Risk-Neutral Probability
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).
Related Terms
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.