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.

We study the short time behavior of the early exercise boundary for American style put options in the Black–Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integ...

Recently a reparametrized version of HJM model has been proposed which leads naturally to the innnite dimensional Markov process of forward curves. In this paper we discuss some consequences of the Markovian structure of forward rate dynamics. In particular, we obtain price of the swaption as a solution to the innnite dimensional "Black-Scholes" partial diierential equation.

Comparing with the linear Black–Scholes model, fractional option pricing models are constructed by taking account some more parameters like, for example, transaction cost, so that it becomes difficult to find exact analytical solution. In this paper, we analyze a nonlinear Black and Scholes solution using novel numerical method, based on mixture of efficient techniques. particular, combine (1) ...

In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying the one-dimensional solvable processes with the class of integrable superpotentials introduced recently in supersymmetric quantum mechanics, we obtain new anal...

Abstract Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work appropriate for capturing market fluctuations which random white noise has the potential to accurately estimate put option premiums while providing good numerical convergence. aim of pape...