Principle:Avhz RustQuant European Vanilla Option Contract
| Knowledge Sources | |
|---|---|
| Domains | Derivatives, Option_Pricing |
| Last Updated | 2026-02-07 20:00 GMT |
Overview
A standardized financial derivative contract giving the holder the right, but not the obligation, to buy (call) or sell (put) an underlying asset at a predetermined strike price on a specific expiration date.
Description
A European vanilla option is the most fundamental type of option contract. Unlike American options, European options can only be exercised at the expiration date, not before. The "vanilla" qualifier distinguishes these from exotic options with more complex payoff structures.
The payoff at expiry is defined as:
- Call: max(S_T - K, 0)
- Put: max(K - S_T, 0)
where S_T is the underlying asset price at expiry and K is the strike price.
European options are the building block for option pricing theory. The Black-Scholes formula provides a closed-form solution for European option prices under certain assumptions (log-normal returns, constant volatility, no dividends in the base case).
Usage
Use this principle when modeling European-style options on equities, indices, or FX. This is the starting point for both analytic and Monte Carlo pricing workflows. The European vanilla option contract must be defined before any pricing engine can be applied.
Theoretical Basis
The European option payoff function is a piecewise linear function of the terminal asset price:
The present value of the option is the discounted expected payoff under the risk-neutral measure Q:
Key properties:
- Exercise only at expiry (European style)
- Linear payoff beyond the strike (no cap)
- Call-put parity: C - P = S_0 e^{-qT} - K e^{-rT}