Welcome to today's Felix Life session, and the topic is going to be option mechanics.

My name is Thomas Crow. I'm head of financial product here at Financial Edge.

And, um, it's my pleasure to walk you through the session here today.

Um, and as always, uh, let's start with a very quick look at the agenda IE what to expect from this session here.

We're going to take a closer look at the, um, world of Financial options today, and that means we're going to introduce the, uh, option terminal, some of the main option terminology.

We're gonna refresh our knowledge on, uh, the general concepts of options and how they differ from Delta one Uhers.

We're gonna touch on things like the moneys of options.

We're gonna, uh, define the different exercise styles, and then we're gonna move and have a closer look at the premium of an option. And we're gonna do this, uh, in an intuitive way.

So while we mention Black sos, uh, there's not gonna be a detailed, uh, discussion of this, um, model, for example, uh, today.

Uh, and then towards the end, we will just start having a look at some, uh, common option strategies, mostly in the context to explain as to why people might actually use options.

In addition to, um, the other instruments that are available out there, let's get, um, into the content.

And as I said, we're gonna start with a refresher on options.

We're gonna, uh, talk a little bit about the terminology, and we're gonna also have a quick recap as to why there needs to be an option, um, premium.

And I think a fairly common definition of financial options, uh, is the one that you find here on the slide.

The, uh, financial option. Give the option buyer, uh, the right, uh, to buy an underlying asset. And then we're talking about a call option or the right to sell, uh, an underlying asset that we're talking about.

A put option. Um, and, um, not only do you have the right to buy or sell, but you also have the right to buy or sell at a predetermined level.

IE the strike price.

And this right, usually is limited in terms of time. There's a specified date until you have to exercise the right or make use of this, right? And if you don't do at that expiry date, we call the state, um, the latest, then the option will expire and, uh, you will not have any sort of economic benefit of that option anymore.

So, um, to put all those things in context here, quick practical example, you see at the bottom of the, uh, slide there that we're looking at the 12 months call option here, uh, it had a strike price of $105, meaning whoever buys that call has for the next 12 months, the right to buy that underlying asset at a price of 105 um, dollars.

And as it's an option trade, the buy off the option has to pay an option premium.

And this in this case was, uh, $7 and 90 cents.

What makes this option premium and the components we're gonna look at in more detail a couple of Minutes from now, but just let's, uh, fast forward 12 months.

Now look at this, um, option at expiry, and we're just gonna take a quick run through this p and l profile, this classic hockey stick that you, uh, will see when you look at options on a regular basis, um, fairly regularly.

So where does this line, uh, come from? What are the driving factors here? And we can, um, you know, identify one very important point here immediately.

And that's a level of $105 reason being, that is the strike of the option. That is where the biopsy option has the right to buy the asset at.

And at 105, in other words, assuming that in 12 months from now the underlying, uh, will trade at a spot price of 105, then you could argue there's no advantage in using the option. There's no disadvantage either.

So the buyer will be in different weather to exercise or not, because they have the right to buy the underlying at 105 strike price through the option, but they can also buy that same underlying at 105 in the spot market.

So the economic value of the option at that point will be exactly zero.

Why does a p and L have a negative, um, value here? Well, simply because remember, the option buyer has to pay the premium at the time they're buying the option usually.

So that was a $7 90, uh, outlay.

And that premium will not be recovered, right? That premium is the price you pay for buying the right, and when you don't use the right or you use the right, that premium is not gonna be, uh, repay to you.

So in case of our $105 scenario, what happens is the, uh, ops option will not have any economic value.

Uh, we paid $7 90 for it, we get nothing in return.

Hence, we have a $7 90 negative p and l impact, um, in, you know, to be 100% transparent.

Um, obviously here we've made a slight simplification because technically if you buy the option, um, and you pay $7 90 at the moment of trade, trade inception or two days later, um, then of course you need to fund this premium for the next 12 months.

So reality is depending on interest rates, the actual p and l might be no, no, will be, uh, a little bit higher in absolute terms from a negative 'cause the premium will grow in, you know, and we should have calculated the future value.

