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

Hello my name is patrick boyle welcome to my video today we’re going to learn about delta hedging a call option so delta hedging i’ve got a whole video on what delta is if you want to watch that and i have a whole playlist on the greek so i’ll link to both of those but delta hedging refers to trading in the underlying asset alongside your options position with

The goal of remaining delta-neutral so in our example we’re going to say that we are long a call option that has a delta of 0.5 so if this call option covers a hundred shares of the underlying that means that we have a risk exposure as if we were long 50 shares by owning this call option so suppose our trader is worried about the price of the underlying falling in

Value which would mean that our call option would fall in value but they might sell 50 shares of the underlying against this option in order to be dealt a neutral now once we’re delta-neutral for small rises and falls in the price of the underlying we wouldn’t expect to really have any really large gains or losses on our portfolio where we’re henge so the graphic

Up on the screen right now is showing you long a call option short 0.5 shares times the number of shares that’s covered by that call options are short 50 shares and that gets us delta-neutral this is an at the money call so the strike and the spotter at the same level so anyhow no sooner have we hedged ourselves than the price of the underlying rises so the first

Thing that we do the first thing we always do when we’re delta hedging is just recalculate our delta so we calculate our delta again and we now find that this new price of the underlined the delta is now 0.6 now we’re short fifty shares but we need to be now short sixty shares so what our trader does is they sell another ten shares and once again we’re dealt

A neutral so this is all we’re doing as the price is rising we’re gonna find ourselves selling shares and as the price is falling we’re gonna find ourselves buying them back so let’s see what happens next so the next next thing that happens is that the price falls and in fact it falls right back to where it started its back to to the strike price of the auction

Then we calculate our delta and once again we find that our delta is 0.5 so in order to be hedged we need at this point to be 0.5 times a hundred shares of the underlying short so what we have to do is we have to buy back 10 shares of the underlying in order to be delta-neutral again so we do that and that’s gonna continue on as the price rises we’re going to be

Selling as the price falls we’re gonna be buying and this is just a the natural thing that happens because that’s how the delta is going to change for this option so let’s think a little bit about this now we’ll imagine if not very much time passed we’ll imagine this rise and fall in the price of the underlying happened in a couple of minutes and what happened for

Us well we got delta-neutral and as soon as the price rose we found ourselves selling 10 shares and when the price fell back to where it started we bought those 10 shares back so overall our option is actually going to be worth about the same right because it’s a 0.5 delta it’s an add the money call option it’s at the same price it was out when we initiated this

Position no real time has passed so we’ll neither have made no lost money on our option but interestingly enough we seem to have made a little money with our hedging there right because when the price rose we saw sold 10 shares and when the price fell we bought those 10 shares back now we won’t have made a fortune on that but we’ll have made a little bit of money

And that’s kind of an interesting thing so let’s look at what happens next so the next thing that happens is the price of d on their line falls and we recalculate our delta once again that’s what we’re we’re doing and today’s class is recalculating tells us a lot so we recalculate our delta and now the delta is 0.4 so let’s think what we have to do well we’re we’re

Short 50 shares of d on their line but we’re smen to be short point four times a hundred so we’re actually only meant to be short 40 shares of the underline so what we have to do is buy buy 10 shares of our short position in order now to have the short position of 40 shares so we’re now short for these years once again what happens next the price rises okay it goes

Back to where we started and so what do we have to do we just bought 10 shares and it goes back to where it started the deltas back and at 0.5 so we have to sell that additional 10 shares so as you can see when it rises we’re selling shares and when it falls were buying shares and when it goes back to the center we’re back to around this 50 share thing so it should

Start to be obvious to you that all of this hedging it’s making us little drips and drops of money so why is that happening and why is that interesting well positions only remain delta hedged for short periods of time and when the price stays within a fairly tight range each time the underlying share price moves our trader has to rebalance the shares hedge in order

Remain delta-neutral now options are an aggregation of various risks we’ve got we’re exposed to movements in the price of the underlying were exposed to implied volatility were exposed to interest rate we’re exposed to imply dividends a bunch of other little risks like that but you know our main risk with an option initially is we’re exposed to changes in the price

Of the underlying now when we’re delta hedging we’ve hedged out that risk so we’re no longer really exposed to that but we do have to rebalance whenever the price moves so what that means is that we’re exposed to volatility the more the underlying moves the more we have to hedge now as you can see in this example the more it moves the more we hedge and when we’re

Hedging we seem to be making money there seem to be little profits being generated by this edge and this is because we are long a call option and when you’re long a call option or when you’re long any option if you’re long a call or longer foot you’re long volatility so we are long volatility and thus the more the price of the underlying moves that means the more

Volatility underlying is the more we find ourselves having to hedge and the more that we have to hedge the more money we’re generating in in our hedging profits but from from selling high and buying low or from buying low and selling high so that’s something that’s happening now is this is this just totally free profit or we just people to do this and profit for

For nothing no because we of course paid for this option right so we paid premium for this option so we wrote a check and bought this option ok and the amount of money we paid in premium is of course initially at least greater than email you were making backward are hedging now should the underlying move by the amount that was implied in the implied volatility when

We bought we would probably make back all of the money that we’ve spent in premium in our volatility hedging if it moved less than expected where we were long volatility and it didn’t move enough and therefore we would lose money or at least we wouldn’t make back all the premium we spend and of course if it moves more than than was implied in the implied volatility

Well then our hedging is making more money than we spent on premium so that is what it means to be trading volatility we are long volatility and we’re making money the more volatility underlying is because every time it moves a reasonable amount we get to hedge and when we hedge it seems to make us a little bit of money so that is delta hedging that’s kind of how

We try and extract profits from delta hedging so if you trade options only to take a view on the markets implied volatility levels you must delt ahead so that’s why we do this is that our goal with this option was not to trade based upon our belief that the underlying would move to a certain level we weren’t trading directionally we’re putting on a delta-neutral

Trade with the goal of making money based on the volatility so in order to do that we have to get rid of our exposure to the price of the underlying by hedging and then once we’re done delta hedging we have to periodically rehash in order to flatten out our exposure if we’re long volatility will make money in that hedging and if we’re short volatility we will

Lose money in that hedging so let’s move on to another example we’re gonna we’ve just looked at a long volatility example where we were long a call option let’s now look at a delta-neutral a trader and work on our volatility traders will call them i’m working compare their trading to the trading of a person who is a directional trader now we know how a directional

Trader makes money they buy an option and if the price moves in their favor they make money and if it doesn’t they don’t make money or did they lose money on based on the premium they spend but let’s see how a volatility trader is going to make money here so we’ve got our two traders we’ve got a directional trader and a graphics i’m going to call that person dt

For a directional trader and then we’ve got our volatility trader that will call vt4 volatility trader and so our directional trader buys an option and our volatility trader sells that option to them now of course our volatility trader will only sell that option they don’t have a view on the direction but they do have a view on the volatility so our volatility

Trader is only going to sell that option if they feel they’ll be adequately compensated in terms of implied volatility so they’ll only sell what they consider richly priced options and they’ll then delta hedge that until maturity hoping to earn a profit in the manner we described earlier so let’s look at how each party could make or lose money in this example so

Our directional trader dt buys a thousand puts and is bearish right if you buy a put you’re hoping at least if you’re a directional trader and you buy put you’re hoping that the price of the underlying will fall and did you make money from that fall in the price of the underlying our directional trader is bearish our volatility trader sells those puts – our directional

Trader but they don’t actually have an opinion on the direction they just have an opinion on the volatility they’re neutral on the price the underlined so they are going to quickly calculate their delta and they’re gonna hedge that out so in this example our directional traders long a thousand puts will say they spent a dollar on them our volatility trader short

Those tiles inputs they calculate the delta and find that it is minus 0.3 and so they sell 300 shares short in order to hedge their exposure to the price of the underlying so and in our example here the underlying is trading at 20 when all of these positions were put on so let’s see what happens next well the first thing that happens is the price of the underlying

Falls now our directional trader of course is happy about this right because they they bought a put option they profit from a fall in the price of the underlying so they’re happy to see the price of the underlying fall and they’re gonna make some money based upon that now a volatility trader is hedged so they they don’t necessarily care about this and for small

Moves you know this is a 1% fall you know roughly speaking our volatility trader will neither have gained nor lost money on the portfolio now they’ll of course have lost money on the option but they’ll have made the same amount of money roughly speaking on the 300 shares that they were short now what they have to do next is what our volatility traders are always

Doing they have to recalculate their delta ok so a volatility trader quickly recalculates their delta and they find that now with this lower price the delta of this put option is minus 0.4 now they’re only short 300 shares but they should now be short 400 shares so they’re gonna have to sell an additional hundred shares in order to be hedged if they don’t do this

They are exposed to the directional risk the price risk of the the underlying stock so they’re gonna do this and they’re hedged again so what happens next well the price of the underlying now right by two percent so that’s that’s a you know decent rise in the price of the underlying unfortunately for a directional trader it’s a rise and they were longer put options

So they’re losing money on this move our volatility trader is hedged but of course you know this is a sizable enough move so the next step for our volatility trader is to recalculate their delta so that they can adjust their hedge and make sure that they are still adequately hedged once because if this move were to continue on they could start losing money so a

Volatility trader can calculates the the delta of this option and now it is minus 0.2 so a volatility trader of course has to hedge and so they buy back 200 shares of their short and now they are sure 200 shares right because before they were short four hundred they bought back 200 now they’re just short two hundred shares so as you can see here the price us the

Price of the underlying is moving our volatility trailer isn’t really making or losing significant sums in the overall portfolio but they they do have to rehash now you’ll notice a difference in this read hedging to the retention that was happening the last time because if we look back here we see that when we started out with a delta point three and we were short

Three hundred shares and the price the price fell we had to sell more and when the price rose we had to buy them back so in this case we seem to always be selling low and buying high which is you know not making less money it’s costing us money we’re losing money so why why are we losing money every time we hedge now when we were making money ever time we hedged

In a prior example will the reason for this is because in the prior example we were long volatility and so our hedging made us back the money we expected premium in this example we are short volatility we sold those put options so as the price moves the more volatile that is the more it moves the more we have to hedge and the more we hedge the more money we lose

And so basically what’s happening is we received premium to begin with as the price moves around we’re losing money and if the price of down the line moves around in line with the implied volatility in line with market expected expectations we would lose the entire amount of money in our hedging that we have brought in in the form of option premium so hopefully

At this point you’re starting to see how delta hedging works how how dynamic hedging works i guess and how how option traders think about think about volatility and think about trading so we’re gonna do another another video tomorrow which will just call volatility trading where i’ll try and even spell this out in a much more graphic maybe simpler example but

Hopefully hopefully you guys understand this if you’re interested in following along in the text well the textbook that we’re using is called training and pricing financial derivatives it’s a textbook that i wrote to offer for this course and there’s a link to it in the description below and in one of my videos from i believe two days ago a link to that there is

A way for you to win a copy of that textbook if if you’re interested so anyhow have a great day and i’ll be back with another video tomorrow bye

Transcribed from video

Volatility Trading – Call and Put Options – Trading Tutorial By Patrick Boyle