American options are priced numerically using a spaceand timeadaptive finite difference method. The generalized Black-Scholes operator is discretized on a Cartesian structured but non-equidistant grid in space. The spaceand time-discretizations are adjusted such that a predefined tolerance level on the local discretization error is met. An operator splitting technique is used to separately hand...

I examine the role of programming parameters in determining the accuracy of Genetic Programming for option pricing. I use Monte Carlo simulations to generate stock and option price data needed to develop a Genetic Option Pricing Program. I simulate data for two different stock price processes – a Geometric Brownian process and a JumpDiffusion process. In the jump-diffusion setting, I seed the G...

In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different adjustments denoted generally as xVA are nowadays added the risk-free financial derivative values and PDE approach allows their easy incorporation. The aim of is show how solve analytically in Black-Scholes setting get new semi-closed formulas compare widely standard approximation...

The multi-dimensional Black-Scholes equation is solved numerically for a European call basket option using a priori–a posteriori error estimates. The equation is discretized by a finite difference method on a Cartesian grid. The grid is adjusted dynamically in space and time to satisfy a bound on the global error at the expiry date. The discretization errors in each time step are estimated and ...

Abstract. In this paper we present a hybrid finite difference scheme on a piecewise uniform mesh for a class of Black-Scholes equations governing option pricing which is path-dependent. In spatial discretization a hybrid finite difference scheme combining a central difference method with an upwind difference method on a piecewise uniform mesh is used. For the time discretization, we use an impl...

The studied model was suggested to design a perfect hedging strategy for a large trader. In this case the implementation of a hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of the Black-Scholes partial differential equation. Using the Lie group theory we reduce the partial differential equation in special cases to ordinary differe...

In this Paper, HomotopyPerturbation method (HPM) which is one of the most recent approximate analytical solutions is implemented to solve diffusion-convection-reaction equations (DCRE). The calculations are carried out for two different types of DCRE’s such as the Black-Scholes equation used in financial market option pricing and FokkerPlanck equation from plasma physics. The behavior of the ap...

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