The Greeks, proved and verified. Differentiate the closed form for delta and three terms appear — but the ★ identity, proved from the ratio of the Gaussian densities, forces two of them to vanish, so Δ = Φ(d₁) exactly (checked against a finite difference to six figures). The same identity collapses vega to S·√τ·φ(d₁) > 0 — which dies in the wings, exactly where our ladder lives. So Newton’s method blows up there (it divides by a near-zero vega), and we choose bisection instead: strictly monotone price, a unique root by the intermediate value theorem, the bracket halved every step, below machine precision in a hundred iterations. We solve our own implied vol from mids — never the feed’s. Delta is the real exposure; gamma is the cost of discrete time; theta is the tailwind. The desk, in three Greeks: long delta, short vega, long theta.
~105 minutes, all the way down — building it, running it, and using it to manage permanent capital.
The Aloha Machine · The Master Class — training & educational content, open to everyone. Fund A is pre-launch; every figure shown is hypothetical and model-derived (SEC Rule 206(4)-1) and does not predict results. No roster or weights are shown. Not an offer to sell or a solicitation of an offer to buy any security. Leo is a fictional AI presenter; the voice is AI-generated — not a recording of any real person. 🤫 AlphaAlohaOS · Alphabets 27 · hushh