  Market illiquidity, feedback effects, presence of transaction costs, risk
from unprotected portfolio and other nonlinear effects in PDE based option
pricing models can be described by solutions to the generalized Black-Scholes
parabolic equation with a diffusion term nonlinearly depending on the option
price itself. Different linearization techniques such as Newton's method and
analytic asymptotic approximation formula are adopted and compared for a wide
class of nonlinear Black-Scholes equations including, in particular, the market
illiquidity model and the risk-adjusted pricing model. Accuracy and time
complexity of both numerical methods are compared. Furthermore, market quotes
data was used to calibrate model parameters.
