# Hedge Pricing

In this section, we include the effect of trading fees on risk-neutral pricing, which we will denote with the variable $$c$$. 

![](https://398575907-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FaSJHG27D6yEvbos52Fsy%2Fuploads%2Fby1duXtmWtVRYY4BcbPW%2FUntitled%20Diagram.jpg?alt=media\&token=baf8ef6a-be45-4c9e-902f-6e1b98181b41)

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 

$$
APR\_k=12\times\left(\frac{1-c}{1-\phi\_k}\right),
$$

and in order for a no-arbitrage environment, we must have the relation 

$$
P\_k=\frac{\phi\_k}{1-c}.
$$

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.