The Black-Scholes-Merton model makes the assumption of constant volatility. In practice, we observe something called the volatility smile. Basically, options struck at the money have less volatility if you solve for volatility in BSM than options struck far in or out of the money. This is an interesting phenomenon that finance professors like to write about and hedge funds try to exploit.
I wonder whether equity index options (in particular just b/c I know that the 10 month MA strategy works on them and they have a long history) experience different volatility smiles when above the 10 month MA or below the 10 month MA. If the volatility doesn't change, I would look to a situation where calls are cheap when the market is trending up and puts are cheap when the market is trending downwards. I imagine it would take significant work to look into this. If no one else does (let me know if you do), then I might take a stab at looking into this problem sometime within the next six months. Nevertheless, I think it is an interesting question and could present arbitrage opportunities. Volatility is traditionally higher when equity markets are below 200 day moving averages, but I wonder if it is high enough given historical volatility during these times and the small (mostly negative) returns.
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Not sure if anyone has looked at that specifically but this is a similar idea: http://img129.imageshack.us/img129/8232/skewtt2.jpg
Skew definitely increases in falling markets, I guess the question here is how persistent the increase is when the market isn't aggressively falling (rather just sitting below 10MA)
I trade equities and not options. I'm aware that the shape of the volatility surface shifts, but I haven't really spent much time investigating it. My knowledge of options is pretty much limited to the class I took at Courant in Derivatives. So as I learn more I'll try to look into it. Anything else you figure out about its persistence, feel free to shoot me an email so I can check it out.
My first inclination is to say that there is no such possibility of arb by simply looking at the moving average and vol skew. I would be very surprised if you found some anomaly with a greater potential for profit than the bid/ask spread. The vol smile is an area, especially for option traders, that has been studied in depth, and since there are several trading companies out there that specialize in index options (Chicago Trading Company, Susquehanna), the chances of finding some discrepancy is that much smaller.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=721345
There are lots of similar papers that look at the predictability of returns using the skew. I don't think it has a large enough range to wiggle around (see the chart I linked in my first reply) to significantly decrease during uptrends, it is clearly highly correlated to volatility
That looks like an interesting article and I'll check it out. I've looked at other papers that note that puts and calls struck out of the money are rarely profitable while some options struck in the money are more likely profitable.
http://www.cxoadvisory.com/blog/external/blog3-19-08/
That article also corrects for bid/ask spreads which I imagine will be pretty important. At the very least it might make sense that a strategy buying the in the money calls when above the 200 day moving average would get better returns than using futures or etfs. I would be more than happy to admit that the optimal strategy may not be in arbitrage.
I'm not so sure about that one, you should be able to get the same leverage at lower rates and for lower transaction costs unless you're trading a small personal account.
From those papers that you're talking about I think they typically find that calls tend to have a slightly lower return than what you'd expect given the inherent leverage and the return of the underlying, correct me if I'm wrong
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