September 21st, 2011, 10:48 am
I think you are suggesting that you will somehow make a positive profit on this "gamma scalping" activity of yours. That may indeed be the case, but it pretty much requires that the market price is mean reverting on an intra-day basis. This is not technically inconsistent with the assumptions of standard option pricing models, but it would require a pretty amazing risk premium process. This is probably not what you assume, so I think this comes down to a deeper misunderstanding of the equality of gamma and theta in the Black-Scholes model (up to sign, factors of one half, carry, etc.). This equality makes a position in an option a "fair bet", and this is true whether or not you carry out a delta hedging program. In particular, it is not like you are somehow systematically losing money on the option theta that you have to earn back through delta hedging (or gamma scalping in your parlance). If this were the case, why wouldn't you just forget about the option market altogether and harvest the gamma scalping profits in the underlying market on imaginary option positions all day (and night) long? In the standard theoretical models, hedging is ex ante a zero NPV activity. In the real world, hedging (in and of itself) is always ex ante a negative NPV activity, due to a variety of transaction costs incurred. Hedging is something we do because we want to limit the risk/required capital incurred when putting on derivatives positions that we think are favorably priced, ideally locking in an arbitrage profit. To the extent that "hedging" activities systematically make a profit they incorporate an element of proprietary trading that could probably be separated from the execution of hedges based on option pricing models.