Delta: Breaking Down the First of the Greeks
Hey guys, I've seen a few threads on options trading and how important the Greeks are to your overall options trade. I found a great read courtesy of OptionsHouse that breaks down Delta for those that are interested.
Delta is a numerical value that describes an option in several interesting and useful ways, such as how much the option’s price should move for a $1 move in the underlying stock, how much the option is almost exactly like its stock, and what the probability is of the option being in-the-money by expiration.
A short definition of delta would be the sensitivity of an option’s price to changes in the underlying price. A shorter definition would be the speed of the option. If an option has a delta of 0.500, you can think of this as 50% and it means that if the underlying stock moves $1 (higher or lower), the option price will move only 50 cents (again, higher or lower).
The option pricing model assigns a probability to every option that quantifies the likelihood of that option finishing in-the-money (ITM). This number is the delta, and it changes dynamically as underlying prices change and time passes. The number produced by the pricing model is between 0.000 and 0.999, and traders speak of 0.103 as a “10-delta” and 0.591 as a “60-delta.”
How to Use Delta to Gage Option Buying vs. Selling
Some traders may use changes in delta to figure out if options are being bought or sold. Since option markets are so liquid and competitive, option prices tend to move in lock-step during the trading day with their stocks. So you would expect all “30-delta” options to move about 30 cents for every $1 move in the underlying stock. A $1 up move would have the calls up 30 cents and the puts down 30 cents, and vice versa for a $1 move lower in the stock.
What if the stock moved $1 higher and the 30-delta calls only moved 15 cents higher? Someone was probably selling those calls (trading them on or near the bid) and the market makers were perfectly willing to let them do so. What if the stock moved $1 lower and the 30-delta puts moved 50 cents higher? It’s likely that someone was buying those puts (at or near the ask price) because they moved far higher in price than their delta would dictate was fair value.
Three Ways to Think About Delta That Make It Such a Great Tool
Here’s a handy reference guide to delta to help you remember its power…
1. Delta is the rate of change of the option relative to its underlying stock—in essence, the speed of the option.
2. Delta is the probability the option will finish in-the-money—i.e., how likely is it the option will end up trading for parity because it is virtually equal to a position in the stock from the strike price?
3. Delta is the “hedge ratio” or equivalence to the underlying stock—i.e., it tells you how much stock you need to buy or sell to exactly hedge an option position.
Awesome, thanks for the read.
Awesome, thanks for the read.
Take out point 2 in the
Take out point 2 in the interpretation of delta. Other than that its a good read.
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^I believe that from a purely
^I believe that from a purely theoretical perspective, point 2 is correct.
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Great post - looking forward
Great post - looking forward to the series. As a PE investor, the more technical aspects of option trading have flown a bit under my radar, but I've always regretted not taking that derivatives class in college. SB for you, with more promised for the upcoming posts. I also front paged it.
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Nice. I was thinking of doing
Nice. I was thinking of doing a series explaining the Greeks, but you beat me too it. For that, I owe you a debt of gratitude, lol.
BSB... This is an excelent
BSB... This is an excelent piece. I'm looking forward to the rest. Good stuff... I wish they taught me the Greeks like this when I started instead of trial by fire.
delta is not the probability
delta is not the probability of the option finishing in the money. it's often close enough, but that is not correct. there are exotics which can have deltas far higher than 100%
alexpasch wrote: ^I believe
^I believe that from a purely theoretical perspective, point 2 is correct.
No it is not. There was a whole discussion on this before.
I'm looking forward to discussing GoV and Vanna.
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Good post, makes me want to
Good post, makes me want to whip out my John Hull text.
SB for you :)
You have a really clear style
You have a really clear style of writing which makes this easy to understand. Thanks, look forward to the rest of the series.
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Good stuff, let the Greeks
Good stuff, let the Greeks keep on cominnn!
Revsly wrote: alexpasch
^I believe that from a purely theoretical perspective, point 2 is correct.
No it is not. There was a whole discussion on this before.
I'm looking forward to discussing GoV and Vanna.
I said "from a purely theoretical perspective", so a plain vanilla B-S option (since someone else mentioned exotics). I did not state that that was the case in reality. I believe that, in theory, it is the probability of finishing in the money. If you could link to the discussion you refer to that would be most helpful.
B-S is very theoretical and beautiful from a mathematical perspective. Since delta is synonymous with how many shares of the underlying you own, it makes sense to me, intuitively, that the number of shares you own is equivalent to the contract size (i.e. 100 for equity options) times the probability of it finishing in the money as of that precise moment.
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alexpasch wrote: Revsly
^I believe that from a purely theoretical perspective, point 2 is correct.
No it is not. There was a whole discussion on this before.
I'm looking forward to discussing GoV and Vanna.
I said "from a purely theoretical perspective", so a plain vanilla B-S option (since someone else mentioned exotics). I did not state that that was the case in reality. I believe that, in theory, it is the probability of finishing in the money. If you could link to the discussion you refer to that would be most helpful.
B-S is very theoretical and beautiful from a mathematical perspective. Since delta is synonymous with how many shares of the underlying you own, it makes sense to me, intuitively, that the number of shares you own is equivalent to the contract size (i.e. 100 for equity options) times the probability of it finishing in the money as of that precise moment.
Revsly is correct. Go search dervistrading's old post...
From a purely theoretical perspective, Delta a.k.a N(d1) is NOT the likelihood that option finishs in the money under risk neutral measure. N(d1) is, only under stock-numeraire measure, which is used in building efficient lattice-based option pricing models where the risk-free rate and volatility of the stock price are not constant.
In reality, no one knows the probability that option finishes in the money. The volatility is not constant, the interest rate may not be constant during the life of the option. The distribution of the stock return is not log normal. there are transaction cost... the list goes on...
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As an options amateur, I had
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alexpasch][quote=Revsly
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Two things: 1. Since delta's
Delta is a shitty American
Where I unload on Twits and take verbal S***s
Nevermind the relevance about
Black-Scholes: the wrong
edtkh, please just go away
ArbitRAGE. wrote: As an
^^^ This doesn't have
laudrup wrote: edtkh, please
edtkh wrote: Was I addressing
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derivstrading wrote: Actually
edtkh wrote: Actually, you
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derivstrading wrote: Wow you
How do you not understand
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derivstrading wrote: How do
This was a really clearly