Solving for Implied Volatility: Making Newton's Method Production-Ready
Why This Matters I plan to write about calibrating a full volatility surface, and that work rests on a clear understanding of a simpler problem: solving for implied vol from a single option price. At its core, this is a root-finding problem. Given a market quote, we look for the volatility at which the model price matches the market price. A common algorithm for this is Newton’s method. I learned it in class, saw it in textbooks, and implemented it in the traders’ tools at work. Most of the time it just works. I knew convergence wasn’t guaranteed, but that stayed abstract until I hit an edge case. ...