# Option Pricing Formula

* $$S$$ - spot price
* $$\Delta$$ - option delta
* $$\Delta\_{offset}$$ - delta % offset
* $$\epsilon$$ - delta offset
* $$K\_{\Delta}^{call/put}$$ - delta strike computed using $$\Delta$$
  * $$K\_{\Delta}^{call}$$ - delta strike computed for a call option
  * $$K\_{\Delta}^{put}$$ - delta strike computed for a put option.
* $$\tau$$ - time to maturity
* $$g : \Delta \rightarrow K\_{\Delta}^{put/call}$$ - delta strike function which maps the delta parameter $$\Delta$$ to the strike price
* $$f\_{oracle}: (S,K,\tau) \rightarrow \sigma$$ - oracle function which maps the parameters $$S,K,\tau$$ to implied volatility $$\sigma$$

The price curve can be calculated as follows:

$$
K\_{\Delta}^{put/call} = g(\Delta)
$$

$$
K\_{\Delta - \epsilon}^{put/call} = g(\Delta - \epsilon)
$$

$$
\sigma\_{\max} = f\_{oracle}(S,K\_{\Delta}^{put/call},\tau)
$$

$$
\sigma\_{\min} = \sigma\_{\max} \pm \sigma\_{\max}(\Delta\_{offset})
$$

$$
t\_{percent} = \frac{t\_i - t\_0}{t\_{total}}
$$

$$
\sigma\_{\text{market}} = \sigma\_{\max} - t\_{\text{percent}}\cdot(\sigma\_{\max} - \sigma\_{\min})
$$


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.knox.premia.finance/appendix/option-pricing-formula.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
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.