Numerical Approximations of a Nonlinear Volatility Model with European Options

Black-Scholes model plays a very significant role in the world of quantitative finance. In this paper, focus are on both nonlinear and linear (BS) equations with numerical approximations. We aim to find an effective approximations for model. Several models from most relevant class European option analyzed study. The problem is approached by transforming into convection-diffusion equation later it approximated help finite difference method (Crank-Nicolson). result schemes (Crank-Nicolson) several volatility presented, including Risk Adjusted Pricing Methodology (RAPM), Leland’s Barles’-Soner’s Model. At same time, attempted illustrate comparison different models. case model, we approximate (FDM) element (FEM) compare results. All implemented MATLAB corresponding graphs also presented here. GANIT J. Bangladesh Math. Soc. 42.1 (2022) 050- 068