Risk-Neutral Pricing Calculator

Pricing Principle:
The value of a derivative equals the discounted expected payoff under the risk-neutral probability measure.

$$V_0 = e^{-rT}\,\mathbb{E}^{\mathbb{Q}}[\text{Payoff}]$$

Risk-Free Rate r (decimal): Time to Maturity T (years):

Payoff Scenarios

Model Interpretation

The expected payoff is computed under the risk-neutral measure (𝑸)
Risk preferences do not enter the pricing equation
All assets are assumed to earn the risk-free rate in expectation

Key Assumptions

No arbitrage opportunities
Complete or sufficiently hedgeable market
Constant and known risk-free interest rate
Correct specification of the payoff distribution under 𝑸
Continuous compounding

⚠️ This framework is the foundation of Black–Scholes, binomial trees, and Monte Carlo pricing.