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Options Greeks: Theta, Gamma, Delta, Vega And Rho
Chris Young posted a article in SteadyOptions Trading Blog
What Are Options Greeks? Financial derivatives can be volatile and sensitive to factors such as changes in the pricing of the underlying asset. Each character denotes the of sensitivity of an option’s price to the change in some attribute of the underlying asset, such stock price and volatility. These attributes are components of risk that a trader needs to control if he/she is to manage the risk of their portfolio. The Greek characters are easy to calculate and are a popular tool amongst derivatives traders, especially since the letters are very useful in portfolio hedging, which enables the investors to protect their investments from adverse changes within the market. Not only that, the Greek alphabets allow an investor to determine how much risk their portfolio is facing and from which area is the risk the greatest. The 5 related Greek Characters are: Delta, Gamma, Vega, Theta and Rho. (Vega is a bit of cheat: there is no such greek letter. Often epsilon is used instead). We will look at each in turn and, in particular, how we will use them to control our trades’ risk. Options Greeks: Delta What Is Delta? Delta measures option price sensitivity to changes in the price of the underlying asset. Option Delta is perhaps one of the most vital measurement methods of all, as it can investigate the level of sensitivity that an option’s price will move, if there is a change in the underlying stock price. (As with all the other options Greeks, we assume that all other of the options parameters don’t change when looking at delta). If the option has a delta of 1.5, it means that there will be a price movement of 1.5 cents for every cent the underlying stock moves. Therefore, this shows that an option with a high delta reading will increase or decrease in value more considering the direction of the price change. As compared to another option with a low delta which will not move as much from changes in the price of the underlying stock. Delta signs for long and short options: How is Delta Used? The importance of the information that the Greek Delta can provide is indispensable. This is especially the case where, in the real world, investors rarely hold options until maturity. Knowing how much profit that can be reaped or the potential losses that will be incurred from a single movement in price will be one factor an investor uses to determine whether they should still hold the option or sell it. Complication Unfortunately there is a complication with delta: it also moves as the price moves. So that 1.5 delta option may move 1.5 cents higher for 1 cent move in the underlying, but then the delta may have changed to 1.6. Hence any further increase in share price will cause an even bigger increase in the price of an option. This effect is an example of positive gamma – to be explained in our next lesson – and can be thought of as the price ‘accelerating’ higher. Click here for more on the greek: options delta. (NB We have recently published a post on the related concept of Position Delta). Options Greeks: Gamma What is Gamma? We saw above that the Greeks are an important measure of risk to used by options traders to assess the impact in changes of certain variables on the price of an option. In particular we looked at one of these, delta: the sensitivity of option prices to changes in the price of the underlying security. Unfortunately, again as we saw, the relationship between stock price sensitivity (delta) and the stock price is not linear. For example if a stock moves up, call options will become even more sensitive to further changes to the stock price. This effect is called gamma. It measures the change in delta, i.e. sensitivity to stock price movements. Positive gamma means that as a stock rises the option’s price will more sensitive to further stock changes. Negative gamma means the opposite: stock price rises cause stocks to be less sensitive. Why should we be concerned about Gamma? Gamma is the key enemy of many of the options strategies we use. It tends to rise as an option moves closer to expiration. Hence in the last week of an option’s life small changes in stock prices cause large, and accelerating, swings on options prices. This is unfortunate as many of our favorite strategies – such as the iron condor or calendar spread – rely on time decay. They relay on time passing to make money. Often a trader has to weigh up the potential profits, from time decay, of leaving a strategy on versus the increasing risk of the stock moving and wiping out those profits. It is for this reason that most experienced options traders rarely keep a trade on until expiration. We take a particularly risk averse line: we tend to remove our standard time decay exploiting trades at least 2 weeks before expiration. For example, look at our trade rules for putting on this calendar spread. Notice the last ‘Trade Management – Exit’ rule. We would get out of the trade within 2 weeks of expiration to avoid the gamma risk. Such is the power of gamma that trading with positions with large gamma – expiration week trades for example – is known colloquially as ‘riding the gamma bull’. Not for the faint hearted. Uses of Gamma We’ve seen that Gamma is often seen as an enemy. But this is usually only relevant to those trades, admittedly the most popular, that relay on time decay to profit. Some trades, however, take the opposite course: they take advantage of the accelerating price sensitivity from gamma to make money from expected changes in stock prices. One good example of this is the simultaneous purchase of an atthemoney put and call, called a long straddle, Let’s say a stock was $650. We expect significant stock movement, from a product launch for example, over the short term and so buy a $650 call and a $650 put. Such a purchase has strong gamma. Stock movement