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The Option Greeks and the Passage of Time

In one of my live interactive meetings with Gold Members at Options for Rookies Premium, we were talking about the passage of time and whether option premium (and thus, bid/ask quotes) were adjusted smoothly with the passage of time or whether they ‘jumped’ each morning as a result of it now being ‘one day later.’ This is a typical (good) question from someone who is new to trading options.

By the way, the answer to the above question is ‘neither.’ Other bloggers, including Mark Sebastian, have discussed this point in detail (Option Pit) , but let me say that market makers have a system for marking the passage of time. My guess is that each uses a proprietary method and that everyone’s timepiece would not read the same time. In simple terms, the ticking clock speeds up as we move from Monday to Friday.

Regardless of the specific details, the people who set the markets accelerate time decay as the end of the week approaches. In other words, the theoretical clock ticks much faster on Friday than on the previous Monday. Why would market makers do this? It’s an attempt to smooth out the passage of time when taking into consideration that the markets are not open for trading on the weekends.

If the option traders used the ‘true’ Friday theoretical values for their bids and offers, when Monday morning arrived each option would (assuming an unchanged sock price) be lower than on Friday. This would be especially obvious as expiration week arrives. To discourage others from ‘dumping’ option premium of Friday and repurchasing Monday, the passage of time used to determine the value of an options is not measured in real time – at least not as weekends approach.

Whether this is a good idea (no markets are open over the weekend) or a bad idea (wars can start over a weekend) is not the point.

That discussion brought us to more questions about how time affects other greeks (in addition to theta). Does delta, gamma, vega change as time passes? The answer is yes, it does. Most of the time, beginners are not introduced to these concepts because they are not important factors on a day to day basis. There are general themes that are important (such as how does delta change as expiration nears), but the details are often overlooked. The math gets complex, but as will all math used in the options world, we have calculators to do the difficult tasks.

With that background, I believe it’s a good idea to introduce you to some of the second order greeks – with the understanding that this is basically a FYI discussion. If you want to get a deeper glimpse into the world of risk measurement when using options (the greeks), read on.

The following is from Wikipedia

Higher-order Greeks

Charm

Charm, or delta decay, measures the instantaneous rate of change of delta over the passage of time. Charm has also been called DdeltaDtime [the rate of change of delta with respect to time]. Charm can be an important Greek to measure/monitor when delta-hedging a position over the weekend. Charm is a second-order derivative of the option value, once to price and once to the passage of time. It is also the derivative of theta with respect to the price of the underlying

Practical use

The mathematical result of the formula for charm is expressed in delta/year. It is often useful to divide this by the number of days per year to arrive at the delta decay per day.

This use is fairly accurate when the time to option expiration is large. When an option nears expiration, charm itself may change quickly, rendering full day estimates inaccurate.

Color

Color, or gamma decay (or DgammaDtime) measures the rate of change of gamma over the passage of time. Color is a third-order derivative of the option value, twice to underlying asset price and once to time.

Color can be important to monitor when maintaining a gamma-hedged portfolio. It can help the trader anticipate the effectiveness of the hedge as time passes.

Practical use

The mathematical result is expressed in gamma/year. It is often useful to divide this by the number of days per year to arrive at the change in gamma per day. This use is fairly accurate when time to expiration is large. When an option nears expiration, color itself may change quickly, rendering full day estimates inaccurate.

DvegaDtime

DvegaDtime, measures the rate of change of vega with respect to the passage of time. DvegaDtime is the second derivative of the value function; once to volatility and once to time.

Practical use

It is common practice to divide the mathematical result of DvegaDtime by 100 times the number of days per year to reduce the value to the percentage change in vega per one day.

There are other 2nd and 3rd order greeks. Today’s discussion is untended to introduce you to the fact that the greeks are all sensitive to the passage of time. And as with the first order greeks with which we are familiar, an approaching expiration date can produce sharp changes in their values.

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Adjusting with the Greeks

Mark,

I have been spending a great deal of time lately looking into making adjustments and all the various methods people use as part of developing my overall plan. I understand and subscribe to your idea that first and foremost you MUST want to own the adjusted position as a new position not just to save yourself from a "loss".

I have gone back and read some of your old posts about the three stages of adjusting and about your kite strategies. I am wondering if now would be a good time to post a refresher and maybe some new examples of the various ways one could consider adjusting positions and how to focus on Greeks when making different adjustments.

Thanks again for the great Blog and book. 

Scott

 Thanks for the suggestion.

My business is doing my best to help others learn about options – especially those in the earlier stages of their learning or trading careers.

