Thursday, March 25, 2010

The Straddle, Volatility Plays, and the Greeks – Part 2

In the last post we saw how a long straddle can work in your favor when the stock moves around and you have taken a delta (∆) hedge approach. I also touched on the concept that as time passes ∆, gamma (Γ) and theta (θ) become larger in absolute terms for the near-the-money-options. In the case of the long straddle that we were examining, Γ evolves to a greater positive number, θ to a larger negative number, and ∆ to greater value depending on whether it is above or below the strike. I have included a chart of what approximately happens to the three Greeks in question if the SPY stays at 116.50 and implied volatility remains constant over the life of the contract. This represents day to day changes except for the shaded area at the right, which represents the last day of trading (expiration Friday). Since the SPY calls are in-the-money and the puts are out-of-the-money the straddle position finishes the cycle at +1000 ∆'s for the 10 contract position. A few things stand out: 1) Γ plunges on the final day to 0 because the options are either in-the-money or out-of-the-money, there is no in between, 2) θ's decline rate is also extremely rapid as the 4 PM bell approaches, in other words, although there may be some time value left at the opening , it diminishes rapidly as the day progress as a result of 3) the ∆ on each call option rapidly approaching 100 and the put ∆ approaching 0. Obviously, this scenario is unrealistic, but it exemplifies what is happening to each option over time which is important to understand with any option position.

It is the goal of the long Γ trader to have enough swings, up and down, over the life of the position to offset the continued loss of time value. In the process you buy low and sell high, again and again . . . at least in theory.

In the example provided in the last post, I chose a somewhat arbitrary 1.5% move in the SPY since the investment in the straddle involved a premium outlay of roughly 3% of the value of the underlying. More commonly, traders use some ∆ value as a reference to place their hedges; perhaps every 200-300 ∆'s. Whatever parameters you choose, the most important thing is to be consistent in your hedging. Also, hedging does not guarantee a profit since it is always possible that the underlying will not move sufficiently up and down or that it moves only in one direction. None the less, it is probably worthwhile to employ some sort of hedging methodology if you are going to trade a long straddle.

Finally, there is the consideration of implied volatility. If the stock is really not moving, then IV is likely to decline which will accelerate the option's rate of decay and negatively impact your position. On the other hand if the stock becomes extremely whippy the value of your position is likely to increase with IV up until expiration day when the options will ultimately approach values of 0 or parity. If the stock is whippy, however, there should be additional opportunities to flip the stock more frequently making it easier to cover the θ. Should IV really spike, you may also have the opportunity to close the position out on that move alone.

We will continue this discussion next time with a look at the risks of a short straddle.

No comments:

Post a Comment