Comment by seanhunter

It’s a cool blog post so I’m making those observations from what I hope you will see as a helpful place. It’s been a long time since I was in the industry, and the sources you’re looking at (eg Shreve) are all great. One thing you might want to check out as well is “The Volatility Surface: A Practitioner’s Guide” by Jim Gatherall. I remember really enjoying it back when I worked in Equity Exotics and it was very highly regarded by the people I really respected in the financial maths stakes.