Transformed method for solving black-Scholes pde of the Asian option

الملخص EN

Analytical solution of the arithmetic Asian options of the Black-Scholes partial differential equation (PDE) is not known in a closed-form solution, this is due to the difficulty of transforming this PDE to a simpler equation, which could be easier to solve.

In this paper, we derive a closed form solution for a continuous arithmetic Asian option by means of partial differential equations.

and provide a new transformed method for solving arithmetic Asian options PDEs using general transformation techniques, this transformation reduces the two dimensions PDE of the arithmetic Asian options to the classical Black-Scholes PDE with one dimension.

In addition, we use Mellin transform to obtain the final solution to the arithmetic Asian option partial differential equation.