Pricing Barrier Options using Monte Carlo Simulation in Python
Published in
6 min readMay 17, 2022
Modelling Exotic Options
When modelling exotic options, one has to make a fundamental decision very early in the process: should you model the option in a continuous-time, Black-Scholes type of model, or in a binomial model.
- Generally many exotic options are initially priced via a binomial model, and then at some point traders figure out a closed-form pricing model.
- Sometimes, it turns out that no closed form solution is ever found.
- Indeed, for certain highly path-dependent options, one cannot even work backwards in a lattice, instead one must use a Monte Carlo method to value the option.
1. Barrier Options
Barrier options are options that have a payout that is dependent not only on the terminal stock price, but also depend upon whether the stock attains some “barrier” during the life of the option.
If the price of the underlying does not rise above the barrier level, the option acts like any other option — it gives the holder the right but not the obligation to exercise their call or put option at the strike price on or before the expiration date specified in the contract.
