Black-Scholes equation as one of the most celebrated mathematical models has an explicit
analytical solution known as the Black-Scholes formula. Later variations of the equation,
such as fractional or nonlinear Black-Scholes equations, do not have a closed form
expression for the corresponding formula. In that case, one will need asymptotic expansions,
such as the homotopy perturbation method, to give an approximate analytical solution.
However, the solution is non-smooth at a special point. We modify the method by first …