Keywords: Black–Scholes equation Completely monotonic function Finite difference scheme Laplace Transform M-Matrix Positivity-preserving Post–Widder formula a b s t r a c t In this paper we explore discrete monitored barrier options in the Black–Scholes framework. The discontinuity arising at each monitoring data requires a careful numerical method to avoid spurious oscillations when low volati...

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...

The object of this study was to investigate some implications of the tenets of behavioral finance on the pricing of financial derivatives. In particular, based on the work by Wolff et al (2009) we have investigated how prospect theory (Kahneman and Tversky, 1979) can be intregrated into the Black and Scholes (1973) option pricing framework. We have then used the resulting " behavioral version "...

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...

The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black–Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for studying the nonlinear Black–Scholes equation with a nonlinear volatility arises from option pricing models taking into account e.g. nontrivial tr...

This paper analyses the model of Black–Scholes option pricing from point view group theoretic approach. The study identified new independent variables that lead to transformation equation. Furthermore, corresponding determining equations were constructed and symmetries found. As a result, findings demonstrate integrability present an invariant solution for Ornstein–Uhlenbeck stochastic process.

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined Black-Scholes closed form solution modified (MBS) partial differential equation using Crank-Nicolson finite difference method. These equations were approximated to obtain Call Put prices. The explicit price both options found accordingly. solutions c...

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...