Efficient numerical method for solving Cauchy problem for the Gamma equation

摘要

In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black‐Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ? = ?VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard‐Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non‐differentiable functions. Results of numerical simulations are given.