The greeks, one volatility at a time
A short, math-heavy series on how each option greek behaves as you turn the volatility dial — the mechanism, the Black-Scholes formula, and the picture a trader actually carries. More technical than the plain-English Concepts; the interview drills live in the Interview Questions.
- 4 min read
Delta, Volatility, and the Two Faces of d₁
Why a book's deltas cluster near 0.5 as you raise volatility — even though a call's delta tends to 1 as σ→∞. The d₁ decomposition, N(d₁)→1 vs N(d₂)→0, and an everyday picture.
Read the note - 3 min read
Gamma, Volatility, and the Slope of Delta
Raise volatility enough and gamma goes to zero — because a flat delta curve has no slope. The Γ = N'(d₁)/(Sσ√τ) argument, the collapsing gamma table, and the trader's picture.
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Theta, Volatility, and the Rent on Gamma
More volatility makes your option decay faster — the daily rent you pay for holding gamma. The identity Θ = −½σ²S²Γ, the decay table, and break-even as realised vs implied vol.
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Vega, Volatility, and Why Long-Dated Options Are All Vol
Vega is your exposure to the level of implied vol — always positive for a long option, largest at-the-money, and above all a maturity story. Where gamma and theta die, vega dominates.
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