Monte Carlo Pricing of a European Barrier Option

In this video we look at pricing Barrier Options using Monte Carlo risk-neutral pricing approach. We show how you can implement the barrier tree model to price an up-and-out put option in Python.

For those who just want to code, please skip ahead to the Python Implementation section. I will take you through two implementations of a slow Python implementation stepping through the monte carlo simulation step by step. The other is a fast implementation using numpy arrays to vectorize these steps , improving overall computation time as N time steps increase.

In this tutorial series we will be breaking down the theory described and published in Steven Shreve’s book’s Stochastic Calculus for Finance I & II. As a guide for implementing these concepts in Python, we will refer to the numerical methods and practices outlined in Les Clewlow & Chris Strickland’s book Implementing Derivatives Models.

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00:00 Intro
00:24 Theory
04:00 Step by Step
07:00 Vectorized

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