I'm pretty much a newbie at this, so I'm going to freely admit my ignorance and save you experienced folks the trouble of pointing it out! I've been reading Natenberg's book and, if I understand correctly, any single option that appears to be undervalued relative to the expected volatility of the underlying can be played by purchasing that option, hedging delta neutral, and then periodically updating the hedge back to neutral at some set time interval. On this basis, I'm wondering if the OTM SPX/SPY calls are attractively priced at this point. The SPX NOV 06 1400 calls were trading today at about 7.8% implied volatility, 34 days till expiration. According to ivolatility.com, historical 30-day volatility has been bouncing around between approximately 7.5 and 8%, with 52 week low of 6.96% on September 28. I also understand that we are heading into a historically more volatile period, so it seems that buying volatility at 7.8%, betting on a vol increase, might be reasonable. My questions are: - What's the best means of hedging the long SPX calls? Choices that I can see are the same strike SPX puts (long side), ITM SPX calls, emini SP futures and/or SPY shares from the short side. Since I'm new to this and would like to start with only a few contracts the first two options don't seem practical, as the ratio of long OTM calls to long puts or short ITM calls would be fairly high to get neutral- probably not feasible with only a few long contracts. - What's the optimal hedging time interval? Seems like the simplest approach would be to rebalance at the end of each day, thereby matching the ivolatility.com calculation method. - Would a movement based re-hedging interval make more sense - maybe every time SPX moves 10 points? - Will the trading costs associated with the frequent rebalancing eat up most of the potential profit? I'm on TOS and pay minimum $5 for stock trades, $3.50 per side for futures, flat $1.50 for options. Good time to open an IB account? - Is this approach considered "gamma scalping", or is there another name for it? - I'm concerned about the market getting quiet during expiration week when most of the theta he gets sucked out - should I scale out of the position towards the end, trying to keep position theta approximately constant? I think I remember reading that the market is typically more volatile during expiration week, so maybe this is exactly the wrong thing to do. Thx, -Steve

Steve, Re the Natenberg reference. This is just a restatement of the theory underlying (unrealistic) assumptions of the basic Black-Scholes formula, eg zero or negligible costs and no bid-ask spread. âundervalued relative to the expected volatilityâ .The expected volatility is the implied volatility, ie what the market expects. So what is the basis for this under-valuation? I can only think of historical volatility, which has no predictive value, and I doubt, any correlation with implied volatility. I think this answers all your questions. However, donât be put off. Despite the flaws of the B-S model, it still forms basis of the majority of pricing models used today, from the private investor to the largest banks. Do a Google search of âimplied volatilityâ, and youâll have find enough reading to keep you going for years. Also enter âDermanâ and âFiglewskiâ, the former (of Goldman Sachs) is especially lucid. Grant.

Appreciate the response Grant - good points! Prior to reading Natenberg I thought there were basically only two ways to play an underpriced option, in this case the OTM call. Method one was to buy the call and do nothing - most of the time it would expire worthless, but the few times it paid off it would more than cover the losers if it were truly underpriced. Second method was based on continuous hedging which, as you mentioned, unrealistically assumed no costs or bid/ask spread. The new insight I got from Natenberg was that you could hedge at arbitrary time intervals. If you assume that the underlying prices are distributed as predicted by the model, each slice of time has the same mathematical expectation. The shorter the time between hedges, the less variance from the expected result. Is this a correct interpretation? To clarify, let's assume the SPX is going to move with exactly 10% volatility and a lognormal distribution for the next 34 days. If I were to purchase the call, and hedge continuously (at no cost), my gain should be exactly the difference between the price of the call today and what its price would've been at 10% implied volatility. If, instead, I hedge at some arbitrary time interval, my expected return is the same but with higher variance. If I did the same trade a hundred times, the average gain should be pretty close to what I would've made by hedging continuously. Make sense? I went to a TOS seminar were the instructor said that, in his opinion, the best estimate of expected volatility was current implied volatility, just as you said. However, he seemed to think it was based on the implied volatility of the ATM options, which is several points higher than the OTM calls in this case, as I believe is generally true for the indexes. In the section in Natenbergs book on volatility forecasting, he suggested there was some degree of serial correlation. One example method was to calculate a weighted sum of historical volatility, giving higher weight to the more recent observations. My approach is much more primitive - I merely observed that 7 1/2 percent is a repeatedly visited "support" level for historical volatility - that's my main basis for considering the calls undervalued, or at least fairly valued. Maybe it makes more sense to wait until vol starts going up again, but I'm guessing that when it does it will spike - if I'm not in already I'll probably miss it. I guess the thing I really like about this approach is that it seems to take advantage of at least one of the flaws in the B-S model's assumptions; non-lognormal fat tail events are welcome! Not familiar with Derman or Figlewski - will check them out. Again, thanks for responding! -Steve

