> 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/pricing.md). # Pricing Pairity uses the oracle spot, series strike, time to expiry and the pair's current volatility to mark the Base leg. The implementation uses a zero-rate Black-Scholes decomposition. ## Inputs ``` S = oracle spot price K = selected strike price T = time to expiry in years sigma = current pair volatility ``` The oracle value must be valid and fresh enough for the configured market rules. An expired series is not priced as an active trade. ## Base mark The Base mark is: ``` d1 = (ln(S / K) + 0.5 * sigma^2 * T) / (sigma * sqrt(T)) d2 = d1 - sigma * sqrt(T) Base = S * N(-d1) + K * N(d2) Base = min(Base, S, K) ``` `N()` is the standard normal cumulative distribution function. The cap keeps the decomposition valid: ``` Call = S - Base Put = K - Base ``` At expiry the formula converges to intrinsic value and the explicit expiry values are used: ``` Base = min(S, K) Call = max(S - K, 0) Put = max(K - S, 0) ``` ## Before and after pricing A trade can change sigma. To avoid using only the pre-trade price for a large move, the quote path considers both states: 1. Read `sigmaBefore` from the current AMM state. 2. Calculate the pre-trade Base, Call or Put mark. 3. Solve the post-trade AMM state using the applicable inventory value delta. 4. Calculate `sigmaAfter` from the updated state. 5. Calculate the post-trade mark using `sigmaAfter`. 6. Use the average of the before and after marks as the fair trade price. The final quote then adds or subtracts protocol fees and applies the direction-specific rounding rule. This is a state transition quote, not a TWAP. The requested instrument's fair quote always uses its own before and after prices. The value delta used to move the AMM can be different when the vault route changes Base inventory; see [Volatility AMM](/protocol/volatility-amm.md#inventory-aware-trade-impact). ## NAV marks Vault NAV uses the oracle to value underlying collateral and the same Base/Call/Put decomposition to value active series inventory. NAV is separate from the AMM's virtual pricing reserves, although TVL is used when the AMM is rebased. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation by asking a question. Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters: ``` GET https://docs.pairity.fi/protocol/pricing.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.