# Hedge Sugar-ing

This section takes into account the impact of trading fees on risk-neutral pricing, represented by the symbol.

<figure><img src="https://243453531-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FgJ3evKFYCTOt5HvIW8Jx%2Fuploads%2FUve1ObJEGV9WKBRv3mqK%2FAdd%20a%20subheading%20(4).png?alt=media&#x26;token=097fc9fb-dbb3-4af9-9900-3033e0170037" alt=""><figcaption></figcaption></figure>

using $$\phi_k$$ to denote the proportion of the hedge purchased for a given strike in a given epoch, the return for "selling" it can be shown as&#x20;

$$
APR_k=12\times\left(\frac{1-c}{1-\phi_k}\right),
$$

and in order for a no-arbitrage environment, we must have the relation&#x20;

$$
P_k=\frac{\phi_k}{1-c}.
$$

It should be noted that although the APR for selling a hedge may seem quite high, there is always a probability $$P_k$$ of the seller's entire position being liquidated.&#x20;