not only increases the price of the spread, these price changes are increased the more the stock changes, either way. (Don’t worry too much about the mechanics of this: we will have a more detailed course on straddles later). The catch, and key risk, is time, the opposite of the trades mentioned above. Time decay works against us here: if there is no stock movement then the spread will gradually lose money. Indeed the spread loses value every day – all things being equal – and so there is an amount of stock movement required each day just to break even. The trader has to be sure that the stock move, and move quickly, for the trade to be profitable. (This example is taken from a real life trade here. We used an APPL straddle to exploit expected movement from the iphone5 launch. Ignore, for now the discussion on increases in implied volatility: this will be part of the Vega lesson). Gamma vs. time: Gamma scalping One advanced use of gamma is ‘gamma scalping’, something you may hear about from experienced traders. It’s pretty complex – it takes advantage of the ‘boost’ in option price changes from excessive stock movement whilst managing delta risk (I said it was complex) – and I may include it in a later advanced post, but I suggest that most of you don’t worry about this strategy at present. Click here for more on the greek: options gamma. Options Greeks: Vega What Is Vega? Vega is a measure of an option’s sensitivity to changes to implied volatility (IV). As we’ve seen earlier, implied volatility is the market’s estimate of the volatility (measured by standard deviation) in the future. It’s an input into the standard options pricing models and hence any change in this expectation, in other words any change in implied volatility, will affect the price of options. How does it affect the price? In general bought options, either calls or puts, increase in value as IV increases. This makes sense: an option seller would want to be compensated more for the increased future risk, as priced by the market, of the option moving in the money. Stocks expected to be more volatile, and hence have higher IVs, have higher options prices, everything else being equal. Short options decrease in value, the higher IV is for the same (but opposite) reasons. Things get interesting once options are combined in a spread. Some combinations such as a Calendar Spread increase in value as IV increases. Others, such as the Iron Condor, decrease. Uses of Vega Many options strategies rely on picking the way volatility moves. For example should be believe that we are to have a market correction we would, of course, be interested in the effect of stock price falls on our options positions. But we’d be also interested in what the associated increase in IV would have on the position. There are some trades that rely solely on Vega: volatility trades. IV tends to be mean reverting and so any short term deviation could produce a correcting change in the near future. For example many traders look for the difference between historical volatility – how volatile the market is right now – to implied volatility – a future volatility prediction. There is some evidence to say if these two indicators diverge than they will soon get closer together. This can be traded if you know the volatility effect of IV on an options trade. In other words, Vega. Click here for more on the greek: options vega. Options Greeks: Theta What Is Theta? Theta is a measure of the time decay of an options, or option spread. As we have seen elsewhere in the courses, options are a decaying asset: they reduce in value over time. All things being equal an option is worth more the longer it has to go until expiry; an option with 60 days of time left to expiry will be worth more than one with only 30 days. The expected drop of an option value, again all things being equal, in the next 1 day is Theta (expressed as a negative). For example, at the time of writing, you can buy an ATM June 13 445 APPL call with 23 days until expiration for about $12. It has a Theta of 0.24, meaning it will lose $0.24 in the next 24 hours if nothing – share price, volatility etc – changes. Uses of Theta Theta is the basis of many of the standard options trades we use in this course. Strategies which involve selling options – or at least there are ‘more’ sales than purchases – have positive theta (ie they rise in value over time). If we were to sell the above AAPL call options for $12 and nothing changed, we could buy them back at $11.76, the next day for $0.24 profit. If nothing else changed of course. This rather simplistic example shows the way to more (and much less risky) ways we can profit from theta. Take the vertical spread. Let’s say you thought Apple wasn’t going to rise in the next 23 days. You could sell a 450 call and buy a 480 call and receive a net credit of $4.70. The 450 call has a theta of 0.24; the 480 call a theta of 0.14 and hence the net theta is 0.10. We have reduced our risk (of a significant share price increase) but are still making $0.10 a day all things being equal. Effect of time on Theta Theta is the effect of time on options pricing. However it too changes with time. In general theta increases as expiration nears. Another way of saying this is that the time decay accelerates closer to acceleration. You can see this from our sold AAPL 445 call above. It will lose $0.24 between day 23 and day 22. If theta was constant it would only lose 23x$0.24=$5.52 of its value between now and expiration. But it is worth $12 – which must all be lost by day 23. Hence Theta must increase at some stage this to happen. Here’s a graph of what happens: Options Time Decay Notice how the value of the option (time value) accelerates near the end of its life. This is the theta increasing. Gamma and Theta So why don’t you wait until the last few days to sell your options? All that nice accelerating time decay should reduce your option price quick only for to buy them back or let them