But you know, uh, you get the idea. Okay, so that's at 105.

Now, what if the price of the underlying is trading higher than 105 hundred spot market 12 months later? Well then we're gonna exercise the option as the option buyer.

We have the right to buy the asset at 105 through the option.

If, let's say the underlying price is at 115, we will certainly take advantage of having the right to do that.

And we're gonna buy the asset at 105.

We're gonna sell it immediately at 115, extracting $10 of economic value.

However, as you can see, the p and l is not gonna be $10.

Same reason as before.

We paid $7 90 to get the option in the first place, hence $10 intrinsic.

Or, you know, we're going to explain this term intrinsic value, but economic value of the option minus $7 90 paid for it, $2 10, uh, p and l.

And then the higher the asset price goes, the um, higher, obviously the positive p and l is going to be.

So at 130, we have, um, 25, uh, economic value minus $7 90.

So we're, uh, getting closer to the $20 profit mark, et cetera. And then we see this linear increasing, uh, line here at expiry of the option dependent on where the underlying price trades, um, at expiry.

Um, and what if the price has done the other, uh, has moved the other way.

So it hasn't actually gone up, but it has declined.

So we're now looking at an asset price of a hundred at expiry.

Then of course we will as a buyer of the option, certainly not, uh, exercise our right here because why would we want to pay $105 through the option if we can get the same underlying at a $5 lower price in the spot market? So we're going to walk away from the option.

We are not extracting any economic value, but we paid $7 90 for it.

But as you can see here, um, even if the asset price continues to fall, we're not losing more than the premium paid. And that's sort of an often cited reason for people to use options because you can, for example, enter into a long position here, which clearly, uh, the buy off a call will get into, um, with a predefined maximum loss because there's no scenario in which we can actually lose more than the premium, uh, paid initially.

So that's obviously then giving us this legendary hockey stick profile of an option.

Now, um, the premium right, obviously a very, very important factor because it determines, for example, the breakeven point.

Now, we haven't really explicitly mentioned this, but of course, to break even in this long option trade, we need to earn the premium back.

And that means if we're looking at things from an expiry point of view, the economic value of the option needs to be $7 98 expiry, which will be the case when the underlying trades at a price that's $7 and 90 cents higher than the strike price.

In our case, $112 and 90 cents.

That will be the breakeven point with all the simplifications that I've already mentioned.

Um, so it gives us an idea, um, how high the option or the, sorry, the underlying price actually has to move for us to reach the breakeven zone.

And therefore, it's of course, uh, very important, but it's generally, uh, considered to be the price of the option.

So you would n naturally, uh, negotiate an option trade based on, um, the option premium, and therefore we need to have a good understanding as to what drives the option premium.

When should it be high, when should it be, um, low.

Before we go there though, uh, a quick, um, reminder of why the option premium actually, um, is required and why it exists. Because if you think about derivatives like, uh, forwards futures and swaps, then you remember there isn't any premium that's paid for this.

So why is this different for the case of options? And the answer is, as you can see here on that hockey stick, that the payoff profile of an option is asymmetric, whereas it's symmetrical for, uh, delta one derivatives. So if we, um, just draw the payoff profile of a forward contract into this chart, you will immediately see as to why the option premium is required.

And, uh, at the time I took this example, um, the spot price of the asset, and I give you that information here because we need it later, was a hundred.

Uh, and the 12 months forward price of the asset was 105.

So if we would have chosen to go long via forward rather than to go long via call option, then we would've locked ourself into a forward trade at a price of 105, meaning we now would have had the contractual obligation to buy the asset from our counterpart at a price of 105.

So if the underlying worth trading at 105 in 12 months from now, the forward p and l would be zero because the, uh, we buy the asset at 105, it trades at 105 in the market.

So no, um, positive or negative value impact there, but we haven't, like, uh, on the case of the option paid an option premium, so we actually have a zero p and l right at 110 or 115 was the example we looked at earlier.

Um, we would actually have a $10 positive p and l because we buy at 105, sell at 115 in the spot.

Uh, and that gives us then this, um, you know, uh, $10 profit.

