Long Strangle
Buy an OTM call and an OTM put — cheaper than a straddle but needs a larger price move to profit.
Long strangle: buy OTM call(K_high) + buy OTM put(K_low), where K_low < S < K_high. Net debit = C(K_high) + P(K_low). Lower cost than a straddle but wider breakevens: upper breakeven = K_high + net debit; lower breakeven = K_low − net debit. Maximum loss = net premium (if stock expires between the two strikes). Like the straddle, the strangle is a long volatility trade: it profits when realized vol exceeds implied vol and a large directional move occurs.
Straddle
Buying a call and a put at the same strike — profits from a large move in either direction.
Implied Volatility (IV)
The volatility that, when input into the BSM model, makes the model price equal to the market price of an option.
Vega (ν)
The sensitivity of an option's price to a 1% change in implied volatility.
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.