by John Summa (Contact Author | Biography)
Position Greeks can be defined as either the sign or value of any Greek for an outright position, or the net Greeks position when all options legs in a complex strategy are tabulated. Let's begin with basic outright positions, which we have touched on in previous segments of this tutorial when explaining the individual Greeks and what they represent.
The sign on the Greeks is easy, as was seen in previous tables. What is more complicated is the degree to which any Greek is either negative or positive.
We know that all puts have a negative Delta, which stems from the fact that when the underlying rises, put values fall (an inverse relationship). Long calls have a positive Delta because when the underlying rises, so does the premium on the option, all other things remaining the same (ceteris paribus). But what happens if we have a long call and long put with the same strikes (known as a long straddle)? What is the position Delta? Here is where the story gets somewhat gray.
For example, we know that a long straddle involves buying an at-the-money call and at-the-money put, in combination. At-the-money options have a Delta that is 0.50 (where two long calls equal 100 shares of the underlying or one futures contract). Therefore, if we own a call (positive Delta) and own a put (negative Delta), both of which have the same Delta value but different signs, then we can calculate the position Delta easily. The Deltas of -0.50 and +0.50 cancel out, leaving position Delta at zero (or Delta neutral).
Now this is at one point in time when the underlying is at the strikes of the straddle. Once we get a move one way or the other, the relative Delta values begin to diverge from equality and with it position Delta neutrality. Take, for instance, a rise in price. Let's say the call gets in the money so that the Delta on the call is now +0.75, having increased from +0.50. This means the long put in the straddle is now out-of-the-money. Let's say its Delta has fallen to -0.25 from -0.50. Remember, the put is now out-of-the-money so its Delta value will be smaller. (For more, see Out-of-the-Money Put Time Spreads.)
Now we have a position Delta that is net positive (+0.75 -0.25 = +0.50). The position Delta is positive by 0.50, meaning it is long the market. If the reverse move occurred, the straddle would show a position Delta of -0.50 (the long put would have a Delta of -0.75 and the long call 0.25, leaving -0.50). The position Delta would be short the market. This simple example using Delta and position Delta for a straddle illustrates two important concepts related to position Greeks.
- Position Greeks are not constant, always changing with movement of the underlying and other variables such as time value decay and volatility levels.
- Movement of the underlying can change the value of position Greeks, and in some cases the sign will flip or invert from positive to negative or vice versa.
If we take a long straddle and move the call and put from at the money to out-of-the-money and sell them instead of buy them, then the position becomes a short strangle. Let's say that the Deltas on each option are +0.25 for the short put (now that the put is sold not bought, the sign changes from negative, or short the market, to positive, or long the market) and -0.25 for the short call (now that we have sold it not bought it, the call position is short the market, not long the market). So individually speaking, each leg of this short strangle has its own Delta, positive 0.25 for the put and negative 0.25 for the call, but when we combine them, we have neutrality again, like with the long straddle example above. And once again, movement of the underlying in any direction will begin to shift neutrality to non-neutrality. To maintain neutrality, adjustments are required to positions to bring Deltas in line again.
Complicating the picture, moving to position Vega now, recall that all short options have negative Vegas. In a short strangle, therefore, the position Vega is negative (short volatility), and it can be calculated by adding the negative Vegas of each option in the strangle.
|Figure 13: IBM short strangle position Vegas. Values taken on Dec. 29, 2007.|
|Source: OptionVue 5 Options Analysis Software|
Looking at Figure 13, we can see how a short strangle will work in terms of position Vega. Remember, all short options strategies, or net short strategies, carry a negative position Vega. In Figure 13, the position Vegas for each leg of the strangle are indicated with a red rectangle. The 115 call has -7.71 short Vegas and the 105 put has -7.27 short Vegas, giving a position Vega of $14.98 (summing the two). This tells us that for each point rise in implied volatility, the position will lose $14.98, assuming no other changes.
These segments of the tutorial on Greeks explained the concept of position Greeks, using a long straddle and short strangle to examine position Delta and position Vega (for a strangle). Using these so-called combination trades, which have two legs in the strategy, it is shown that when combining the Deltas and Vega on each option, we arrive at net position Greeks. The concept of position Delta neutrality is also demonstrated along with the impact on neutrality of a price move of the underlying.
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