In this second example, we consider the pricing of an exotic option: an up-and-out barrier with a call payoff. The details of the approach are shown in the following Bento Box template for FX Barrier Up and Out option (FX2):
Note that there is a great advantage of using Finite Difference Methodology (FDM) with respect to Monte Carlo (MC) in pricing a continuously monitored barrier option. This is because MC is rather complex to incorporate the continuously monitored features, leaving us with little choice but to increase the number of fixing/observation points in the MC program. However, this will significantly increase the computation time in MC. We do not need to do this in FDM, making it more efficient.
Our target is to compute the option premium as we did earlier.
An up-and-out barrier is just like a standard European Call option but with one crucial difference—if the underlying crosses...