âThe shorter the time between hedges, the less variance from the expected result. Is this a correct interpretation?â If I understand this correctly, then logically if continually hedged there would be no variance; if no hedge, then considerable variance, possibly beyond that implied by the model, ie the initial implied volatility will change (increase or decrease).This is known as stochastic volatility. Continually hedged in this context refers to locking in a profit from an arbitrage position arising from a theoretically mis-priced option, ie the implied volatility is incorrect. This is just an illustration of an underlying asssumption of the B-S model. It is theory - these postions, for mere mortals, don't exist. Don't get too pre-occupied with it as a potential strategy. But the theory is invaluable. JC Hullâs Options, Futures and other derivative Securities covers this, and other areas. DA Dubofsky, Options and Financial Futures: Valuation and Uses is less mathematically intense but broader. Both are worth buying, especially the latter at nearly 700 pages. Natenberg offers nothing original or profound. Re volatility forecasting, correlation between what? Implied and historical? Itâs negligible. I wouldnât dispute your observations re historical volatility (if it works for you, use it) as Iâve never gone beyond the superficial. However, I would suggest what you will find instructive is the observation of implied volatility, ie it is mean-reverting. If implied is high, it will tend to drift lower, and vice versa. This is a good basis for selecting positions/strategies based on under/over-priced perceptions. On a very basic level, if implied is high, it can be expected to fall; if implied falls, then the underlying price will rise. So you need a position which will benefit from rising prices/falling volatility, eg short puts (only for the extremely wealthy). Long calls, while benefiting by the rising underlying price, will suffer from the declining implied. For short time periods (how long is a piece of string?) the greeks, especially vega, will help you here. Fat-tail events are a reality but I think you will be wasting your money anticipating these. However, account for them when assessing the potential risk of your positions. Grant.

Not sure about the "theoretically mispriced" part but, from my perspective, if the actual volatility over the next 34 (okay 32 now) days turns out to be anything greater than 7.8%, then the call was underpriced. JC Hullâs Options, Futures and other derivative Securities covers this, and other areas. DA Dubofsky, Options and Financial Futures: Valuation and Uses is less mathematically intense but broader. Both are worth buying, especially the latter at nearly 700 pages. Natenberg offers nothing original or profound. That's kind of been my problem actually - I've read very interesting, mathematical, theoretical texts and then had absolutely no idea how to make money with the knowledge gained. Natenberg seemed to bridge the gap between the college textbooks and "George Fontanills Teaches You to Trade Options" type books. Based on my understanding of Natenberg, this seems like a very simple strategy to make a bet that volatility will be higher than the amount implied by the call. I guess it really comes down to whether or not that's a reasonable expectation and, if it is, whether this is the best way to bet on it. Re volatility forecasting, correlation between what? Implied and historical? Itâs negligible. Historical and historical - i.e. the volatility of the last 30 days is somewhat predictive of the volatility of the next 30 days. On a very basic level, if implied is high, it can be expected to fall; if implied falls, then the underlying price will rise. So you need a position which will benefit from rising prices/falling volatility, eg short puts (only for the extremely wealthy). Makes sense, and I think you just pointed out the reason why this strategy is probably generally not optimal - because it doesn't take advantage of the fact that volatility expands or contracts as a function of the trend. I can't help feeling though that even if the current uptrend continues that both actual and implied volatility aren't likely to get much lower. Then again, I probably would've said exactly the same thing last month, and been proven sadly mistaken. Fat-tail events are a reality but I think you will be wasting your money anticipating these. However, account for them when assessing the potential risk of your positions. Quite so. I'm not quite man enough to lie here and bleed for months on end like my man Taleb, but this seems like it could be at least modestly profitable and, if the 10 sigma event comes along all the better! -Steve

Steve, First, a correction. âtheoretically mis-priced optionâ in my last post should be a mis-priced equivalent synthetic position. My knowledge of motor mechanics is zero. Therefore, my expectations for the performance of my car is based on what? Why wonât my car reach 120 mph or more? Maybe the wrong tyres. Not enough petrol. A knowledge of mechanics, physics, chemistry and aerodynamics would tell me of the design weaknesses. So, while I still wonât break the sound barrier, I would not have unrealistic expectations, nor waste time, money and effort to achieve them. Similarly with options. Stochastic calculus and fourth order polynomials may not guarantee wealth but at least they should help you reduce, or avoid, bad positions. Thereâs a very basic calculation (something like, underlying x implied vol x time (days/365), and I stand corrected) â which provides a range for the underlying over a specific period. So if you take an option position expecting a rise (fall) of X points in a month, for example, this simple calc will show whether your expectation is reasonable or justified. Doesnât mean to say your wrong, but you you should be sure of your ground. College textbooks, Natenberg, Fontanills. If you understand the textbooks, you donât need these two. Examine all the common strategies and their rationale, and then work out their weaknesses beyond what is stated. Get a programme which calculates the greeks. Thereâs plenty on the net, cheap or gratis. Given your interests, I would suggest looking at âscapling the skewâ. See Tower, http://www.elitetrader.com/vb/showt...=76105&perpage=6&highlight=tower&pagenumber=2 âif the actual volatility over the next 34 (okay 32 now) days turns out to be anything greater than 7.8%, then the call was underpricedâ. Foresight is a rare gift. Historical vs historical â I wonât argue with that, but to repeat, I think comparing implied vs implied is a better bet. âif the current uptrend continuesâ¦both actual and implied volatility aren't likely to get much lowerâ. I think thatâs reasonable. Therefore, a long volatility, market neutral position may be appropriate â long put, long call. If bullish(bearish), then long call (long put). I won Â£10 on the national lottery on Saturday. I also live in hope of the fat-tail event. Grant.

Thanks a lot for the input, Grant - your insights have been helpful. I'll let you know how the trade goes - or maybe I'll just buy a lottery ticket. -Steve