This paper compares the performance of Black-Scholes with an artificial neural network (ANN) in pricing European style call options on the FTSE 100 index. It is the first extensive study of the performance of ANNs in pricing UK options, and the first to allow for dividends in the closed-form model. For out-of themoney options, the ANN is clearly superior to Black-Scholes. For in-the-money optio...

The Black-Scholes model is the standard approach used for pricing financial options. However, although being theoretically strong, option prices valued by the model often differ from the prices observed in the financial markets. This paper applies a hybrid neural network which preprocesses financial input data for improving the estimation of option market prices. This model is comprised of two ...

The nonlinear Black-Scholes equation has been increasingly attracting interest over the last two decades, because it provides more accurate values by considering transaction costs as a viable assumption. In this paper we review the fully nonlinear Black-Scholes equation with an adjusted volatility which is a function of the second derivative of the price and then we prove two new theorems in th...

In recent years, many advanced techniques have been applied to financial problems; however, very few scholars used the Lie theory. The purpose of this study was examine options for a trade account through symmetry analysis. According our results, it is effective determining analytical solutions pricing issues and solving other partial differential equations. proposed solution can be by further ...

The Black-Scholes ( 1973) option pricing model is a universal standard among option valuation models. Despite its widespread popularity, however, the model has some known deficiencies in actual applications. For example, when calibrated to accurately price at-the-money options, the Black-Scholes model frequently misprices deep in-the-money and deep out-of-the-money options. Pricing biases assoc...

We consider asset price processes Xt which are weak solutions of onedimensional stochastic di erential equations of the form dXt = b(t; Xt) dt + t Xt dWt: Such price models can be interpreted as non{lognormally{distributed generalizations of the geometric Brownian motion. We study properties of the I divergence between the law of the solution Xt and the corresponding drift{less measure (the spe...

Differentiation matrices provide a compact and unified formulation for a variety of differential equation discretisation and timestepping algorithms. This paper illustrates their use for solving three differential equations of finance: the classic Black-Scholes equation (linear initial-boundary value problem), an American option pricing problem (linear complementarity problem), and an optimal m...

A technique is proposed for the construction of Green’s functions for terminal-boundary value problems of the Black-Scholes equation. The technique permits an application to a variety of problems that vary by boundary conditions imposed. This is possible by extension of an approach that was earlier developed for partial differential equations in applied mechanics. The technique is based on the ...

We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coeffic...