> 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/instruments.md). # Base, Call and Put ## The decomposition Pairity represents an option series as a Base leg plus one option leg: ``` Oracle spot = Base + Call Strike = Base + Put ``` The decomposition is exact at the mark level. Given a Base price: ``` Call = Oracle spot - Base Put = Strike - Base ``` Both option legs are non-negative, and Base is capped at the smaller of spot and strike. ## Call complete set One unit of underlying collateral can be split into: ``` 1 Underlying -> 1 Base + 1 Call ``` The Call leg represents the upside above the shared Base value. If the vault already has the requested Call inventory, it may deliver it directly. Otherwise, a route can create a complete set and sell or merge the other leg as needed. ## Put complete set One strike value of quote collateral can be split into: ``` 1 Strike value of Quote -> 1 Base + 1 Put ``` The Put leg represents the downside value between the strike and the shared Base value. ## Merging Holding matching Base and option tokens allows the pair to be merged back into its collateral: * `Base + Call` can be merged into underlying collateral. * `Base + Put` can be merged into quote collateral equal to the strike value. This relationship is used by the vault's inventory manager and route logic. It is also why Base, Call and Put balances should be treated as separate inventory rather than as three unrelated markets. ## At expiry At expiry the time value disappears: ``` Base = min(spot, strike) Call = max(spot - strike, 0) Put = max(strike - spot, 0) ``` Only the in-the-money option leg retains intrinsic value. The Base leg remains the shared portion of the collateral value. --- # 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/instruments.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.