Quote from mr_spread:
I have seen option prices move little, not at all or even down when stock price goes up. (I have no specific examples)
Could following a stock too close (min by min) cause this strange occurrence? I was under the impression that options moved as fast as stock. Still I would like to know more about the greek relationship. . .
If there is a formula like:
delta = .5 at said time / vega
I will understand that the easiest.
Thanks!
The four Greeks you are most likely to concerned about as a new options trader are delta, gamma, vega and theta.
They are inter-related but not in the way you describe above.
Delta: At its simplest, delta measures how much an option will move relative to the underlying security. Additionally, delta represents the likelihood an option will settle in the money. Since most options models assume the underlying will follow "random walk" - all at the money options (both calls and puts) will have a delta of .5. In other words, if the underlying is 15.00, both the 15.00 calls and puts will have a .50 delta. If the call is worth .30 and the underlying moves from 15.00 to 15.10, the option will be worth .35 (((15.10 - 15.00) * .5) + .30)). Similarly, the put will be worth .05 less as a result of this move.
At 15.10, the likelihood of the 15.00 call settling in the money increases. Therefore the delta of the 15.00 call will increase. If the delta increases the options will be more sensitive to price movement. For example, if the delta increased to .60 after this move and the stock went up by another 10 cents, the call would be worth .41 (.35 + .06).
The reason you don't always see this relationship hold is because of something called volatility skew. The above example assumes that volatility is the same across the strike series. The 14.00, 14.25, 14.50, 14.75, 15.00, 15.25, 15.50⦠calls and puts all have the same volatility (say 15%). I donât know what you are watching, but virtually all futures contracts I am aware of skew volatility. In that case, as a contract is rallying your option may be going down the skew. This means that instead of the 15% volatility you saw when the contract was at 15.00 the volatility may now be at a 14% when the contract moved to 15.10. As a result, even though the contract went higher the call may not have gained any value (it may have even lost value) because of its now lower volatility.
Gamma: Gamma simply measures how much the delta of an option will change relative to a change in the underlying asset price. As you might imagine, skew messes this up as well.
As an aside, because of the skew â very few traders I know use Delta and Gamma. There are other measures (very cleverly) called skew delta and skew gamma that takes the skew into account and doesnât force you to put an ice pick through your eye when option values donât do what you expect them to.
Vega: Some people call this Lambda or Kappa as well. What Vega measures is the amount of money an option price changes based on a 1% change in volatility. This is usually expressed as a dollar amount though sometimes it is expressed in points. To give an example: Letâs say you bought 10 15.00 calls. Letâs further assume that volatility is 15%. Since you purchased options you are long volatility or long Vega. In other words, you make money if volatility goes up (assuming no price change in the underlying). If your Vega is $100.00 and volatility increases from 15% to 16% your net liquidity goes up by $100.00. Of course, if volatility decreases from 15% to 14%, you will be $100.00 poorer.
This is the reason guys that sold calls before 9/11 lost money even though the market was crashing. The market dropped hundreds and hundreds of points but volatility went up 30%. So even though their calls were far out of the money, they were worth more than when they sold them. (I am personally a volatility seller â but beware of the adage that all volatility sellers know âeat like a bird â crap like an elephantâ).
Theta: Theta measures how much less an option will be worth - holding price and volatility constant. This is also called time decay. As you move closer to the expiration of an option theta will increase and Vega will decrease.
Hope this helps.
By the way, when people tell you to simply look at Black Scholes to figure this stuff out â tell them that, while they are trying to sound superior, they don't know what they are talking about. Black Scholes assumes European exercise. That is why the futures exchanges use CRR, Whiley or binomial models and not BS.