If by hedging one can manage to get 0 then this is IMO still very valuable... Because then one just would need to add an "offset" to the calculations and by this would make "0 + offset" profit... (just thinking loud about mathematical possibilities... )
botpro, I actually just simulated hedging a long call. Since I used excel to generate my Monte Carlo points (~3000 each time), I was not able to get enough accuracies to get the true Monte Carlo outcome, so every simulation was slightly off but after enough tries I was able to see things approaching zero. However, I was using the current risk free rate which is < 1% and my computation did not have enough to converge to a resolution < 1%. I relooked at the Black Scholes derivation, it assumes a no arbitrage world and that one can hedge continuously, then, the portfolio of (options - delta*stock) = earns the risk free rate of return. Two questions for everyone: 1. If that is true, my simulation should approach the risk free return instead of zero? 2. If I short options, in a BS world, if I continuously hedge, would I then lose the risk free rate of return since in that case I am the counter party? Any comments are welcome.
Ironchef, for point number 2, yes if you are a dealer you will lose the risk free rate on the option trade however because you sold it, the money you got from the sale will earn the risk free rate in your bank account, so you will come out to exactly zero.
Ah! Great answer! I missed that part! So, if I were the buyer, I spend x and will get x + rt back at the end. It is the same as if I deposit x in the bank and get x + rt back. What does the seller get? He pays the risk free rate for the use of the funds. Make sense. Thank you blueplayer.
hello botpro, When you are short premium and are putting on hedges you are actually locking in losses; not profits. Since the option pricing itself is based on continuous hedging (google it up), its not really a way to locking in any gains - check your sources. Try searching "reverse gamma scapling". Might help. regards! -gariki
Weird world! When I in my testing framework do simulate options selling with dynamic hedging, then I always make a profit of approximately the size of the credit. Other people here tell that one can earn only the risk-free interest (however they might define this, because it is not given in any of the params... ie. r=q=0 ). So, what is the truth about the expected profit from options selling with dynamic hedging? Either my logic is weird, or my code is buggy (indeed long and complicated code), or I maybe have found a holy grail with this and the rest of the world is crazy wrong in this. Pls just tell me what it is. Thx!
Everybody is telling you you are wrong (including several option-veterans), yet you keep insisting you are right ... what do you honestly think ...
Can you make a statement about the profit one can make with options selling combined with dynamic hedging?
yes, it's zero ... that's what the whole options theory is about: you try to artificially recreate an option ... market makers use it to hedge there exposure when they buy or sell options ... Black, Merton and Scholes won the Noble prize for it ...