expire for a quick profit. Easy. Well, unfortunately not. We have been looking at Theta in isolation. But we know from our last course that another of the Greeks increases with time: gamma. This is the acceleration of the effect stock price has on the option price. Increasing time decay is matched with increasing sensitivity for price changes and so any time decay could be wiped out by an adverse move in the share price. This is a good example of the interplay between the Greeks. In general strategies that exploit theta have to contend with gamma and vice versa. We will see more interrelationships later. In the meantime though we will look at the last of the major Greeks, Rho. Click here for more on the greek: options theta. Options Greeks: Rho What Is Rho? Rho is a measure of the sensitivity of options prices to changes in interest rates. It is defined as the increase in price of an options, or options portfolio, as a result of a 1% increase in interest rates. Relevance Rho is often ignored by options traders as interest rates are unlikely to change (much) during the course of most options spreads. Hence changes in interest rates are usually ignored. However there are times where more notice should be taken of Rho. Long term options, such as LEAPS, are more sensitive to changes in interest rates, ie have a higher Rho. At the time of writing an at the money AAPL call option with 32 days to go has a Rho of 0.3 (a 1% interest rate rise would produce a small, 0.3%, increase in the options price). However a LEAP with 578 days to go has a Rho of 2.2. Hence any LEAP strategy, such as our LEAP Covered Calls, would be affected somewhat by a change in interest rates. The other time Rho should be at least considered is, of course, when interest rates are changing. At the time of writing, for example, there is a strong possibility that the Fed will remove its QE program thus causing, amongst other things, an increase in interest rates. Hence, all things being equal, may be see an increase in options prices over the next few months/years. In conclusion Rho can be an important factor in certain circumstances – when interest rates are expected to change and/or we are looking at long term options – but in general Rho is a far less important Greek than Delta, Gamma, Theta and Vega. Click here for more on the Greek: options rho. About the Author: Chris Young has a mathematics degree and 18 years finance experience. Chris is British by background but has worked in the US and lately in Australia. His interest in options was first aroused by the ‘Trading Options’ section of the Financial Times (of London). He decided to bring this knowledge to a wider audience and founded Epsilon Options in 2012. Subscribe to SteadyOptions now and experience the full power of options trading at your fingertips. Click the button below to get started! Join SteadyOptions Now! Related articles: Options Delta Explained: Sensitivity To Price Options Theta Explained: Price Sensitivity To Time Options Gamma Explained: Delta Sensitivity To Price Options Vega Explained: Price Sensitivity To Volatility Options Rho: Sensitivity To Interest Rates 
The Gamma is one of the most important Options Greeks. It generally is at its peak value when the stock price is near the strike of the option and decreases as the option goes deeper into or out of the money. Options that are very deeply into or out of the money have gamma values close to 0. Effect of volatility and time to expiration on gamma Gamma is important because it shows us how fast our position delta will change as the market price of the underlying asset changes. When volatility is low, the gamma of AtTheMoney options is high while the gamma for deeply into or outofthemoney options approaches 0. The reason is that when volatility is low, the time value of such options are low but it goes up dramatically as the underlying stock price approaches the strike price. When volatility is high, gamma tends to be stable across all strike prices. This is due to the fact that when volatility is high, the time value of deeply in/outofthemoney options are already quite substantial. Thus, the increase in the time value of these options as they go nearer the money will be less dramatic and hence the low and stable gamma. As the time to expiration draws nearer, the gamma of AtTheMoney options increases while the gamma of InTheMoney and OutofTheMoney options decreases. How to put gamma work for you In simple terms, the gamma is the option's sensitivity to changes in the underlying price. In other words, the higher the gamma, the more sensitive the options price is to the changes in the underlying price. When you buy options, the trade has a positive gamma  the gamma is your friend. When you sell options, the trade has a negative gamma  the gamma is your enemy. The closer we are to expiration, the higher is the gamma. When you buy options and expect a significant and quick move, you should go with closer expiration. The options with closer expiration will gain more if the underlying moves. The tradeoff is that if the underlying doesn't move, the negative theta will start to kick off much faster. When you sell options, you have negative gamma that will increase significantly as the options approach expiration. This is the biggest risk of selling weekly options. Should you trade weekly options? Selling options with closer expiration will give you higher positive theta per day but higher negative gamma. That means that a sharp move of the underlying will cause much higher loss. So if the underlying doesn't move, then theta will kick off and you will just earn money with every passing day. But if it does move, the loss will become very large very quickly. Another disadvantage of close expiration is that in order to get decent credit, you will have to choose strikes much closer to the underlying. As we know, there are no free lunches in the stock market. Everything comes with a price. When the markets don't