In this paper two different methods are presented to approximate the solution of the fractional BlackScholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the applic...

Numerical Approximation of the Black-Scholes Equations: A Practical Experience By Dylan Connor Black and Scholes equations for pricing of derivatives are an interesting and up-to-date topic of research, where both backgrounds in math and finance are fundamentals. In this work we aim at experiencing the mathematical approach and the numerical approximation of this differential problem. We will a...

This paper describes and analyses the history of the fundamental equation of modern financial economics: the Black-Scholes (or Black-Scholes-Merton) option pricing equation. In that history, several themes of potentially general importance are revealed. First, the key mathematical work was not rule-following but bricolage, creative tinkering. Second, it was, however, bricolage guided by the goa...

In this paper, we try and valuate preemption rights by modifying the Black-Scholes model, which is widely used to valuate options and other derivatives. Here we first present the basics of the Black-Scholes model and then we discus modification of the model to be fit for preemption right valuation. At the end, we valuate four of the preemptive rights using the proposed model

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black–Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option price variable. The dynamics of the latter is constructed and formulated in terms of a master equation. The numerical efficiency of the approach is demonstrat...

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast m...

We are concerned with a model for asset prices introduced by Koichiro Takaoka, which extends the well known Black-Scholes model. For the pricing of contingent claims, partial differential equation (PDE) is derived in a special case under the typical delta hedging strategy. We present an exact pricing formula by way of solving the equation.

This paper gives a connection between the theory of semigroups of operators (functional analysis) and mathematical finance through the Black-Scholes equation. Besides using this theory obtain the solution of this equation via the infinitesimal generator of a group of evolution. Mathematics Subject Classification: Primary 91G80; Secondary 47D06