American Option Pricing with Binomial Trees || Theory & Implementation in Python
In this video we look at pricing American Options using the Binomial Asset Pricing Model and show how you can implement the binomial tree model to price an American option in Python. We also show why it is not optimal to early exercise an American Call option with no dividend (or positive interest rates).
For those who just want to code, please skip ahead to the Python Implementation section. I will take you through two implementations of a simple American tree model in Python, one that will use ‘for loops’ to step through each node at each time step (a function I have defined as binomial tree slow), and the other (binomial tree fast) will vectorize these steps using numpy arrays, improving overall computation time as N time steps increase. Although not necessary for the example today, using numpy arrays and vectorizing our calculations will improve computations as we delve deeper into financial mathematics and implementation heading forward.
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.
00:00 Intro
00:35 Theory || What are American Options?
01:05 Theory || Early exercise is not optimal for American Call
04:44 Theory || American Put Options
06:52 Theory || Some other considerations
08:30 Python Implementation || American Tree Slow
18:10 Python Implementation || American Tree Fast
21:55 Python Implementation || Comparing the Slow vs Fast Implementation
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