Using Scipy to Find the Prices of a Stock and its Volatility from a Call Spread Price

In a previous video, we looked at how to calculate the stock price based on an option price assuming we knew the volatility. In a comment, someone asked if the same could be done using a short call spread rather than a single option. I wasn't going to do a video on this but then after thinking about it some more, there are some interesting aspects to this problem. After writing up some test code, I realize there was a potential issue that could cause a solution to fail under certain circumstances.

In this video I will consider two scenarios. The first is where we know the price of each individual leg of the spread. We do not know the stock price or the implied volatility. In the second case, we will consider the situation where we know the price of the spread but not the individual legs. In this case we wouldn't need to know the implied volatility.

Github: https://github.com/kpmooney/numerical_methods_youtube/blob/master/root_finding/fsolve/option_spread/Price%20From%20Call%20Spread.ipynb

Finding Stock Prices from Option Prices: https://youtu.be/NF-XMP8RjJo
Finding Implied Volatility Using Newton’s Method: https://youtu.be/Jpy3iCsijIU

Fsolve documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html
Minimize documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html

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