move, trading close expiration might seem like a genius move. The markets will look like an ATM machine for few weeks or even months. But when a big move comes, it will wipe out months of gains. If the markets gap, there is nothing you can do to prevent a large loss. Does it mean you should not trade weekly options? Not at all. They can still bring nice gains and diversification to your options portfolio. But you should treat them as speculative trades, and allocate the funds accordingly. Many options "gurus" describe those weekly trades as "conservative" strategy. Nothing can be further from the truth. Example Lets sat you have a call with a delta of .60. If the price of the underlying security rises by $1, then the price of the call would therefore rise by $.60. If the gamma value was .10, then the delta would increase to .70. This means that another $1 rise in the price of the underlying security would result in the price of the option increasing by $.70, and the delta would also increase again in accordance with the gamma. This highlights how moneyness affects the delta value of an options contract, because when the contract gets deeper into the money, each price movement of the underlying security has a bigger effect on the price. The gamma is also affected by moneyness, and it decreases as an in the money contract moves further into the money. This means that as a contract gets deeper into the money, the delta continues to increase but at a slower rate. The gamma of an out of the money contract would also decrease as it moved further out of the money. Therefore, gamma is typically at its highest for options that are at the money, or very near the money. List of gamma positive strategies Long Call Long Put Long Straddle Long Strangle Vertical Debit Spread List of gamma negative strategies Short Call Short Put Short Straddle Short Strangle Vertical Credit Spread Covered Call Write Covered Put Write Iron Condor Butterfly Long Calendar Spread Summary Gamma measures the rate of change for delta with respect to the underlying asset's price. All long options have positive gamma and all short options have negative gamma. The gamma of a position tells us how much a $1.00 move in the underlying will change an option’s delta. We never hold our trades till expiration to avoid increased gamma risk. Watch the video: Related articles: The Options Greeks: Is It Greek To You? Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Delta For Direction Options Trading Greeks: Vega For Volatility Why You Should Not Ignore Negative Gamma Short Gamma Vs. Long Gamma Want to learn how to put the Options Greeks to work for you? Join Us

In this article, I will try to help you understand Options Greeks and use them to your advantage. The Basics First, a quick reminder for those less familiar with the Options Greeks. The Delta is the rate of change of the price of the option with respect to its underlying price. The delta of an option ranges in value from 0 to 1 for calls (0 to 1 for puts) and reflects the increase or decrease in the price of the option in response to a 1 point movement of the underlying asset price. In dollar terms, the delta is from $0 to +$100 for calls ($0 to $100 for puts). Delta can be viewed as a percentage probability an option will wind up inthemoney at expiration. Therefore, an atthemoney option would have a .50 Delta or 50% chance of being inthemoney at expiration. Deepinthemoney options will have a much larger Delta or much higher probability of expiring inthemoney. The Theta is a measurement of the option's time decay. The theta measures the rate at which options lose their value, specifically the time value, as the expiration draws nearer. Generally expressed as a negative number, the theta of an option reflects the amount by which the option's value will decrease every day. When you buy options, the theta is your enemy. When you sell them, the theta is your friend. Option sellers use theta to their advantage, collecting time decay every day. The same is true of credit spreads, which are really selling strategies. Calendar spreads involve buying a longerdated option and selling a nearerdated option, taking advantage of the fact that options expire faster as they approach expiration. The Vega is a measure of the impact of changes in the Implied Volatility on the option price. Specifically, the vega of an option expresses the change in the price of the option for every 1% change in the Implied Volatility. Options tend to be more expensive when volatility is higher. When you buy options, the vega is your friend. When you sell them, the vega is your enemy. Short premium positions like Iron Condors or Butterflies will be negatively impacted by an increase in implied volatility, which generally occurs with downside market moves. When entering Iron Condors or Butterflies, it makes sense to start with a slightly short delta bias. If the market stays flat or goes up, the short premium will come in and our position benefits. However, if the market goes down, the short vega position will go against us  this is where the short delta hedge will help. The Gamma is a measure of the rate of change of its delta. The gamma of an option is expressed as a percentage and reflects the change in the delta in response to a one point movement of the underlying stock price. When you buy options, the gamma is your friend. When you sell them, the gamma is your enemy. Selling options with close expiration will give you higher positive theta per day but higher negative gamma. That means that a sharp move of the underlying will cause much higher loss. So if the underlying doesn't move, then theta will kick off and you will just earn money with every passing day. But if it does move, the loss will become very large very quickly. You should never ignore negative gamma. Example Lets analyze the Greeks using one of our recent trades as an example: Buy to open 4 ORCL July 17 2015 44 put Buy to open 4 ORCL July 17 2015 44 call