Post by Bozur on May 8, 2008 23:29:51 GMT -5
Becoming a Greek Geek
Guy Halpin
May 5, 2008
Understanding the greeks is extremely important when assessing whether a trade should be entered, managing an existing position and when it comes to closing out a trade. In this article I will explain the four main greeks Delta, Gamma, Vega and Theta. Each of these will be explored in conjunction with a risk so that you can relate the greeks to what the risk graph is showing you. When I started out I only knew of the greeks by definition and not what the actual numbers meant to my trading. I based my trading decisions on what the risk graph was showing me. In hindsight I knew a lot more about the greeks earlier on in my trading than I thought I did and it was simply a matter of linking the two together. I hope this article will help you to do this.
Delta
Definition: the change in the price of an option relative to the change of the underlying security.
In plain English, Delta answers the question: how much can we expect our position to make/lose for a one point move in the underlying security. For example, if a long call has a Delta of 0.35, a $1 move up in the stock would lead to the option position gaining $35 (0.35 x 100) in value. If we had:
* 2 contracts our position would increase in value by $70 (0.35 x 100 x 2)
* 3 contract increase by $105 (0.35 x 100 x 3)...
Figure 1 below has two graphs. The one on the left represents a long call with a Delta of 0.35 and the graph on the right is a graph of Delta itself and how a change in the share price at various days until expiration will impact the Delta value. Bit of a mouthful? I will break it down a little more.
Figure 1: Long Call Risk Graph (left) and Delta Graph (right)
The chart on the left and the corresponding numbers mean the following:
1. From looking at the graph the number 1 is out-of-the-money [OTM]. You can tell this without even knowing the current stock price, strike price or expiration (black) line. How? The long call risk graph slope is becoming more vertical the lower the share price (vertical axis) is. All readers would know that if a long call is becoming further OTM it is expected that the value of the option will decrease by less and less as the share price moves lower. Therefore is it not true that as an option becomes further OTM the Delta will decrease? This is exactly what is happening!
The right hand graph at number 1 is doing just as described in the above paragraph. As the share price falls (vertical axis) from 2 to 1 the value of Delta is decreasing at a slower rate, that is, the line is becoming more vertical. The thick black line that represents the risk graph at expiration is a vertical line from number 2 down. This is as expected because OTM options have a Delta of 0 at expiration (worthless) and as can be seen this line goes straight down to 0.
2. The number 2 on the left hand chart is at the strike price or when the option would be at-the-money [ATM]. As we move from 1 to 2 the Delta of the position is increasing quicker and quicker. Between a Delta of 0.35 and 0.5 is the part of the risk graph we want to be riding with a long call. Just after 2 is still good but the closer to 3 the rate of change of Delta decreases (Gamma).
The right hand graph shows a change in concavity at 2. The technical name for this is the point of inflection. (More on this in the section about Gamma.)
3. At the number 3 the risk graph on the left shows the lines flattening out. This is telling us the further in-the-money [ITM] the trade, is the more dollars we make. This should sit well with you as the further a long call is ITM the higher the Delta.
The graph on the right at number 3 is becoming more vertical as each day passes until expiration when it is vertical. All ITM options at expiration have a Delta of 1. The graph is showing us exactly this. Follow the black line down from 3 and it has a Delta value of 100 (1 x 100).
So for a directional trade we want the risk graph to be pointing more east-west than north-south as Delta will be working for us. For a non directional trade we want Delta to be close to zero (more vertical position risk graph). Now that Delta has been covered it is time to move onto Deltas close cousin Gamma.
Gamma
Definition: The change in the Delta of an option with respect to the change in price of its underlying security. Gamma helps you gauge the change in an option''s Delta when the underlying asset moves.
In simple terms, gamma answers the question to what will the new Delta be if there is a $1 movement in the stock price. Gamma is commonly labeled the Delta of Delta. For example the above long call had a Gamma value of 0.0421. So if the share was to increase by $1 the new Delta would be 0.3921 (0.35 + 0.0421). If the shares were to decrease by $1 the new Delta would be 0.3079 (0.35 0.0421).
Looking at Figure 1, Gamma can be explained as follows:
1. From number 1 to 2 the lines in both graphs are moving to the right at a faster pace. This is telling you the Delta is increasing at a faster rate, or to put it another way, the value of Gamma is becoming larger and larger up until the number 2.
2. At number 2 the Delta curve changes concavity (point of inflection). This happens around the strike price and is the point where the option will gain or lose value at the quickest rate. Great if you get it right as you will make money the quickest and terrible if the position goes against you. When an option has a Delta of 0.5 it is at this point Gamma will be the greatest.
3. From number 2 to 3 the lines in the graph on the left is flattening whilst the line of the right is becoming steeper. As the share price moves deeper ITM the Delta becomes closer and closer to 1. 1 is the maximum value Delta can be, so as the option becomes deeper ITM, the rate of change of Delta (which is Gamma) slows. The right-hand graph is showing you this. Look at the green line (30 days until expiration). The time taken from a Delta of 70 to 80 is two squares up where as the time from 80 to 90 is three squares.
