No Arbitrage
The no-arbitrage principle requires prices to exclude a feasible portfolio with no net investment, no possible loss, and a positive payoff in at least one state.
Pricing concepts that connect replication, risk-neutral probabilities, binomial trees, and mean-reverting short-rate models.
No-arbitrage pricing starts with tradable payoffs rather than an investor’s preferred expected return. No Arbitrage defines the price-consistency condition. Risk-Neutral Probabilities provide pricing weights under that framework, not forecasts of actual outcomes.
The Binomial Option Pricing Model applies these ideas in a discrete tree. The Vasicek Interest Rate Model applies a mean-reverting process to the short rate and, under pricing assumptions, to zero-coupon bond valuation.
flowchart LR
A["Define traded payoffs and financing"] --> B["Apply no-arbitrage restrictions"]
B --> C["Derive pricing weights or a replicating portfolio"]
C --> D["Price by backward induction or discounted expectation"]
D --> E["Check market frictions, calibration, and model risk"]
| Need | Start with | Boundary |
|---|---|---|
| Test whether prices permit a dominant zero-cost payoff | No Arbitrage | Real implementation depends on executable trades, costs, funding, and legal rights |
| Understand adjusted probabilities used for pricing | Risk-Neutral Probabilities | Pricing probabilities are not real-world forecasts |
| Value an option through discrete price branches | Binomial Option Pricing Model | Tree output depends on step design, inputs, exercise rules, and convergence |
| Model a mean-reverting instantaneous short rate | Vasicek Interest Rate Model | One Gaussian factor can miss the observed yield curve and allows negative rates |
Return to Asset Pricing, Stochastic Processes, and Risk-Neutral Models for the companion stochastic-process and factor-model branch.
This section provides financial-modeling education. It does not provide a market forecast, executable hedge, valuation opinion, or personalized investment advice.
Choose a subsection first. Deeper term pages live inside each subsection, which keeps large topic hubs readable.
The no-arbitrage principle requires prices to exclude a feasible portfolio with no net investment, no possible loss, and a positive payoff in at least one state.
Risk-neutral probabilities are pricing weights that make discounted traded-asset prices consistent with no arbitrage; they are not forecasts of actual outcomes.
The Vasicek model represents the instantaneous short rate as a one-factor Gaussian process with constant volatility and mean reversion.