Options valuation by using radial basis function approximation
This paper describes the valuation scheme of European, barrier, and Asian options of single asset by using radial basis function approximation. The option prices are governed with BlackScholes equation. The equation is discretized with CrankNicolson scheme and then, the option price is approximated with the radial basis functions with unknown parameters. In the European and the barrier options, the prices are governed with BlackScholes equation. The governing option of the Asian option, however, is different from them of the others. In that case, one has to adopt the other radial basis functions than that for the original BlackScholes equation. Finally, numerical results are compared with theoretical and finite difference solutions in order to confirm the validity of the present formulation.
radial basis function asian option barrier option option contract european option