I elaborate on my previous question.Looked at a couple of papers briefly, esp. a nice empirical study by Ni, Pearson, and Poteshman. (Stock PriceClustering on Option Expiration Dates). I don't quibble with the data -- definitely something going on.Here is the main theoretical explanation: long vol + delta hedging -> pinning at the strike.The argument is starting to bug me a little.Here is my summary of the theory argument:Consider hedging a long call under Black-Scholes. It's easy to show or visualize that d Delta/dt flips sign as the stockprice crosses the strike (and as time to expiration shrinks to zero.). After all, Delta is tending to 1 or 0 on either side.If you imagine S near K and Delta(t) near 1/2, then Delta(t) will be increasing on one side and decreasing on the other as time passes. The implications: If you're long a call and delta-hedging your position, then you're going to be selling stock to adjust your position when S(t) > K and buying if S(t) < K. If you're doing this in size and your counter-parties aren't, then this will tend to pin the stock price at S(T) = K. The argument also works if you're long a put. Does this argument hold water? How model independent is it?-If- the stock price, say, is going to be pinned at the strike, then thestarting formula (Black-Scholes) is badly flawed since the process is not GBM at all. Of course, we know the GBM idea is flawed for other reasons.But there's something a little fishy here -- a lack of self-consistency or at least closure in the argument. Suppose you're a market maker who is net long vol. in agroup of market makers who tend to delta hedge. Expiration is coming up and the stock priceis close to a strike. You anticipate that it may be pinned. What do you do? Since everybodyis thinking the same way, what is the net result? (Honest question - if anybody can close the argument, I'd appreciate hearing it.)
Last edited by Alan
on January 11th, 2007, 11:00 pm, edited 1 time in total.