I am trying to understand the paper "Option Pricing: A Simplified Approach" by Cox-Ross-Rubinstein (available online here).
To my frustration, I already don't understand the paper starting from just page 3. It is said there:
Consider forming the following levered hedge: (1) Write three calls at $C$ each, (2) buy two shares at $\\\$50$ each, and (3) borrow $\\\$ 40$ at $25\%$ to be paid back at the end of the period. Table 1 gives gives the return from this hedge for each possible level of the stock price at expiration. Regardless of the outcome, the hedge exactly breaks even on the expiration date. Therefore, to prevent profitable riskless arbitrage, its current cost must be zero; that is, $3C - 100 + 40=0$.
I take it from this that, apparently, the "cost" of this is equal to $3C - 100 + 40$.
I don't understand this. I always thought that the "cost" of something is what one would pay for it, that is, its value. In this case, it seems to me that the cost (the value) would therefore be equal to $-3C +100 -40$ (since e.g. we are buying two shares at $\\\$50$, so that would cost us $\\\$100$ for those two). This is exactly the negative of what is stated above. Of course, in this particular case it happens to be equal to zero anyway, so it doesn't matter, but the point is that the suggestion is made that the cost is equal to $3C - 100 + 40$. Thus, either this is indeed the cost, and what I thought to be the case is simply false and I'm insane; or, what is stated is wrong.
In the table right below the above text (see Table 1 in the paper), for the present date "$3C - 100 + 40$" is mentioned, whereas for expiration date the value of the portfolio (for instance in case that $S^* = 100$ it is $-150+200-50$) is mentioned.
What is meant by "cost" here? (It is, of course, undefined in the paper--who would need a definition of something so important?) It makes no sense to me at all. Could someone clarify this to me?
