> ## Documentation Index
> Fetch the complete documentation index at: https://docs.rails.xyz/llms.txt
> Use this file to discover all available pages before exploring further.

# Pricing & Greeks

> How prices, implied volatility, and Greeks work

Every contract carries a **mark price**, **implied volatility (IV)**, and a full set of
**Greeks**, published live on the
[Contracts Stream](/latest/options/websocket-api/contracts-stream). This guide explains
what they mean; for the underlying math see the
[Pricing & Greeks formulas](/latest/options/formulas/pricing-and-greeks).

## Pricing Model

Rails prices options with the **Black-76** model, which values an option from the
**forward** price of the underlying (its expected price at expiry) and an annualized
risk-free rate. Each contract publishes three prices, one per side of the market:

| Field       | Meaning                                           |
| ----------- | ------------------------------------------------- |
| `markPrice` | Fair value from mark IV — used for margin and PnL |
| `bidPrice`  | Buy-side reference price, from bid IV             |
| `askPrice`  | Sell-side reference price, from ask IV            |

## Implied Volatility

Implied volatility is the market's expectation of future movement, expressed as the
volatility input to the Black-76 model — it's what `markPrice`, `bidPrice`, and `askPrice`
are computed from. It is published per side as `markIV`, `bidIV`, and `askIV` (annualized
decimals — `0.55` = 55%). Going the other way — from a candidate price to its implied
volatility and Greeks — is the Black-76 inversion described in the
[Pricing & Greeks Formulas](/latest/options/formulas/pricing-and-greeks).

## Greeks

Greeks describe how an option's value responds to changing conditions:

| Greek   | Sensitivity to…                                       |
| ------- | ----------------------------------------------------- |
| `delta` | a `1` move in the underlying price                    |
| `gamma` | the rate of change of `delta` as the underlying moves |
| `vega`  | a change in implied volatility                        |
| `theta` | the passage of time (time decay)                      |
| `rho`   | a change in the risk-free rate                        |

<Note>
  Greeks are normalized to match market convention before publishing: **vega** is per **1%** IV
  change, **theta** is **daily** decay, and **rho** is per **1%** rate change. See
  [Normalization](/latest/options/formulas/pricing-and-greeks#normalization) for the exact
  conversions.
</Note>

## Where to Get the Numbers

* **Live:** subscribe to the [Contracts Stream](/latest/options/websocket-api/contracts-stream)
  for mark price, IV, and Greeks that update as the market moves.
* **For a specific price:** compute IV and Greeks yourself with the Black-76
  [Formulas](/latest/options/formulas/pricing-and-greeks).