for valuing financial derivatives, modeled by two nonlinear…
Recently, a nonlinear Poisson equation has been introduced to model nonlinear and nonlocal hyperpolarization effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due to a strong nonlinearity associated…
In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice…