What Is Options Delta? The Options Greeks

These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link.

Hello youtube welcome back this video is the second video in a series on the greeks for options investors in this video we’re going to be learning about delta which is one of the most important greeks delta is the amount that the options price changes for one unit change in the price of the underlying so what we’re trying to work out here is when we look at our

Option we’re saying how much will it change when the underlying moves by will say 1% now to a lot of people they think well because it’s an option we’ll say if it’s a call option it is the right but not the obligation to buy the underlying at a pre agreed price which is our strike price and so they would look at that and say well if the price of the underlying

Goes up 1% the option will move up by 1% but that’s not actually the case what we find is that because our option has that payoff diagram like we’ve seen in some of our earlier videos the option actually doesn’t move in a linear manner with the price of the underlying instead it moves slightly less and hopefully that makes a little bit of sense to you because it

Couldn’t actually move more than the price of the underlying because the right to buy something could never move up by more than the price of the thing that you have the right to buy right and so it can’t move up more than that and equally it has to have some relationship to it so delta is basically a mathematical description of that relationship so mathematically

Speaking delta is the first derivative of the options price with respect to the underlying it’s typically expressed in terms of the amount in options positions value will change for a 1 percent move in the price of the underlying now these estimates of the price change are only approximate so delta is an approximation and the reason for that is because it is a

Linear approximation of a curved function ok so an option actually has a curved payoff function and delta is linear summation of that so we can think of delta as of ratio comparing the change if the price of the underlying asset to the corresponding change in the price of the derivative so for example if a call option had a delta of 0.6 you’d expect the call to

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Rise by 60 cents for every $1 rise in the price of the underlying stock now delta can be viewed as well another way of thinking of it is the slope of the tangent line to the option value now the option value line is a curved line and so delta is the slope of that it’s once again as i said earlier a linear approximation the delta of a vanilla call option can only

Range between 0 and 1 and that’s you know as i explained earlier can’t move more than the underlying and it has to have some relationships so it’s somewhere between 0 and 1 now delta will be low at low spot prices relative to the strike of the option and high at high spot prices relative to the strike price of the underlying and have a little image of that up on

The screen now let’s think a little bit about that why would that be the case well let’s think about an option that is way way way way out of the money so we’ll say if there is an option with a strike price of 100 so you’ve the right but not the obligation to buy the underlying out $100 but let’s say the underlying is actually only trading at 50 cent’s right so

It has to go up an awful awful awful lot in order to for that option to sort of become activated and and in order for that option to seem likely to even pay off at all now should now that will be a cheap option because it’s so out of the money but should the price of the underlying double if it were to go from 50 cents to a dollar you wouldn’t actually expect the

Price of our option to double simply because for it to go from 50 cents all the way up to $100 is kind of far away and maybe a little bit on line klee and it’s not a whole lot more likely even though it’s doubled in value and is now at a dollar because it still needs to go up another 99 dollars before it even starts to look like it’s gonna be profitable so that is

A way out of the the money option and it’s delta is going to be quite low so if the underlying doubles and valued the option probably wouldn’t really move all that much in value now if we move in the opposite direction let’s think of a very deep in the money option so we’ll flip those numbers around entirely and we’ll say that the the underlying is trading out a

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Hundred dollars and there’s a call option with a strikes price of 50 cents on it well a call option with that’s that deep and the money almost starts to look like a futures contract because it would have to fall so so much in order to not have a payoff very much like just owning the underlying that in truth for a 1% change in the price of the underlying you you’d

Kind of expect that option to move 1% as well it’s it’s almost like owning the underlying so so that is how delta is going to change with the money nosov an option so more about delta delta is always positive for long calls and negative for long put options and then the opposite so if you’re long a call you’ll have a positive delta if you’re sure to call you’ll

Have a negative delta if you’re long a put you’ll have a negative delta and if you’re sure to put you’ll have a positive delta what that means is that the value of a call option will increase with a stock prices increase and the value of a put option will decrease if the stock price increases given a european call and put option for the same underlying strike price

And time to maturity so essentially identical options but one is a call one is a pod with no dividend yield the delta of the call minus the delta of the put will equal one this is due to put call parity a long call plus a short put replicates a forward which is a delta equal to one if the delta of a call is known to be 0.3 you can easily calculate the delta of the

Corresponding put at the same strike as follows 0.3 minus 1 equals minus 0.7 to calculate the delta of the corresponding call from the delta of a put you can simply add 1 to the put delta as follows- point 7 plus one equals 0.3 so that’s at let’s talk now about the intuition of delta options values change in a nonlinear manner with a complicated formula for precise

Calculations delta is just a quick way of determining at a given spot price how option values change for small movements in the price of the underlying over the next short period of time delta also tells you how long or short your portfolio is at a given point in time you can think of the delta of an option in terms of being long or short the underlying asset if

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You’re long one at the money call with a delta of 0.5 and that’s a call option that controls 100 shares of the underlying if it has a delta of 0.5 it’s an awful lot like being long 50 shares because if you think about it if the underlying goes up by 1% and our our option increases by half of that amount it’s kind of like owning half as many shares owning that bad

Option traders usually refer to a 0.6 delta call as a 60 delta call presenting the delta as a percentage of the total number of shares represented by the options contract this is useful as the option will for small price changes behave like the number of shares indicated by the delta for example if an american call option which covers a hundred shares on a given

Stock has a delta of 0.3 or 30% it will gain or lose value just like 30 of abc as the stock price experiences small price movements the total delta of a portfolio of options on the same underlying asset can be calculated by simply taking the sum of the deltas for each individual position since the delta of underlying asset is always warned a trader could delta

Hedge the entire position in the underlying by buying or shorting the number of shares indicated by the total portfolio delta this hedge will work for small movements in the price of the underlying for a short amount of time and not withstanding changes in other market conditions such as volatility and the risk-free rate to learn more about delta take a look at my

Next video which is coming out tomorrow on delta-neutral portfolios if you’ve made it this far in the video please hit the like button below and subscribe if you’d like to see more and also you can hit that bell button if you want to be notified in your emails please comment below if there’s any other topics that you’d like me to cover in these videos they’re all

Based on my book which is linked to in the description below and that’s all for now talk to you later bye

Transcribed from video
What Is Options Delta? The Options Greeks By Patrick Boyle

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