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Hedge Pricing

In this section, we include the effect of trading fees on risk-neutral pricing, which we will denote with the variable
cc
.
using
ϕk\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
APRk=12×(1−c1−ϕk),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
Pk=ϕk1−c.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
PkP_k
of the seller's entire position being liquidated.