Price: $2.66 debit This trade is called a straddle option strategy. It is a neutral strategy in options trading that involves the simultaneously buying of a put and a call on the same underlying, strike and expiration. A straddle is vega positive, gamma positive and theta negative trade. That means that all other factors equal, the straddle will lose money every day due to the time decay, and the loss will accelerate as we get closer to expiration. With the stock sitting at $44, the trade is almost delta neutral. Lets see how other Greeks impact this trade. The theta is your worst enemy as we get closer to expiration. This trade had 44 days to expiration, so the negative theta is relatively small ($3 or 1% of the straddle price). As we get closer to expiration, the negative theta becomes larger and the impact on the trade is more severe. The gamma is your best friend as we get closer to expiration. That means that the stock move will benefit the trade more as time passes. The vega is your friend. If you buy options when IV is low and it goes higher, the trade starts making money even if the stock doesn't move. This is the thesis behind our preearnings straddles. Make them Work For You If you expect a big move, go with closer expiration. But if the move doesn't materialize, you will start losing money much faster, unless the IV starts to rise. It basically becomes a "theta against gamma" fight. When you expect an increase in IV (before earnings for example), it's a "theta against vega" fight, and the large gamma is the added bonus. When you are net "short" options, the opposite is true. For example, Iron Condor is a vega negative and theta positive trade. That means that it benefits from the decline in Implied Volatility (IV) and the time decay. If you initiate the trade when IV is high and IV is declining during the life of the trade, the trade wins twice: from the declining IV and the time passage. However, it is also gamma negative and the gamma accelerates as we get closer to expiration. This is the reason why I don't like holding the Iron Condor trades till expiration. Any big move of the underlying will cause big losses due to a large negative gamma. The gamma risk is often overlooked by many Condor traders. Many traders initiate the Iron Condor trades only 34 weeks before expiration to take advantage of a large and accelerating positive theta. They hold those trades till expiration, completely ignoring the large negative gamma and are very surprised when a big move accelerates the losses. Don't make that mistake. One possible strategy is to combine vega positive and theta positive trades with vega positive and theta negative ones. This is what we do at SteadyOptions. A Calendar spread is an example of vega positive theta positive trade. When combined with a straddle trades which are vega positive theta negative, a balance portfolio can be created. Conclusion: when you trade options, use the Greek option trading strategies to your advantage. When they fight, you should win. Like in a real life, always know who is your friend and who is your enemy. The following videos will help you understand options Greeks: Related articles: Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Delta For Direction Options Trading Greeks: Gamma For Speed Options Trading Greeks: Vega For Volatility We invite you to join us and learn how we trade our Greek options trading strategies. We discuss all our trades including the Greeks on our options trading forum.

And of course, a lower delta reveals a less responsive likely reaction among option contracts, to movement in the underlying. Delta and other socalled “Greeks” are used by many traders to compare option values and volatility. The other three most often cited are Gamma, Theta and Vega. Delta is the most popular and most relevant because it compares option volatility and underlying volatility. This is a reliable test of implied volatility, at least in the moment. It will vary based on proximity between strike of the option and current price of the underlying; and also on time remaining until expiration. When strike and underlying price are close, you expect volatility to respond more, and of course when farther away, it responds less. The range of Delta is between a high of +1 and a low of 1. When you are holding long calls, Delta is positive when the underlying rises; if you hold short calls, Delta is a negative factor as the underlying rises. For long puts, Delta is a negative factor if the underlying is declining, and a positive factor if the underlying is rising. None of this should come as a surprise to anyone who has traded options. Delta is of value, however, when comparing two or more options whose underlying is similar. It allows you to articulate even a subtle difference in volatility. The Other Greeks Three other Greeks are worth mentioning. Gamma measures how sensitive Delta is to movement in the underlying. In a sense, Gamma is the Delta of Delta. It addresses the question of the stability in Delta and likely future volatility levels. When options are in the money, Gamma will be higher; and atthemoney or outofthemoney Gamma will be lower. Theta is a measurement of time decay. How rapidly is time value declining. This varies with moneyness of the option and time to expiration, as you would expect. But given identical attributes of two or more options, Theta will not always track. It measures and compares time decay and enables you to determine which options decline quickly. Vega measures the option’s behavior relative to historical volatility in the underlying. Although Vega is not an actual Greek letter, it is always included in any discussion of the “Greeks” for options trading. The more time remaining until expiration, the greater the expected impact of volatility on the option’s price, notably when at or close to the money. When options are far from expiration and several points away from current underlying value, historical volatility’s role is likely to be little if any. Computing the Greeks is complex, but there is a solution. The Chicago Board Options Exchange (CBOE) offers a free calculator to discover the Greeks for any situation. Go to CBOE Option calculator to use this calculator. Michael C. Thomsett is a widely published author with over 80 business and investing books, including the bestselling Getting Started in Options, coming out in its 10th edition later this year. He also wrote the recently released The Mathematics of Options. Thomsett is a frequent speaker at trade shows and blogs on his website at Thomsett Guide as well as on Seeking Alpha, LinkedIn, Twitter and Facebook. Related articles: The Options Greeks: Is It Greek To You? Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Delta For Direction Options Trading Greeks: Gamma For Speed Options Trading Greeks: Vega For Volatility Why You Should Not Ignore Negative Gamma Why Delta Dollars Will Change Your Trading

In other words, an option premium that is not intrinsic value will decline at an increasing rate as expiration nears. The Theta is one of the most important Options Greeks. Negative theta vs. positive theta Theta values are negative in long option positions and positive in short option positions. Initially, out of the money options have a faster rate of theta decay than at the money options, but as expiration nears, the rate of theta option time decay for OTM options slows and the ATM options begin to experience theta decay at a faster rate. This is a function of theta being a much smaller component of an OTM option's price, the closer the option is to expiring. Theta is often called a "silent killer" of option buyers. Buyers, by definition, have only limited risk in their strategies together with the potential for unlimited gains. While this might look good on paper, in practice it often turns out to be death by a thousand cuts. In other words, it is true you can only lose what you pay for an option. It is also true that there is no limit to how many times you can lose. And as any lottery player knows well, a little money spent each week can add up after not hitting the jackpot for a long time. For option buyers, therefore, the pain of slowly eroding your trading capital sours the experience. When buying options, you can reduce the risk of negative theta by buying options with longer expiration. The tradeoff is smaller positive gamma, which means that the gains will be smaller if the stock moves. Option sellers use theta to their advantage, collecting time decay every day. The same is true of credit spreads, which are really selling strategies. Calendar spreads involve buying a longerdated option and selling a nearerdated option, taking advantage of the fact that options expire faster as they approach expiration. You can see the accelerated curve of option time decay in the following graph: As a general rule of thumb, option sellers want the underlying to stay stable, while option buyers want it to move. List of positive theta options strategies Short Call Short Put Short Straddle Short Strangle Covered Call Write Covered Put Write Long Calendar Spread Vertical Credit Spread Iron Condor Butterfly Spread List of negative theta options strategies Long Call Long Put Long Straddle Long Strangle Vertical Debit Spread Watch this video: Related articles: The Options Greeks: Is It Greek To You? Options Trading Greeks: Vega For Volatility Options Trading Greeks: Delta For Direction Options Trading Greeks: Gamma For Speed Want to learn how to put the Options Greeks to work for you? Start Your Free Trial

In this article, I would like to show how the gamma of the trade is impacted by the time to expiration. For those of you less familiar with the Options Greeks: The option's gamma is a measure of the rate of change of its delta. The gamma of an option is expressed as a percentage and reflects the change in the delta in response to a one point movement of the underlying stock price. This might sound complicated, but in simple terms, the gamma is the option's sensitivity to changes in the underlying price. In other words, the higher the gamma, the more sensitive the options price is to the changes in the underlying price. When you buy options, the trade has a positive gamma  the gamma is your friend. When you sell options, the trade has a negative gamma  the gamma is your enemy. Since Iron Condor is an options selling strategy, the trade has a negative gamma. The closer we are to expiration, the higher is the gamma. Lets demonstrate how big move in the underlying price can impact the trade, using two RUT trades opened on Friday March 21, 2014. RUT was trading at 1205. The first trade was opened using weekly options expiring the next week: Sell March 28 1230 call Buy March 28 1240 call Sell March 28 1160 put Buy March 28 1150 put This is the risk profile of the trade: As we can see, the profit potential of the trade is 14%. Not bad for one week of holding. The second trade was opened using the monthly options expiring in May: Sell May 16 1290 call Buy May 16 1300 call Sell May 16 1080 put Buy May 16 1070 put This is the risk profile of the trade: The profit potential of that trade is 23% in 56 days. And now let me ask you a question: What is better: 14% in 7 days or 23% in 56 days? The answer is pretty obvious, isn't it? If you make 14% in 7 days and can repeat it week after week, you will make much more than 23% in 56 days, right? Well, the big question is: CAN you repeat it week after week? Lets see how those two trades performed few days later. This is the risk profile of the first trade on Wednesday next week: RUT moved 50 points and our weekly trade is down 45%. Ouch.. The second trade performed much better: It is actually down only 1%. The lesson from those two trades: Going with close expiration will give you larger theta per day. But there is a catch. Less time to expiration equals larger negative gamma. That means that a sharp move of the underlying