In this paper we develop a high-order adaptive finite difference space-discretization for the Black–Scholes (B–S) equation. The final condition is discontinuous in the first derivative yielding that the effective rate of convergence is two, both for low-order and high-order standard finite difference (FD) schemes. To obtain a sixth-order scheme we use an extra grid in a limited spaceand time-do...

This paper compares the performance of Black-Scholes with an artificial neural network (ANN) in pricing European style call options on the FTSE 100 index. It is the first extensive study of the performance of ANNs in pricing UK options, and the first to allow for dividends in the closed-form model. For out-of themoney options, the ANN is clearly superior to Black-Scholes. For in-the-money optio...

The Black-Scholes model is the standard approach used for pricing financial options. However, although being theoretically strong, option prices valued by the model often differ from the prices observed in the financial markets. This paper applies a hybrid neural network which preprocesses financial input data for improving the estimation of option market prices. This model is comprised of two ...

We present a review and some new results on form methods for generating holomorphic semigroups on Hilbert spaces. In particular, we explain how the notion of closability can be avoided. As examples we include the Stokes operator, the Black–Scholes equation, degenerate differential equations and the Dirichlet-to-Neumann operator. Mathematics Subject Classification (2000). Primary 47A07; Secondar...

We show that the problem of recovering the time-dependent parameters of an equation of Black-Scholes type can be formulated as an inverse Stieltjes moment problem. An application to the problem of implied volatility calculation in the case when the model parameters are time varying is provided and results of numerical simulations are presented.

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for ...

Using explicit Forward Time Centered Spaace (FTCS) on the reduced Black-Scholes partial differential equation, we report pricing of European options. We have done our experiments on a shared memory multiprocessor machine using OpenMP and report a maximum speedup of 3.43 with 16 threads.

In [3] it was shown that by writing the solution of the Black-Scholes partial differential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we explore the generalization of the technique to basket options.