Related papers: High-order compact schemes for Black-Scholes baske…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
We propose a fourth--order compact finite--difference (HOC--FD) scheme for the transformed Bates partial integro--differential equation (PIDE). The method employs an implicit--explicit (IMEX) Crank--Nicolson framework for local terms and…
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…
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting…
In this paper, we present an implicit finite difference method for the numerical solution of the Black-Scholes model of American put options without dividend payments. We combine the proposed numerical method by using a front fixing…
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…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. The formulae are obtained by using a…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
The main purpose of this article is to give a general overview and understanding of the first widely used option-pricing model, the Black-Scholes model. The history and context are presented, with the usefulness and implications in the…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise…
A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a…
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient…
The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem: standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step…
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…
This paper proposes and analyzes a finite difference method based on compact schemes for the Euler-Bernoulli beam equation with damping terms. The method achieves fourth-order accuracy in space and second-order accuracy in time, while…
This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…
We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the…