Risk-Neutral Probability
The artificial probability measure under which all assets earn the risk-free rate, used to price derivatives by expectation.
Under the risk-neutral measure Q, the expected return on all assets equals the risk-free rate r. In the binomial model: p* = (e^(rΔt) − d)/(u − d). Option price = e^(−rT) × E^Q[payoff at expiry]. Risk-neutral probabilities are NOT real-world probabilities — they are mathematical tools that capture market risk aversion and allow pricing by expectation. The connection to real probabilities requires specifying the market price of risk (risk premium).
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.
Discount Factor (DF)
The present value of $1 receivable at a future time T, derived from the zero curve: DF = e^(−rT).
Binomial Option Pricing Model
A discrete-time model that prices options by working backward through a tree of possible stock price paths.
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.
Theta (Θ)
The rate at which an option loses value as time passes — time decay per calendar day.