Option trading is not mathematics. It is not an exact science. One problem I face is that when I express an opinion, some readers accept that as THE TRUTH. While that may be flattering, it's not my purpose. I believe in offering ideas that I'd like readers to consider. Obviously I believe each idea is sound, and is a reasonable alternative for the given situation.

When making such comments, I never know my audience on a personal level. Some readers are more sophisticated and can tackle more complicated ideas. Others are in position to seek higher gains and are willing to take greater risk to achieve their goals. Still others are very conservative traders who abhor risk.

The point is that it's difficult to give general advice that is appropriate for everyone. With that in mind, I'll tackle Scott's request.

Focusing on Greeks

is an intelligent method for reducing/eliminating specific risk. Good idea. The one aspect of option trading that separates it from all other forms of investing is that it allows specific risks to be measured.; You can measure delta (ok, so can any stockholder), but you also have the ability to measure the rate at which delta changes (gamma). You can determine the effect of time passage on the value of your positions, etc.

It's not so much a matter of focusing on the greeks and making specific trades related to the greeks that's important. Scott, if you look at your vega (or any greek) and let’s say you find that you are short 600 vega and that a 5-point jump in implied volatility will theoretically (the greeks provide an estimate of how the option prices will change; they do not provide a guarantee) make your position lose $3,000.

You can decide:

a) That's ok. The position can stand that much swing or perhaps, ouch. If the former describes how you feel, no vega adjustment is needed. If the latter holds true, then you want to buy some vega. It's not complicated. You could cover some short options, or perhaps buy a new positive vega spread.

b) Such a move is likely, so if 'ouch' is how you feel, you should take some risk-reducing action.  Or, you may feel that although it would hurt, it's so unlikely that you won't adjust.

You measure risk; then decide whether you want to take that risk or reduce it.  That's how to use the greeks.  It's not more complicated than that. When you have a good handle on risk, you are in position to take appropriate action.

Kites are too complicated for a review. At least not right now. I never finished all I had to say about them – because so much detail is needed.

I will say this about kite spreads. Any time you can own a naked long option at a cost that you deem acceptable, it does take a lot of risk out of a major market move.  But, it's not for everyone.

Examples

My basic premise on adjusting is that any one trade can illustrate what's possible. Almost any trade that reduces risk is helpful. For iron condor traders, that means reducing delta exposure, and perhaps reducing negative gamma and vega as well.

Examples are just that. There are always alternatives. Your individual needs and comfort zone boundaries often define how to adjust.

Let's say you traded 10-lots of a credit spread (or a whole iron condor) and the call portion is in trouble. With stock trading near 200, 15 points higher than when you opened the trade, you are short a 210/220 call spread that expires in 45 days.

If we take this as the given situation, some traders will object that they would never own this position unadjusted. They would have done something earlier, or say that 10-lots is too many (or too few). Others would say 'what's the problem?' The fact that such positions can be looked at as very risky by some while getting no more than a shrug of the shoulders by others already tells us that any 'examples' may be considered as unrealistic by the majority.

If adjusting a credit spread, iron condor, butterfly – any limited loss trade that has changed the position into one you are no longer willing to own, something must be done. The two obvious choices are to close or reduce. However, if you see something that turns the position into something desirable, then go for it. I don't know how to provide a list of possibilities that may appeal to any trader or group of traders.

A trader could buy calls or puts, buy debit spreads for delta, sell credit spreads for delta – but get even shorter gamma and vega. He/she could own calendars that widen where risk is now greatest. There is truly a large list of potential trades to help any position – depending on how you want to 'help' it. I use a limited number of adjustment trades in my repertoire, but each of us is limited only by our imaginations.

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What Other Bloggers are Saying

 

Register (free) forTradeKing Webinar: Adjusting Iron Condors

Oct 12, 2010;  5 PM (ET)

 


I've often mentioned that I avoid trading near-term options, especially as expiration draws near.  My primary reason:  Negative gamma increases, and that's more risk than I want to accept.

If you are interested in a bit more detail as to why this phenomenon occurs, Jared at CondorOptions and Steven at Investing With Options recently disucssed how time to expiration affects delta (charm) and gamma (color).

If those terms: charm and color are unfamiliar, Wikipedia offers definitions for readers who want a more mathematical description.  Charm and color are among the less well-known Greeks.  They are not Greek letters, but are considered to be options "Greeks."

Charm or delta decay, measures the instantaneous rate of change of delta over the passage of time.  Charm can be an important Greek to measure/monitor when delta-hedging a position over a weekend. Charm is a second-order derivative of the option value, once to price and once to time. It is also then the (negative) derivative of theta with respect to the underlying's price.

