Sorry everyone for the confusion, but thank you also for all of the explanations. Yes, Phil...I meant SP, the futures contracts. And I certainly understand the "value" differences between 1 contract in each ($50 ES; $100 SPX; $250 SP). So....unless I'm still misunderstanding something, here's what I was trying to evaluate: Theoretically then, the following trades would all yield the same result on expiration day(assuming all bought same time, ATM option strikes; same time length): 1. 10 ES long contracts + 10 ES ATM Puts + Interest (Theoretical) 2. 10 ES ATM Calls 3. 5 SPX ATM Calls 4. 2 SP long contracts + 2 SP ATM Puts + Interest (Theoretical) 5. 2 SP ATM Calls Again, I really appreciate everyone's patience in my learning curve.
I always thought that the "cost of carry" is the hedging cost for the person holding the short call. Basically to be hedged they have to own the stock. So the cash to buy that stock is losing the risk free interest rate and apparently it is fair to increase the call price for that factor (per B-S). However, by owning the stock they now have significant downside risk if the stock falls so I am not sure this theory makes sense. If the hedge is accomplished by being delta neutral than I would expect the cost of carry to be related to Delta which would mean about 1/2 the risk free rate for ATM Calls. Maybe someone else can shed some light on this? Don P.S. BTW, to hedge a short put you need to be short the stock which does not have a carry cost.
Cost of carry is based on holding the position, which replicates the original position thru synthetics. A long call is equal to the long put plus long stock. So, in order for the two alternatives to have the same value (i.e. no arbitrage profit) the call price must include the cost of carry. Otherwise, the call would be underpriced and you would trade the reversal to lock in the profit.