Option Question about Delta
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Most make it complicated, I think on purpose. Just reading through this thread confirms that. Arguments all day long, who cares what others "think" just put it on if you are so "right" .
Oh, I have no solid stats on this but often I found making money going against option traders with big positions was nice. They always seem to get the "timing" of most trades wrong. Always great at math but terrible at reading the world around them. Best to wait to see a potfolio in trouble, then and only then contemplate taking a position in the direction of what the original meaning or final end of their option position was, usually made good with little risk. Bad golfers as well, maybe timing issues ?
I use delta when I trade options to calculate position size slightly different than the hedge ratio.
The definition of delta is how much the option moves for a $1 move in the underlying.
If delta is 0.5, and your stock is $100, that option will move 50 cents if the underlying moves up or down $1.
You can then use delta to compute the right number of contracts to put your trade based on this leverage for a target level of return.
If the option was worth $2 to start and your delta was 0.5 and the underlying was $100, your profit percentage wise goes from 2 to 2.5 or 2.5/2=1.25-1=25% change from a $1 move in the underlying. If you were trying to make a 25% return on your options from the $2 level, you would buy contracts equivalent to your allocation on the trade to get that level of return, and your leverage factor from a $1 1% move is 25:1. Knowing that, you'll choose a hedge ratio or number of contracts to trade based on the delta hedge ratio and delta itself. To make a 50% return from this the underlying would have to move $2 and keep relatively the same level of implied volatility.
Say delta is 0.75 in our $100 underlying. A $1 move is 1%, and whatever 0.75 divided by the option price is is the leverage factor, and you can use this to calculate how many contracts to trade for a given set of return or leverage factor.
Delta does not provide a probability. It only is an estimate from implied vol what the option will do for a $1 change in the underlying.
The definition of delta is how much the option moves for a $1 move in the underlying.
If delta is 0.5, and your stock is $100, that option will move 50 cents if the underlying moves up or down $1.
You can then use delta to compute the right number of contracts to put your trade based on this leverage for a target level of return.
If the option was worth $2 to start and your delta was 0.5 and the underlying was $100, your profit percentage wise goes from 2 to 2.5 or 2.5/2=1.25-1=25% change from a $1 move in the underlying. If you were trying to make a 25% return on your options from the $2 level, you would buy contracts equivalent to your allocation on the trade to get that level of return, and your leverage factor from a $1 1% move is 25:1. Knowing that, you'll choose a hedge ratio or number of contracts to trade based on the delta hedge ratio and delta itself. To make a 50% return from this the underlying would have to move $2 and keep relatively the same level of implied volatility.
Say delta is 0.75 in our $100 underlying. A $1 move is 1%, and whatever 0.75 divided by the option price is is the leverage factor, and you can use this to calculate how many contracts to trade for a given set of return or leverage factor.
Delta does not provide a probability. It only is an estimate from implied vol what the option will do for a $1 change in the underlying.
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How can you say there is no relationship between delta and the probability of the option being in the money at expiration? The deeper ITM, the higher the delta. The more OTM, the lower the delta. Higher delta, higher probability, lower delta, lower probability._
Take the same priced stock, and lower the IV. You'll notice the ITM options now have a higher delta, than before, because there is now an even higher chance of staying ITM. (less of an expected chance of movement) with the lower IV, you will notice the OTM options have lower deltas, because of the lower expected movements, there is now a lower chance of being ITM at expiration.
Now, increase the IV. You'll see the opposite. There is more uncertainty. The ITM options delta goes down, the OTM options delta goes up._
One more. Increase time to expiration. The probability of anything occurring increases, so again, OTM option's delta increase, ITM decrease to compensate.
As i have said, The delta is also used as an estimated probability of the likely hood of being in the money._
Take the same priced stock, and lower the IV. You'll notice the ITM options now have a higher delta, than before, because there is now an even higher chance of staying ITM. (less of an expected chance of movement) with the lower IV, you will notice the OTM options have lower deltas, because of the lower expected movements, there is now a lower chance of being ITM at expiration.
Now, increase the IV. You'll see the opposite. There is more uncertainty. The ITM options delta goes down, the OTM options delta goes up._
One more. Increase time to expiration. The probability of anything occurring increases, so again, OTM option's delta increase, ITM decrease to compensate.
As i have said, The delta is also used as an estimated probability of the likely hood of being in the money._
Now that we have our true resident options experts, bwol and tj, weighing in on the subject, it's officially hopeless.
Delta's definition is the dollar based magnitude of the move of the option for a $1 move in the underlying.
Knowing that, when you look at the percentage change the option will move for the percentage change a $1 move would be in the underlying you can find the best level of leverage to use to find the right risk/reward ratio.
Delta has nothing to do with probabilities of ITM, OTM, or ATM.
