# 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:
$K_{\Delta}^{put/call} = g(\Delta)$
$K_{\Delta - \epsilon}^{put/call} = g(\Delta - \epsilon)$
$\sigma_{\max} = f_{oracle}(S,K_{\Delta}^{put/call},\tau)$
$\sigma_{\min} = \sigma_{\max} \pm \sigma_{\max}(\Delta_{offset})$
$t_{percent} = \frac{t_i - t_0}{t_{total}}$
$\sigma_{\text{market}} = \sigma_{\max} - t_{\text{percent}}\cdot(\sigma_{\max} - \sigma_{\min})$