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Put vs. Call
- Thread starter craigatelite
- Start date
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.
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.Quote from Algorithm:
If I understand the original question as; why do long puts and long calls have a price differential when the underlying equity is ATM?
First, this is a good observation and has been debated for a long time.
Second, the best answer I have found has to do with intrest rates and the underlying value of time on money. It goes something like this, when you buy the call you are deferring the purchase of the underlying stock and some of the inherit risk in owning the stock outright (mainly control the shares without the higher cash outlay). Higher interest rates widen the difference between put and call prices, only at a 0% real interest rate would an exact price correlation be 1 to 1 in regards to the puts and the calls. The cost of carry is really the main culprit for the price differential betweent he long calls and the long puts on the underlying equity when it's ATM.
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.
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.