Notes

Breeden-Litzenberger gives you the market's implied distribution over future spot from a strip of vanilla calls. Here's how, and why it's the cleanest way to read sentiment from options.

Implied vol is systematically higher than realized vol. That gap pays sellers of options on average — but the pattern is structural, not free money.

For most analytical workloads, the Polars API is closer to SQL than to pandas, and the speed-up is the smaller part of the win.