> For the complete documentation index, see [llms.txt](https://docs.pairity.fi/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.pairity.fi/protocol/overview.md).

# Overview

Pairity turns a collateralized option series into three linked legs:

* **Base**: the shared value between the oracle spot and the strike
* **Call**: the spot value left after Base
* **Put**: the strike value left after Base

For a selected series, the pricing inputs are:

* `K`: the series strike
* `S`: the current oracle spot price
* `T`: time remaining until expiry, expressed in years
* `sigma`: the pair-wide volatility supplied by the Volatility AMM

These inputs determine the three marks. The protocol first calculates the Black-Scholes Base mark, then derives the option marks from the same Base:

```
Base = BlackScholesBase(S, K, T, sigma)
Call = S - Base
Put = K - Base
```

The full `Base` formula and the expiry case are described in [Pricing](/protocol/pricing.md). The decomposition therefore satisfies:

```
S = Base + Call
K = Base + Put
```

The same Base mark is used to derive the matching Call and Put marks. This lets the protocol represent one complete set in either collateral unit:

```
1 Underlying = 1 Base + 1 Call
1 Strike value of Quote = 1 Base + 1 Put
```

Base is a real inventory leg. It is not only a chart label: the vault can hold, mint, merge and deliver Base tokens as part of a trade route.

## A trade in four stages

1. The oracle supplies the current underlying spot.
2. The series supplies its strike and expiry.
3. The pair-wide volatility AMM supplies the current sigma and updates it for the trade.
4. The vault and router select an inventory route, apply fees and settle the requested asset.

The executable quote is based on the state immediately before and after the trade. The protocol does not use a TWAP for this quote path.

## Pair-wide state

Sigma is shared by all active strikes and expiries in a pair. The series terms still affect the Black-Scholes result, so two series with different strikes or expiries can have different Base, Call and Put prices while using the same pair sigma.

The volatility AMM stores aggregate quote-denominated value reserves `X` and `Y`:

```
X = Base-side pricing value
Y = Call + Put-side pricing value
sigma = X / Y
```

In the current contract, `X` is `baseImplicitValueX18` and `Y` is `optionImplicitValueX18`. When liquidity is synchronized, `X + Y` equals the latest vault NAV used by the engine. These are aggregate pricing-state values, not literal ERC-20 balances. The vault separately tracks real underlying, quote and option inventory for NAV and routing.


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