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Straddle Pricing: ATM straddle is 0.8 * S * sigma * sqrt(T) / 16. Sigma is annual vol and T is the number of trading days. This uses sqrt(2/pi) = 0.8 and sqrt(252) = 16.
IV Estimation: ATM vol is (straddle / S) * (16 / sqrt(T)) * 1.25. This is the inverse of the straddle pricing.
Put-Call Parity: C - P = S - K + revcon. Revcon is the cost of carry i.e. K - Ke^(-rT) - PV(divs). For intuition, the synthetic is the intrinsic plus the cost of carry / the call is the intrinsic plus put plus cost of carry, since you save money by avoiding funding the stock / the put is the intrinsic plus the call minus cost of carry, since you are deferring receiving the cash for the stock.
Compounded Growth: Stock with r% growth per period doubles every 72 / r periods.
AM-GM: Geometric mean = arithmetic mean - 0.5 * variance. Follows from Itô's Lemma.
Hedge Ratio: If you have Q of A and want to hedge with B, you hedge Q * (vol(A) / vol(B)) * r, leaving idio vol of sqrt(1 - r^2).
Discrete Kelly: If you have p% chance of winning b + 1 for every 1 you bet, your Kelly fraction is f = ((p/100)*(b+1) - 1)/b.