Again, delta is the estimated change that the option will make for a $1 change in the underlying. Equating those will give you your hedge ratio, but will also estimate how many contracts you would have to buy if you were trying to find a target level of return or maximum level of risk relative to the percentage change a $1 move would imply in the subsequent percentage change of the option.
Knowing that, when you look at the percentage change the option will move for the percentage change a $1 move would be in the underlying you can find the best level of leverage to use to find the right risk/reward ratio.
Delta has nothing to do with probabilities of ITM, OTM, or ATM.
Again, delta is the estimated change that the option will make for a $1 change in the underlying. Equating those will give you your hedge ratio, but will also estimate how many contracts you would have to buy if you were trying to find a target level of return or maximum level of risk relative to the percentage change a $1 move would imply in the subsequent percentage change of the option.
You may be right Martin.
My point was just to say that delta is not a probability at all, and I thought that could be helpful for newbies.
Since I said that, 'Bronsky Beat's people who can't stay out of a thread tried to tell us we were morons, just for fun. Great ! You know, those guys who always were former market makers ( for 25 years, bla bla bla....). Who the f**k wasn't a former market maker for 25 years on ET ? cmon !
Then, Atticus came in ! My man.
We missed the "dvega/dgamma....bla bla bla ...convexity...blablabla" 's shit and that's pretty a good thing. Of course we got "bullshit arguments", "equation", "keep editing your posts",.... bla bla bla...., but nothing wrong with that. He can't resist.
The marvellous point was done by sle : " as an experienced exotics book runner" ha ha ha. That's the joke ! My man, you don't even understand BS and basic math and you're trying to tell people you're an experienced exotic options trader. ROTFMAO, ha ha ha. You made our week end. Thank you !
Please, copy and past your post about probabilities on NP, I bet you're gonna be famous !
Ok, you've convinced us that you are a big swinging dick and that I am actually a teenager posting on ET from my moms house.
However, the points I am trying to make for a noob (and I will reiterate them for you):
(1) Delta of a vanilla option is a reasonable approximation of probability being ITM at expiry, as long as volatility/carry are low enough and option expiry short enough (e.g. 3m S&P 500 options in a normal environment).
(2) Assuming the limitations above, for most trading applications of "probability" (for example, calculating relative value of the longer-dated skew via probability-adjusted dvega/dspot), delta and gammaP are sufficient.
Do you agree or do you not agree? Also, do you really believe that I do not understand the impact of volatility and carry on the delta-neutral strike, given that in the very first post I said "carry/ito adjusted probability"?
Could you redo your anal ysis for ATM strike, distinguishing what moves from what does not move?
Sorry If Iâve been rude, « big swinging dick », « bullshit », ....were not part of my words, but I will improve myself.
Let me be clear :
1) the real probability of being in the money at expiry just canât be known. If it were, all traders would tell you that a quite simple statistical arbitrage would make you a lot of money.
The only probabilities that are known using options are risk neutral probabilities which assume that every asset has a drift that equals the cost of carry. Do you think itâs true, every asset has a drift that equals cost of carry ? I mean, really ?
You said « reasonable » : please be my guest â price it !
Well, you may say « it depends on what means « reasonable » to you ! ». Guys would know what an approximation means to you.
Okay, price it, here on ET !
Iâm sure that youâre aware that if risk neutral probabilities would equalize delta, an ATMF call would be worth zero ! Do you really think itâs true ? I mean, in the real world ?
What an approximation !
Hence, do you really think it's a tool to give to newbies ?
2) You want to talk about exotic options, be my guest !
Where on earth did you see someone talking about gammaP on this thread ? Please, quote them !
Delta and gammaP are enough for most trading applications of « probabilities » : You got to be kidding ! cmon, it's winter sales, but you !
Nothing wrong with you sle. But « Iâm an experienced exotics book runner » is just no response to me.
Let me be clear :
1) the real probability of being in the money at expiry just canât be known. If it were, all traders would tell you that a quite simple statistical arbitrage would make you a lot of money.
The only probabilities that are known using options are risk neutral probabilities which assume that every asset has a drift that equals the cost of carry. Do you think itâs true, every asset has a drift that equals cost of carry ? I mean, really ?
You said « reasonable » : please be my guest â price it !
Well, you may say « it depends on what means « reasonable » to you ! ». Guys would know what an approximation means to you.
Okay, price it, here on ET !
Iâm sure that youâre aware that if risk neutral probabilities would equalize delta, an ATMF call would be worth zero ! Do you really think itâs true ? I mean, in the real world ?
What an approximation !
Hence, do you really think it's a tool to give to newbies ?
2) You want to talk about exotic options, be my guest !
Where on earth did you see someone talking about gammaP on this thread ? Please, quote them !
Delta and gammaP are enough for most trading applications of « probabilities » : You got to be kidding ! cmon, it's winter sales, but you !
Nothing wrong with you sle. But « Iâm an experienced exotics book runner » is just no response to me.