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Keywords:

  • barrier option;
  • finite difference;
  • local volatility;
  • smoothing

Abstract

In this paper we develop accurate technics to price continuous barrier options using a one-dimensional finite difference scheme, allowing for time-dependent drift as well as time- and state-dependent volatilities. We provide numerical examples which demonstrate the smoothness and accuracy of such methods in the Black-Scholes context as well as in the Dupire Local Volatility model.