Vega
Definition: The change in price of the option relative to its change in its volatility. Vega tells you how much your position will change for a one-point increase/decrease in volatility.
Looking at the long call example, we see that the Vega value is $0.0792. What this means is if the IV were to increase in value by one point, the trade would be worth $7.92 more (0.0792 x 100). Conversely, if IV were to decrease by one point, the position would be worth $7.92 less.
Figure 2, below, shows the same long call risk graph on the left and the accompanying Vega in dollars per point change on the right. The various numbers are showing that:
1. At number one the option is OTM. The further OTM we go (from 2 to 1) the less impact Vega will have. This makes sense in that the further OTM an option is the less time value it has. The less time value it has the less impact a change in volatility will have. Remember implied volatility can only affect time value. It cant impact intrinsic value (in this case there is none)!
2. ATM options have the greatest time value and therefore at this point Vega will be the greatest. The graph on the right shows us that the call option with a current Delta/Vega value of 0.35/7.92 respectively will increase to just over 9 when the option is ATM (Delta of 0.5).
3. The exact same as stated in point 1 applied for point 3 except the option is ITM rather than OTM. The further along the lines from 2 to 3 the less impact Vega will have in terms of dollar change.
Figure 2: Long Call Risk Graph (left) and Vega (right)
Theta
Definition: The change in the value of an option with respect to the change in its time to expiration.
The long call shows a Theta of 0.0191. What this means is if the share price and IV remain the same the long call will lose $1.91 (0.0191 x 100) from today to tomorrow. ATM options have the greatest amount of time value and therefore it is at this point (2) that Theta will have the greatest value. As we move towards points 1 or 3 the value of Theta diminishes. Also as each day passes if there is no change in the share price the value of Theta will increase. This is shown in the graph above on the left hand side. The distance between each line (88-59, 59-30 & 30-0) is increasing as expiration draws nearer.
This article has focused on the long call and how each of the greeks impact this position at different places. Below is a quiz for you to test your understanding. The answers can be found by scrolling down. Good luck!
Make it happen!
Guy Halpin
Senior Writer & Options Strategist
Optionetics.com.au ~ Your Options Education Site
Quiz
Use Figure 3 for questions 1-4.
Figure 3: Verisign Risk Graph
1. What is this a risk graph of?
2. By looking at the risk graph of today (red line) what is the approximate value of Delta? How can you tell?
3. Knowing that the actual Delta is 5.55 what will be the profit/loss of this position tomorrow if Verisign increases by $1 in price?
4. What would be the new position Delta if Verisign moved down $1 today?
Use Figure 4 for questions 5-8.
4.
Figure 4: Citigroup risk graph
5. What debit strategy is this a risk graph of?
6. The current price is $25.03. Around what price will Theta be working against the position the greatest?
7. Around what price do you expect Theta to be working for the position the greatest?
8. The day following this risk graph Citi moves down $2.00. What will be the estimated profit/loss of the position?
Quiz Answers
1. What is this a risk graph of?
Answer. Long Strangle (long call and long put)
2. By looking at the risk graph of today (red line) what is the approximate value of Delta? How can you tell?
Answer. It is close to zero - slightly positive. This can be seen from the risk graph being vertical. This means that no matter which way the stock moves the position will not change in value very much. The actual Delta value of this position is 5.55 (you cant calculate it from information provided).
3. Knowing that the actual Delta is 5.55 what will be the profit/loss of this position tomorrow if Verisign increases by $1 in price?
Answer. Profit/loss tomorrow
= Current Value + Theta + Delta
= -20 + -2.85+5.55
= -$17.27
4. What would be the new position Delta if Verisign moved down $1 today?
Answer.
New Delta = Current Delta + Gamma
= 5.55 + -14.292
= -8.74
5. What strategy is this a risk graph of?
Answer. Vertical debit spread or bear put spread.
6. The current price is $25.03. Around what price will Theta be working against the position the greatest?
Answer. At the long strike price, $25, This is close to the current share price. Long options ATM lose value the quickest.
7. Around what price do you expect Theta to be working for the position the greatest?
Answer. At the short strike price, $20. ATM options have the greatest time value so this is the price where the short option will lose the most value as each day passes.
8. The day following this risk graph Citi moves down $2.00. What will be the estimated profit/loss of the position?
Answer. For the first $1 move down Profit/loss tomorrow
= Current Value + Theta + Delta
= -4.00 + -0.55 + 33.75 = $29.20
New Delta will be -33.75 -5.015 = $38.765
For the second $1 move down Profit/loss tomorrow
= Current Value + Delta (Theta already taken into consideration above)
= 29.20 + 38.75 = $67.95 profit
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