Color or gamma decay  measures the rate of change of gamma over the passage of time. Color is a third-order derivative of the option value, twice to underlying asset price and once to time. Color can be an important sensitivity to monitor when maintaining a gamma-hedged portfolio as it can help the trader to anticipate the effectiveness of the hedge as time passes.

***

Jared concludes: "Delta decay is of particular interest to traders holding ATM or OTM options near expiration, especially when those options are serving as portfolio hedges."

Steve puts it this way: "So we know that gamma increases in magnitude over time. This is known as charm. So if you are selling puts with 5 weeks left, you will have less overall “heartburn” than if you sell puts with 5 days left. The tradeoff is less theta, but that’s for another post."

 

For more detail refer to these posts.  I understand that this is the Options for Rookies blog.  If the idea of charm and color feel too advanced, all you really have to know is that gamma increases as expiration approaches, and that holding short option positions into expiration comes with extra risk.  I know you have heard that idea before.

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The Greeks. Are they Greek to you? Part II

This is an important, basic two-part post for rookies and anyone who wants to learn about using 'the Greeks' to manage the risk of an option position.  Part I.

Each Greek does its own thing

In your example, the position delta is -59, and that translates into an expected loss when the stock moves higher by one point.  I mentioned that the delta is not a constant number, but changes as the stock price changes.  It's gamma that measures the rate at which delta changes.

Your position has -3 gamma.  In terms you an apply to managing the position, that means:

  • If the stock moves lower by one point, you gain 3 delta.  Negative gamma works against you.  Thus, you get shorter on rallies and longer on dips.  Positive gamma works in your favor

  •  If the stock price moves one point lower, the position delta becomes -56.  If the stock moves one point higher the position delta becomes -62

  • Even that is an approximation because gamma is not constant.  It's rate of change is measured by a different Greek.  For the vast majority of trades made by individual investors, it not necessary to be concerned with such details.  Professional traders, who seek every possible penny in edge and take extraordinary caution to trade as 'Greek neutral' as possible, pay careful attention to these Greeks

  • More sophisticated traders also measure the rate at which change in volatility affects gamma.  To learn more about the less frequently used Greeks, this Wikipedia article is a good place to start.  But it's not necessary for us to delve that deeply into how options are valued


You begin the day short 59 delta.  When the stock rallies by one point, the -3 gamma tells you that the new delta should be -62.  Be careful with this next sentence; it's not tricky:  Thus, on average, you were short 60.5 delta over that one point move (59 at the beginning and 62 at the end).  A better estimate of the real world loss is $60.50, rather than $59.


Time decay

Your position theta is 14.  That should translate into a one-day profit of approximately $14 as a result of time decay.   As you probably already know, theta is not constant.  It accelerates as time to expiration decreases.

So, if you lose money ($60.50) on a one point rally, you can anticipate that the real lose may be $14 less, or $46.50 due to the effect of positive theta.

Vega

If the implied volatility changes, the vega component of your position results in a change in the daily profit and loss. 

Bottom line:  The Greeks provide a
reasonable estimate of risk – or how much to expect to make or lose when
the market moves.  Many Greeks interact, so the final result cannot be
exactly predicted. 

Even if you were able to be that accurate, the real world pricing of options (the option price (called the 'mark') that represents the value of the options in your account) can vary from day to day for random reasons.

Don't drive yourself crazy trying to get an exact handle on profit and loss possibilities.  Look at the bigger picture.  If a certain event (stock moves by 7%, for example) results in a predicted loss of $100, it does not matter if the loss is $105.  What must concern you is being aware when a loss that's too big to handle may occur (perhaps when stock is up 12%) – and taking action to reduce the effect of such an event.  That's referred to as adjusting a position.

Clarification:  If that 12% move is dangerous, you may decide not to do anything right this moment to reduce your exposure to loss.  But, if the stock creeps higher, at some point you cannot continue to close your eyes to a dangerous possibility.  Making a small change to your position can be a good way to reduce your potential loss.

There are no hard and fast rules.  The purpose of this two-part post is to be certain you are aware of how useful the Greeks can be in helping you manage portfolio risk.

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The Greeks. Are they Greek to you?

Hi Mark

Reading thru your blog, I feel I have a lot to learn. I noticed
the graph you use above.  Is there any software you recommend for us?

When I look at Greeks of the positions (I use OptionsXpress), there
are Delta, Pos.Delta, Pos.Gamma, Pos.Theta and Pos.Vega. What is the
difference between Delta and Pos.Delta?

