Pascal Heider (E.ON Trading)

In recent years nonlinear Black-Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black-Scholes concept. The nonlinear equations can be discretized by BDF - methods. These algorithms are fully implicit but require additional Newton iterations. We show that the numerical solution converges to the viscosity solution. The mathematical framework is handy and a wide range of models can easily be handled. The flexibility of the method is shown by application to four representative nonlinear models.