will cause much larger loss. So if the underlying doesn't move, then theta will kick off and you will just earn money with every passing day. But if it does move, the loss will become very large very quickly. Another disadvantage of close expiration is that in order to get decent credit, you will have to choose strikes much closer to the underlying. As we know, there are no free lunches in the stock market. Everything comes with a price. When the markets don't move, trading close expiration might seem like a genius move. The markets will look like an ATM machine for few weeks or even months. But when a big move comes, it will wipe out months of gains. If the markets gap, there is nothing you can do to prevent a large loss. Does it mean you should not trade weekly options? Not at all. They can still bring nice gains and diversification to your options portfolio. But you should treat them as speculative trades, and allocate the funds accordingly. Many options "gurus" describe those weekly trades as "conservative" strategy. Nothing can be further from the truth. Related articles The Options Greeks: Is It Greek To You? Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Delta For Direction Options Trading Greeks: Gamma For Speed Options Trading Greeks: Vega For Volatility The Use And The Abuse Of The Weekly Options The Risks Of Weekly Credit Spreads Should You Trade Weekly Options? Make 10% Per Week With Weeklys? Want to learn more about options? Start Your Free Trial

Vega changes when there are large price movements (increased volatility) in the underlying asset, and falls as the option approaches expiration. Vega is one of a group of Options Greeks used in options analysis, and is the only one not represented by a Greek letter. Volatility Changes In simple terms, the options Greeks vega measures the risk of gain or loss resulting from changes in volatility. Vega for all options is always a positive number because options increase in value when volatility increases and decrease in value when volatility declines. When position Vegas are generated, however, positive and negative signs appear. When you establish a position selling or buying an option, this will result in either a negative sign (for selling) or positive sign (for buying), and the position Vega will depend on net Vegas. Vega is higher on options that have more distant expiration dates. However, since those options are also more expensive in dollar terms, the vega is actually higher on options with closer expiration if we look at percentage gain or loss. Options tend to be more expensive when volatility is higher. Thus, whenever volatility goes up, the price of the option goes up and when volatility drops, the price of the option will also fall. Therefore, when calculating the new option price due to volatility changes, we add the vega when volatility goes up but subtract it when the volatility falls. Vega Risk The options Greeks vega is one of the most important risk metrics an option trader relies upon. It is used to gauge the portfolio’s overall sensitivity to changes in implied volatility, one of the largest risks the option traders faces. For example, a trader with $1 million of vega knows he will make or lose $1m dollars for every 1% change in implied volatility. Often, a decline in IV (also known as vega risk) will offset the impact of price gains in the underlying stock. This is how you can be correct on a stock's direction and still lose money on an options position. Short premium positions like Iron Condors or Butterflies will be negatively impacted by an increase in implied volatility, which generally occurs with downside market moves. When entering Iron Condors or Butterflies, it makes sense to start with a slightly short delta bias. If the market stays flat or goes up, the short premium will come in and our position benefits. However, if the market goes down, the short vega position will go against us  this is where the short delta hedge will help. Following the same logic, it makes sense to start vega positive trades like calendars slightly delta positive, in order to hedge potential IV decrease if the underlying goes up. It also makes sense to use vega positive strategies like calendars when IV is low and vega negative strategies like Iron Condors when IV is high. List of positive vega strategies Long Call Long Put Long Straddle Long Strangle Long Calendar Spread Vertical Debit Spread List of negative vega strategies Short Call Short Put Short Straddle Short Strangle Vertical Credit Spread Covered Call Write Covered Put Write Iron Condor Butterfly Watch the video: Related articles: The Options Greeks: Is It Greek To You? Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Delta For Direction Options Trading Greeks: Gamma For Speed How We Made 23% on $QIHU Straddle in 4 Hours Want to learn how to put the Options Greeks to work for you? Start Your Free Trial

Related Articles: The Options Greeks: Is It Greek To You? Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Delta For Direction Options Trading Greeks: Gamma For Speed Options Trading Greeks: Vega For Volatility Why You Should Not Ignore Negative Gamma Why Delta Dollars Will Change Your Trading Options Greeks Explained Options Greeks Essentials