I may know the definition of each
Greek, but I have no idea what the numbers represent.

For instance, -59
for Pos.Delta, -3.12 for Pos.Gamma, 14.66 for Pos.Theta and -7.49 for
Pos.Vega.(I have an IC with some kite) What message do those numbers
tell us?

Thanks

***

Hi 5teve,

You do have a lot to learn.  It' not difficult to understand what an option is.  Options are not complex.  But putting everything together so you can understand what your position is supposed to do to make or lose money requires an education.   I understand that you are a rookie
option trader and I don't know where you are in your education process.
  Take your time.  You have the rest of your life to trade.   

It's important to be able to speak the language of options and to understand the terminology.  However, memorizing definitions without knowing how to translate those definitions into real world terms, does not help you learn what it is you want to know.  Let's see if I can clear up any
difficulties you may have with the Greeks.

First: Choosing software is personal. I have not found anything I like – at least nothing that is available at no cost.  I don't require complex software, and look at the cost-free alternatives.  For my needs, my broker's offering is good enough.

Now on to the important discussion.

***

I'm sure you understand that each option has certain properties.  For example, you know that a call option has positive delta.  In the options world, each of those properties is represented by a Greek letter (ignore the fact that vega is not from the Greek alphabet). 

Collectively those characteristics of an option are knows as 'the Greeks.'

What purpose do those Greeks serve and why should you care?  The Greeks are used to quantify (in terms of dollars gained or lost) the estimated risk and reward that you will realize for a specific option, or group of options, if certain market events occur. Because you must understand how much you can make – and more importantly, how much you can lose – if the stock moves 5 points, or if three weeks pass, or if the implied volatility increases by 4 points, it's necessary to pay attention to the Greeks.  They allow you to make a very good estimate of just how much money is on the line at all times.

Position Delta

That 'group' of options may be a simple spread, such as a calendar spread or an iron condor.

However, the group of options can include more individual options, such as the entire collection of options in your portfolio.  Using different words, those are all the options that comprise your option POSITION.   Thus "Pos. Delta" represents your 'position delta' or the sum of the individual deltas associated with each of the options in your entire position.

Your position delta is calculated by adding the delta of each option you own and subtracting the delta of each option you are short (i.e., sold).  If you own 10 RGTO Dec 80/90 call spreads, your position delta = 10 x the delta of the 80 call, minus 10 x the delta of the 90 call.

**Remember that calls have positive delta and puts have negative delta.  Thus, when you sell puts, you subtract a negative number, and position delta increases.  When you buy puts, position delta decreases.

What's the point of knowing position delta, or any other Greek, such as position gamma or position vega?  As mentioned, the Greeks provide a good estimate of risk (and reward).  In your example, the message to be derived from: position delta = -59 is: 

If the underlying asset moves higher by one point you can anticipate earning that number of dollars.  In this case that is -$59. In other words, a loss.

Instead of getting confused by positive and negative numbers, look at it this way:  If you have positive delta, you are 'long' and should profit when the underlying rises.  When you have negative delta, you are 'short' and should profit when the underlying falls.

Keep in mind:  Each Greek is merely an estimate.  The market does not 'promise' to deliver a $59 profit if the stock declines by one point.  Other Greeks are in play, and sometimes the effects are additive and sometimes they offset each other (more on that in Part II).  

Repeated for clarification:  The Greeks don't do anything.  They don't make money.  They don't make positions risky.  Greeks allow you to measure risk.  the Greeks allow you to measure potential gains and losses.  They serve no other purpose.

When you measure risk, you have a choice.  You may live with the risk, or you may hedge that risk.  That's why the Greeks are essential for risk management.  When you measure a risk factor (delta, time decay, etc,) you can hedge, or reduce, that risk.  You can ignore the risk or offset all or part of that risk. 

When you trade stock, if you believe you are too long and uncomfortable with the risk, all you can do is sell some shares.

When you trade options, there are many reasonable alternatives to get 'less long.'  One choice is to sell positive deltas or by buy negative deltas.  And that does not mean you must buy or sell calls or puts.  You can hedge (adjust) the position (or portfolio) with any combination of options, including a kite spread.  Obviously some choices are more efficient to trade than others, but knowing how to hedge a position is one of those matters you learn from experience or by reading Options for Rookies.

When you understand how position Greeks translate into real money, you are well-placed to make important risk management decisions.  When the definitions of the various terms are merely a blur, you cannot function efficiently.

to be continued

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