Numpy and Scipy: Using Sparse Matrices to Speed up Calculations (part 1)

In response to a comment on the videos dealing with Monte Carlo models of stocks market movement, and how to calculate the probability of making 50% of max profit on an options trade, I want to revisit some of the concepts presented in those videos. In particular the concept of linear systems which can be represented by matrix equations where the coefficient matrix is sparse. I will go through the calculations used in these videos and show, step-by-step, how the matrices involved are generated. This will be part one of three where we show how sparse matrices and linear algebra are used to speed up calculations. Part two will deal with solving a partial differential equation. Part three will return to to the matrices used in the Monte Carlo calculation.

Github: https://github.com/kpmooney/numerical_methods_youtube/blob/master/prob_50/More%20on%20Linear%20Systems.ipynb

Probability of making 50%: https://youtu.be/yGlkRpqMDVk
Probability of a Touch: https://youtu.be/PRLnusDWSW0

Tip Jar: https://paypal.me/kpmooney