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.

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...

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.

A technique is proposed for the construction of Green’s functions for terminal-boundary value problems of the Black-Scholes equation. The technique permits an application to a variety of problems that vary by boundary conditions imposed. This is possible by extension of an approach that was earlier developed for partial differential equations in applied mechanics. The technique is based on the ...