SF Option Payoff

Let's consider vanila call option. The corresponding payoff looks as following:

\(P_{vanila} = max(S-K,0)\)

However Stochastic.Finance options have a bit of non-trivial payoff as a fraction of the supplied collateral:

\(P_{SF} = \frac{P_{vanila}}{P_{vanila} + S} = \frac{max(S-K,0)}{max(S-K,0) + S}\)

for every ETH supplied collateral, so that in case the collateral is 10 ETH the total payoff would be \(P_{SF}\) * 10 ETH