Implied Volatility – Part 1

While I intended to discuss the impact of implied volatility and time on the strategies we have talked about so far, I felt that some general information on implied volatility might be useful to cover first. I have included a chart that depicts estimated implied volatilities for near-the-money strikes on the SPY. These are the average of the call and put implied vols for the available 2010 months (LEAPS are not shown and there are many more strikes available in each month). What stands out is that the March values exhibit the classic "volatility smile" indicating that the nearest-the-money strikes are "cheapest" while the out-of-the money strikes are significantly more expensive. The April values are beginning to "smile" but still have significant skew, like the further out months. Skew in this case is characterized by higher volatilities in the downside options with the implied volatilities diminishing as the strike prices increase.

To understand this it is important to grasp what implied volatility represents. In theory, implied volatility reflects future expectation of the underlying's actual volatility. In an aggregate sense this is true in that if implied volatility is rising across all strikes then the market is pricing in expectations of increasing actual vol; if it is lower across the board then actual vol is expected to be lower over time. Implied volatility is really, however, a "fitting" of the volatility component of a theoretical options pricing model. In other words, based on supply and demand factors as well as time to expiration, market makers adjust their implied vols to reflect fair value or the approximate mid-point of a given option's bid/ask spread.

You might ask, "What's the difference?" An aggregate metric like the VIX can be used as a general measure of expected volatility (at least over the next 30 days), but the "fitting" of the volatility component is what causes smiles and skews to exist. Longer dated option trading (beyond the front two months) tends to be dominated by hedging, selling covered calls or buying protective puts, thus a downward sloping skew exists. As a given expiration approaches, however, a smile begins to develop since the vega of the out-of-the-money options diminishes causing changes in an option's price to have a greater impact on implied volatility. Natenberg** defines vega as: "the sensitivity of an options theoretical value to a change in volatility", but the caluclation goes both ways. As an example, let's say that a near-the-money option is fairly valued at $1.00 and has a vega of .05 and an out-of-the-money option is valued at $.20 with a vega of .01. Assuming no change in the underlying, if both options increase in value by $.05 then the implied volatility of the first option increases by 1 point, whereas the IV of the second option increases by 5 points. So as time passes and out-of-the-money options approach parity or zero, small price changes can dramatically impact the implied volatility of those options, thus the skew develops into a smile.

In addition to the time factor, order flows begin to change as expiration approaches. More speculators show up in the front two months looking to profit from a quick move in either direction, causing out-of-the-money demand and thus implied vol at those strikes to rise. Also, hedgers who were selling further out calls are now buying those calls back and selling new longer dated calls. For some reason, people are less likely to sell out their put protection, but that is another story.

In sum, over time it is reasonable to expect skew to become a smile. Is this a hard and fast rule? No, because option markets, like the underlyings they are derived from, are fluid. None the less, these points are good to keep in mind when considering the appropriate time to expiration and strike of a potential options position.

Hope I didn't cause too much confusion by getting overly technical today and I will start discussing the impact on strategies very soon.

**Sheldon Natenberg, Option Volatility& Pricing.