The Delta is one of the most important Options Greeks. General The delta of an option is the sensitivity of an option price relative to changes in the price of the underlying asset. It tells option traders how fast the price of the option will change as the underlying stock/future moves. Option delta is usually displayed as a decimal value between 1 and +1. Some traders refer to the delta as a whole number between 100 and +100. Delta of +0.50 is the same as +50. The following graph illustrates the behaviour of both call and put option deltas as they shift from being outofthemoney (OTM) to atthemoney (ATM) and finally inthemoney (ITM). Note that calls and puts have opposite deltas  call options are positive and put options are negative. Call and Put Options Whenever you are long a call option, your delta will always be a positive number between 0 and 1. When the underlying stock or futures contract increases in price, the value of your call option will also increase by the call options delta value. When the underlying market price decreases the value of your call option will also decrease by the amount of the delta. When the call option is deep inthemoney and has a delta of 1, then the call will move point for point in the same direction as movements in the underlying asset. Put options have negative deltas, which will range between 1 and 0. When the underlying market price increases the value of your put option will decreases by the amount of the delta value. When the price of the underlying asset decreases, the value of the put option will increase by the amount of the delta value. When the underlying price rallies, the price of the option will decrease by delta amount and the put delta will therefore increase (move from a negative to zero) as the option moves further outofthemoney. When the put option is deep inthemoney and has a delta of 1, then the put will move point for point in the same direction as movements in the underlying asset. If you have a call and a put option, both for the same underlying, with the same strike price, and the same time to expiration, the sum of absolute values of their deltas is 1.00. For example, you can have an out of the money call with a delta of 0.36 and an in the money put with a delta of 0.64. Delta Sensitivity As a general rule, inthemoney options will move more than outofthemoney options, and shortterm options will react more than longerterm options to the same price change in the stock. As expiration nears, the delta for inthemoney calls will approach 1, reflecting a onetoone reaction to price changes in the stock. Delta for outof themoney calls will approach 0 and won’t react at all to price changes in the stock. That’s because if they are held until expiration, calls will either be exercised and “become stock” or they will expire worthless and become nothing at all. As expiration approaches, the delta for inthemoney puts will approach 1 and delta for outofthemoney puts will approach 0. That’s because if puts are held until expiration, the owner will either exercise the options and sell stock or the put will expire worthless. As an option gets further inthemoney, the probability it will be inthemoney at expiration increases as well. So the option’s delta will increase. As an option gets further outofthemoney, the probability it will be inthemoney at expiration decreases. So the option’s delta will decrease. It is important to remember that Delta is constantly changing during market hours and will typically not accurately predict the exact change in an option’s premium. Delta as Probability Delta can be viewed as a percentage probability an option will wind up inthemoney at expiration. Therefore, an atthemoney option would have a .50 Delta or 50% chance of being inthemoney at expiration. Deepinthemoney options will have a much larger Delta or much higher probability of expiring inthemoney. Looking at the Delta of a faroutofthemoney option is a good indication of its likelihood of having value at expiration. An option with less than a .10 Delta (or less than 10% probability of being inthemoney) is not viewed as very likely to be inthemoney at any point and will need a strong move from the underlying to have value at expiration. As mentioned, the sum of absolute values of delta of a call and a put with the same strike is one. This is in line with the probability idea. When you have a call and a put on the same underlying and with the same strike price, you can be sure that one of them will expire in the money and the other will expire out of the money (unless, of course, the underlying stock ends up exactly equal to the strike price and both options expire exactly at the money). Therefore, the sum of the probabilities should be 100% (and the sum of the absolute values of deltas should be one). Just for clarification, delta and probability of expiring in the money are not the same thing. Delta is usually a close enough approximation to the probability. Example If the delta on a particular call option is .55, then, all other things being equal, the price of the option will rise $0.55 for every $1 rise in the price of the underlying security. The opposite effect is also seen as for every $1 decline in the price of the underlying the option will lose $0.55. If the delta on a particular put option is .45, then, all other things being equal, the price of the option will rise $0.45 for every $1 fall in the price of the underlying security. As with call options the obverse scenario is also true. List of delta positive strategies Long Call Short Put Call Debit Spread Put Credit Spread Covered Call Write List of delta negative strategies Long Put Short Call Put Debit Spread Call Credit Spread Covered Put Write List of delta neutral strategies Iron Condor Butterfly Short Straddle Short Strangle Long Straddle Long Strangle Long Calendar Spread Summary Positions with positive delta increase in value if the underlying goes up Positions with negative delta increase in value if the underlying goes down An option contract with a delta of 0.50 is theoretically equivalent to holding 50 shares of stock 100 shares of stock is theoretically equivalent to an option contract with a 1.00 delta Watch the video: Related articles: The Options Greeks: Is It Greek To You? Options Trading Greeks: Theta For Time Decay Options Trading Greeks: Vega For Volatility Options Trading Greeks: Gamma For Speed Want to learn how to put the Options Greeks to work for you? Start Your Subscription

The following video shows how the Theta impacts options pricing. It examines few live examples of different options strategies. Download video and slides: Options Greeks  The Theta.wmv Options Greeks Theta.pptx
