Purpose The purpose of this article is to propose a detailed methodology estimate, model and incorporate the non-constant volatility onto numerical tree scheme, evaluate real option, using quadrinomial multiplicative recombination. Design/methodology/approach This uses method with volatility, based on stochastic differential equations GARCH-diffusion type value options when stochastic. Findings...

Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black-Scholes problem. Nonlinear models appear when transaction costs or illiquid markets effects are taken into account. This paper deals with the numerical analysis of nonlinear Black-Scholes equations modeling illiquid markets when...

This work presents reduced models for pricing basket options with the Black-Scholes and the Heston model. Basket options lead to multi-dimensional partial differential equations (PDEs) that quickly become computationally infeasible to discretize on full tensor grids. We therefore rely on sparse grid discretizations of the PDEs, which allow us to cope with the curse of dimensionality to some ext...

Black-Scholes (BS) equations, which are in the form of stochastic partial differential fundamental equations mathematical finance, especially option pricing. Even though there exists an analytical solution to standard form, not straightforward be solved numerically. The effective and efficient numerical method will useful solve advanced non-standard forms BS future. In this paper, we propose a ...

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study stochastic equations (SDEs). Firstly provide a algorithm that gives quadratic speed-up multilevel Monte Carlo methods general setting. As applications, apply it to compute expectation values determined classical solutions of SDEs, with improved dependence on precision. We demonstrate the ...

We present a new spectral element method for solving partial integro-differential equations for pricing European options under the Black–Scholes and Merton jump diffusion models. Our main contributions are: (i) using an optimal set of orthogonal polynomial bases to yield banded linear systems and to achieve spectral accuracy; (ii) using Laguerre functions for the approximations on the semi-infi...

Market illiquidity, feedback e ects, presence of transaction costs, risk from unprotected portfolio Note 1: In the title, insert “a” or “the” before “Analytical”? and other nonlinear e ects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a di usion term nonlinearly depending on the option price itself. In this paper, di e...

We consider the valuation of contingent claims with delayed dynamics in a Black & Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression fo...

Modern option pricing techniques are often considered among the most mathematically complex of all applied areas of financial engineering. In particular these techniques derive their impetus from four milestones of option pricing models: Bachelier model, Samuelson model, Black-Scholes-Merton model and Levy model. In this paper we evaluate all related option pricing models based on these milesto...