Stock prices close to the barrier: discrete knock-out options

This thesis explores discrete knock-out options, a distinctive class of financial derivatives, with a particular focus on their behavior near the barrier. Combining theory and simulations, it addresses the challenges posed by the naïve application of the binomial model and introduces a correction technique, utilizing tree methods, applicable to both binomial and trinomial models for various barrier options. The results demonstrate that this technique ensures accurate option prices with a minimal number of time steps, offering a notable improvement over conventional methods, especially in scenarios of high volatility and close proximity of the barrier to the current stock price.