Hedge Pricing

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

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.