In this paper we consider a backward parabolic partial differential equation, called the Black-Scholes equation, governing American and European option pricing. We present a numerical method combining the Crank-Nicolson method in the time discretization with a hybrid finite difference scheme on a piecewise uniform mesh in the spatial discretization. The difference scheme is stable for the arbit...

Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but...

Numerical methods are developed for pricing European and American options under Kou’s jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a...

In this paper, we consider the partial differential equations approach for valuing European and American style options on multiple assets. We use a method of lines finite element implementation available in the software package FEMLAB in order to solve the variational inequality that characterizes the American style option, as well as the partial differential equation that defines the European ...

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...