2 research outputs found
Computing option pricing models under transaction costs
AbstractThis paper deals with the Barles鈥揝oner model arising in the hedging of portfolios for option pricing with transaction costs. This model is based on a correction volatility function 唯 solution of a nonlinear ordinary differential equation. In this paper we obtain relevant properties of the function 唯 which are crucial in the numerical analysis and computing of the underlying nonlinear Black鈥揝choles equation. Consistency and stability of the proposed numerical method are detailed and illustrative examples are given
A robust numerical solution to a time-fractional Black鈥揝choles equation
Dividend paying European stock options are modeled using a time-fractional
Black鈥揝choles (tfBS) partial differential equation (PDE). The underlying fractional
stochastic dynamics explored in this work are appropriate for capturing market
fluctuations in which random fractional white noise has the potential to accurately
estimate European put option premiums while providing a good numerical
convergence. The aim of this paper is two fold: firstly, to construct a time-fractional
(tfBS) PDE for pricing European options on continuous dividend paying stocks, and,
secondly, to propose an implicit finite difference method for solving the constructed
tfBS PDE. Through rigorous mathematical analysis it is established that the implicit
finite difference scheme is unconditionally stable. To support these theoretical
observations, two numerical examples are presented under the proposed fractional
framework. Results indicate that the tfBS and its proposed numerical method are very
effective mathematical tools for pricing European options