This is my first session of my Financial Option Theory with Mathematica track. I provide an introduction to financial options, develop the relevant SDEs (stochastic differential equations), and then apply them to stock price processes and the pricing of (European) options. You can download the notebook at https://s3-tracks-notebooks.s3-us-west-2.amazonaws.com/FO-Intro-SDEs.nb Please also visit my other tracks, for example my Data Science with Mathematica track, https://www.youtube.com/playlist?list=PLaWWOdR4bwEZRN4uhcBwzHh7-Zki3zqj- Correction: obviously the second moment is the variance, not the standard deviation (the latter is the square root of the variance). Starting around 31:40. So instead of StandardDeviation[NormalDistribution[mu, sigma] with sigma it should be Variance[NormalDistribution[mu, sigma]] with sigma^2. My apologies!

This is my second session of my track about Financial Option Theory with Mathematica. I develop the Black/Scholes PDE, then develop the heat equation from it, and then round-trip back from the heat equation to the BSPDE. I develop the Greeks and show how to use CUDA from Mathematica for a blazingly fast computation experience. You can download the .nb at https://s3-tracks-notebooks.s3-us-west-2.amazonaws.com/FO-BSPDE-heatequation.nb You find the whole financial options playlist at https://www.youtube.com/watch?v=UnKidEDXqSg&list=PLaWWOdR4bwEZ0_S0dVVGSHNjo5maea56C Please also visit my other tracks, for example my Data Science with Mathematica track https://www.youtube.com/watch?v=9yuzQKsQfZA&list=PLaWWOdR4bwEZRN4uhcBwzHh7-Zki3zqj-

This is my third session of my track about Financial Option Theory with Mathematica. I first develop two methods to compute historical volatility of a stock. Next I do the same for an estimate of the historical appreciation rate. I then come to the very important topic of the implied volatility, which is absolutely essential for every options trader. Then I solve the Black/Scholes PDE directly for time- and space-dependent volatility, time-dependent interest rates, and time-dependent dividend rates. I show the use or CUDA for many options computations. You can download the .nb at https://s3-tracks-notebooks.s3-us-west-2.amazonaws.com/FO-Volatility.nb You find the whole financial options playlist at https://www.youtube.com/watch?v=UnKidEDXqSg&list=PLaWWOdR4bwEZ0_S0dVVGSHNjo5maea56C Please also visit my other tracks, for example my Data Science with Mathematica track https://www.youtube.com/watch?v=9yuzQKsQfZA&list=PLaWWOdR4bwEZRN4uhcBwzHh7-Zki3zqj-

In my fourth session of my Financial Options Theory with Mathematica track I introduce the American Options. The right to exercise the option before the expiration (and not just *at* expiration) brings with it a whole slew of new pricing challenges. I introduce the Linear Complementarity Problem Formulation and then solve it with a penalty method. I show that the method is robust and show two ways to compute the greeks. As the Black/Scholes PDE makes no stipulation about linearity or constant parameter values, we can handle volatilities that depend on both time and space (here: the stock price), as well as both interest rates and dividend yields to be functions of time. I then show a very efficient third order grid method that computes the American put prices for the whole stock price interval (basically a 1-dimensional grid method with third order interpolation) instead of only one value for a given stock price (as we get with trees), with outstanding speed and precision results, directly compiled into machine code from Mathematica, and then also applied within Mathematica's parallelism framework ("get all for the price of one"). You can download the .nb from https://s3-tracks-notebooks.s3-us-west-2.amazonaws.com/FO-AmericanOptions.nb You find the whole financial options playlist at https://www.youtube.com/watch?v=UnKidEDXqSg&list=PLaWWOdR4bwEZ0_S0dVVGSHNjo5maea56C Please also visit my other tracks, for example my Data Science with Mathematica track https://www.youtube.com/watch?v=9yuzQKsQfZA&list=PLaWWOdR4bwEZRN4uhcBwzHh7-Zki3zqj-