Long call option payoffs - Reading 41 Example 1

Hi all,

I’m looking for a bit of assistance in understanding the Example below - when I think about this from an arbitrage perspective, it seems to make sense in my mind, but for some reason just can’t make sense of replicating the payoff of the option. In short, I feel like the solution below leaves us with 2 x the call option profit/loss. If that’s not the case, could someone please explain why?

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1.) h is the hedge factor and the formula for h is (c+ – c)/(S+ – S)

2.) In the binomial tree, you calculate the value of C0 under one period would be:

C0 = hS0 + (-hS-+c-) /(1+Rf)

If you do the math on the binomial tree, you’ll see its equilvanent.

Calls can be thought of as a leveraged stock investment where hS0 units of stock are purchased using PV(–hS + c) of borrowed funds.

Thanks 125mph