Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing
2000 Mathematics Subject Classification: 65M06, 65M12. The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its second order...