Long Butterfly Spread
Buy a low and high strike call, sell two middle-strike calls — profits if price stays near the middle strike.
Long call butterfly: buy call(K1) + sell 2×call(K2) + buy call(K3), where K1 < K2 < K3 and K2 − K1 = K3 − K2 (symmetric). Net debit = C(K1) − 2C(K2) + C(K3). Maximum profit = K2 − K1 − net debit (if stock expires at K2). Maximum loss = net debit (if stock expires below K1 or above K3). Breakevens: K1 + net debit and K3 − net debit. Butterfly is a short volatility play: it profits when the stock stays range-bound near the middle strike.
Straddle
Buying a call and a put at the same strike — profits from a large move in either direction.
Iron Condor
Sell an OTM put spread and an OTM call spread simultaneously — profits if the underlying stays in a wide range.
Implied Volatility (IV)
The volatility that, when input into the BSM model, makes the model price equal to the market price of an option.
Black-Scholes-Merton Model (BSM)
The foundational option pricing formula that gives the fair value of a European call or put as a function of spot, strike, rate, volatility, and time.
Delta (Δ)
The sensitivity of an option's price to a $1 change in the underlying spot price.
Gamma (Γ)
The rate of change of delta with respect to the spot price — the curvature of the option's value.