Friday, June 5, 2009

Clash of the Greeks

As you progress as an option trader becoming familiar with the nuances of option pricing & theory can be quite advantageous. One such nuance I want to highlight today is the relationship between Gamma and Theta. If you're not already up to snuff with Theta and Gamma basics you can review my overviews here & here.

Gamma and Theta have an inverse relationship.

Positive gamma positions are negative theta positions. For example, long calls/puts or long straddles/strangles. They all lose money as time passes (-Theta), while seeking a big move in the underlying stock (+Gamma).

We could say that when we enter trades that seek volatility, i.e. want the stock to move a lot or +gamma, we always have to fight time decay (-theta). Conversely when we enter trades that profit from time decay (+theta), we constantly have to fight the stock moving too much (-gamma). Hence, there is a constant clash between Gamma and Theta.

We can consider the aforementioned positive gamma trades a race between movement (realized volatility) and time decay. The underlying stock must move enough (+gamma) so that my long options are ITM a sufficient amount (have enough intrinsic value) to offset whatever time decay (-theta) occurs. Suppose I enter a long June straddle on AAPL which is currently trading around $145. There are 14 days to June expiration.

Long Jun 145 Call for $4.45
Long Jun 145 Put for $5.30

The net debit of the trade comes out to be $9.75. Because both options are ATM, at trade inception the entire $9.75 consists of extrinsic value. Remember, at expiration options have no extrinsic value left. Thus, to break even I need to accumulate at least $9.75 of intrinsic value in either the call or put option by expiration. This would require the stock to rise or fall at least $9.75.

The upside break even at expiration is $154.75 (145 + 9.75).
The downside break even at expiration is $135.25 (145 - 9.75).

One of the easiest ways for illustrating the relationship between Gamma and Theta is via a risk graph. As a direct result of time decay (-theta), AAPL has to move more and more as we approach expiration for the position to be profitable. In other words, the upper and lower break even points for this straddle widen as expiration approaches. Consider the following risk graphs (click to enlarge):

14 days to expiration risk graph:
Break even points = $142, $147

7 days to expiration risk graph:
Break even points = $137, $153

Expiration risk graph:
Break even points = $135.25, $154.75

As you can see, as expiration approaches, the break evens widen. This is a direct result of time decay. Thus, the longer we stay in this positive gamma trade, the more the stock must move for us to be profitable.

Here is one other graph to consider. This displays the risk graph juxtaposed with the price chart. I've drawn horizontal lines to illustrate the range that AAPL must trade out of to be profitable in each time frame. Blue lines = 14 days to expiry. Red lines = 7 days to expiry. Black lines = expiration. For simplicity purposes and to better illustrate the relationship between Gamma and Theta, I assumed there were not any changes in implied volatility throughout the trade. In reality a change in IV will influence the break evens of a straddle trade.

In our next installment we'll discuss examples of negative gamma, positive theta trades.

19 comments:

Henry Bee said...

Hi Tyler, very nice post! Which tool do you use to generate the nice screenshots?

Tyler Craig said...

Thanks Henry,

The charting/analytical software I use to produce the risk graphs is the Edutrader. www.edutradersoftware.com
I use SnagIt - www.snagit.com to take a snapshot of the risk graphs and edit them.

Jignesh said...

hi am studying Volatility index, on one site i found that volatility of current month roll to next month or far month before 8 days of expirey is it correct or any other methodology to calculate volatility plz guide me

Tyler Craig said...

Jignesh,

Keep in mind that each option has its own individual implied volatility which can usually be accessed by viewing an option chain with your charting platform or broker.

To view an average of all option implied vols, I personally use the IV Index on Ivolatility.com. Here's a link which provides the details of its calculation: http://www.ivolatility.com/news.j?nid=114&x=19&y=10

I'm not sure if the method you're describing is that of Ivolatility, but if I ever find a discrepancy between some other source and ivolatility, I usually default to Ivolatility's reading as they seem to be the voice of authority in the volatility arena.

Happy Trading-

Jignesh said...

hi thanks for your reply
i want to know one more thing while calculating Delta as per formula change in option price with change in underlying assets so if nifty moves 10 points up then premium increqase by 5 means deltacomes to 0.5 but in the reality some difference is their so plz guide me how to calculte on the basis of only nifty, volatility of options and nifty


bye thanks

Tyler Craig said...

First off, I'm assuming "nifty" is a stock?

Just to clarify, you're asking how to calculate delta only knowing that the stock went up $10 and the option went up $5?

As you mention the "average delta" for that $10 move was .5, but that doesn't mean it's .5 right now. The option could be deep in the money and have a current delta of 1. Either I'm misunderstanding the question or you're making this way to hard. I don't have a formula for calculating delta, nor do I or anyone else need one. If I want to know what the delta is I look at an options chain and it tells me.

So why not just look at an option chain on "nifty" and check the current delta on whatever option you're referring to?

Jignesh said...

hi
NIfty is futue (underlying asstets) and we r hedging so calculation of delta is helpful for me we r useing option chain but some other technique so u can use orally i know its very difficult understand my question

Tyler Craig said...

Gotcha. I know of no other way to calculate delta other than looking at it on an option change or brokerage platform.

Jignesh said...

hi
can u tell me the some site add for learn More on Volatility Index

So its helpful 4 me


Thanks

Tyler Craig said...

Jignesh,

Bill Luby at vixandmore.blogspot.com has a ton of solid information on the VIX. Adam Warner at dailyoptionsreport.com is also a great resource for volatility information. Both guys really know their stuff.

Did you get my e-mail response to the spreadsheet you sent?

Jignesh said...

hi

can u help me for Put call ratio and how to calclulate and what is sign of Bearish or bullish mkt
(1.06 to bullish and below 1 and above 2 is bearish)

this no i will get from net i dont know exactley plz help me out
and i got one site on Volatilty plz visit learningmarkets.com

bye
tc

Tyler Craig said...

JIgnesh,

I don't use put/call ratio so I'm not very familiar with how it's used or calculated. I'll take a look at the site

Jignesh said...

hi Wish u HAPPY NEW YEAR
thanks for your all support.
i heard about options pane?

plz reply me

bye tc

Jignesh said...

sorry its option pain

Tyler Craig said...

Jignesh,

I've heard a bit about options pain, but have never done much research on it or used it in my own trading. As such, I can't really comment on its accuracy or whether it's worth using. I believe Adam over at Daily Options Report mentioned he doesn't really subscribe to the max pain theory, so that's good enough for me.

Jignesh said...

thanks for your reply today i found one software for option thats oprtionoracle i dont how to use it but they are providing online chart for option pain ,PCR ,oi, volatily etc.

if u have nay idea for this software plz tell me how to use it

Tyler Craig said...

Jignesh,

I've never used them before. I use EduTrader for most of my charting and risk graphs. I also use Think or Swim on occasion as well as livevolpro.

Jignesh said...

hi

software suggestion given by it can be use for indian stock market?


thx

QUALITY STOCKS UNDER 5 DOLLARS said...

More of the same.