Barrier option is the most important exotic option on the market and it is becoming more popular, mainly due to its lower cost when compared to standard vanilla options. Nonetheless, exotic options are difficult to price since the payoff is dependent on the path followed by the price of the underlying asset.

This work introduces the fundamental concepts of barrier option valuation theory and continues presenting the nature of discretely monitored barrier options that cannot always be priced analytically. To solve this issue different numerical methods are used, the most commonly used ones are, namely, Monte Carlo simulation (MC) and finite difference method (FD), which we applied for barrier option pricing in this work.

Additionally, software code was developed to find the down-and-out call option prices, which are then compared to the benchmark obtained via the Analytical Solution of Black-Scholes model. Supplementary, we investigate which of the algorithms is more efficient to our option delta hedging, in other words, which one delivers the highest cumulative P&L at the maturity.

The research questions are: “Which barrier option pricing method is more accurate comparing the results to the chosen benchmark?” and “Which of the numerical methods used in barrier option pricing will result in the highest profit and loss (P&L) of the option delta hedging for the financial institution?”

Despite of both methods’ tendency to converge to the benchmark, the findings of our study show that the finite difference option pricing method is faster to converge. Furthermore, the delta hedging using the finite difference method performed better achieving a higher P&L than MC, taking into account the initial price of the option.