The purpose of this short note is to walk through some of the equations used for
the "Black Swan Ponds"in a recent visualization I have been playing with. This was done to double-check some things, and serve as a point of reference in case someone finds an issue with the equations that are being used or their implementation.

"Black Swan Ponds" that represent
where ≥3σ Events Occur Link to Viz

One of the things I had wanted to do with this was to somehow incorporate Nassim Taleb's "Black Swan"
notion. Specifically, convey the regions in which Black Swans "could occur." In the narrow context used here, Black Swans have to do with events that - relative to Gaussian/"standard" assumptions at least - are at some number of standard deviations away from the mean. I don't know if there is an agreed upon number of standard deviations away that represents a Black Swan, but I came across a few
notes that indicated that three standard deviations seemed to be about where this starts.
So, for the purpose of this effort, I used three standard deviations from the stock price's mean to be the boundary of the Black Swan regions. Each of these regions is referred to here as a "Black Swan Pond." The distribution of stock price is assumed to be based on geometric Brownian motion, with parameters from the initial stock price, the volatility, and time-to-expiration.

Previously, I had put together a data visualization that let you explore the Black-Scholes model, which is sometimes used to price stock options. That visualization lets you explore "The Greeks" and see how these change with respect to stock price, strike price, time to expiration, volatility, and the risk-free interest rate.

I've now added more stuff involving stock option strategies and their associated profit/loss curves (with valuations estimated from the Black-Scholes model itself). This is implemented as an additional "tab" added to the previous visualization.

In addition to trying to make it pretty easy to play with different option strategies - custom or standard - I've started playing with being able to fit an option strategy to a set of desired profit/loss points.

Note - not included in the calculations are commission charges, and "slippage" that might occur when trying to exit the positions. For the crazier strategies, there may in fact be no practical way to even exit out all of the positions and capture the profit: that is an area for later research.

As before, this visualization has not yet been optimized much for mobile devices (screenwise or cpu-wise), so for now a desktop is still highly recommended.