And so this looks clearly better than, than the option.

So, you know, what's, uh, what's the deal? Why do people go for call options then it all, and you know, it obviously, uh, matters to look at both sides, um, of the coin here because we've looked only at the upside scenario.

So let's start looking at what happens to the forward p and l if the price is trading below the actual, uh, forward price, um, at expiry IE 12 months later, and if we're now looking at a hundred, we start to see as to, uh, why, um, the call option might be beneficial at some point.

Because at a hundred, we still, because now we're in a forward contract, we have the obligation to buy the asset at 105, regardless of where trades at Ford expiry, we have to pay 105 for the asset, and the asset we're getting is only worth a hundred.

So we're down $5 and at a price of 95 of the asset, we're down $10.

And now we start to realize that there are scenarios which I mark here now, in which the forward outperforms, uh, the long call option.

But there are also, um, price scenarios, these ones here in which the long call outperforms, um, the long forward position.

So they are now sort of, you know, to, to really know, um, which one would've been the better choice.

We need the benefit of hindsight, uh, and then obviously we can do, um, everything pretty awesome if we knew what what's gonna happen in in the future.

So it's a trade off here, right? It's option premium and payoff profile differs, et cetera, et cetera.

But what I think this, this starts to show very well, if there wasn't a premium, I would argue there wouldn't be a forward market, right? If options would be available for free, uh, there shouldn't be, uh, a forward market because just, you know, imagine how the payoff profile of our call option would look like if this was actually available for a premium of zero.

That means no matter if we exercise or not, we will not lose more than zero as the option buyer, but we still can benefit on the upside. Sorry, this is a very poorly drawn line here, so I'll just do that again.

So this light blue line now symbolizes the, uh, p and l of an option that was available for free.

And now you compare that light blue line with the red dotted line, and you would immediately agree that if there was an call option available for free, nobody would ever, uh, trade it forward because it gives you the same upside, but it gives you a much, um, it gives you actually some downside, whereas the option that's available for free has zero per, uh, percent probability of losing money, but a certain chance of winning money.

And of course, if such an instrument ever existed, we we're gonna, uh, buy as much as well take as much as we can because there would be no price attached to this, right? So that clearly cannot be the case.

And also, right as this is conceptually, uh, of course, uh, making absolute sense, uh, who would ever take the other side on the option trade, right? If there was no upside, because, you know, general rule is the buyers, uh, profits are the seller's losses.

And if you now think about an option being sold for free, that would mean somebody puts themselves in a position where they have guaranteed zero profit, but a decent chance of losing a ton of money.

And that doesn't sound sensible at all.

So options will never be sold for free, same as lottery tickets, even if the probability of winning the jackpot is fairly low, uh, there will always be a price attached to that, right? Okay. Um, that is a journal idea.

So now we understand there is this option premium.

And the reason being, um, as it says in the orange box is the fact that, you know, options have a fairly asymmetric payoff profile.

And, um, if there was, you know, no premium, then of course the position of being short, the option would be, um, absolutely unattractive.

And so the premium's purpose is really to incentivize people, uh, to sell, um, optionality.

So this is where we are, um, that's a reasoning for the, uh, option premium.

And now we're gonna spend some more time on some terminology, and then we'll go back to the premium and see the, um, building blocks and stuff.

Um, cool. So, um, we have talked about the long call.

We have talked about the fact that, um, you know, buyers profits are seller US losses.

So if you know the payoff profile of a long call position, you can derive very quickly the, um, p and l profile of a short call position, because all you have to do is basically flip this horizontally, horizontally at the, uh, zero p and L line. And then basically if we just, uh, look at those two profiles here, we can see that obviously, um, in scenarios where the buyer has a negative, uh, p and l, because the option is not, the premium's not gonna be recovered, that's where the seller of the, uh, call makes a profit.

And, uh, then of course, um, vice versa.

Uh, important to note at this stage, this only holds when there's no hedging activity whatsoever from option buyer or option seller, right? So this is just looking at pure single option, um, p and l impact at expiry, nothing before, nothing, uh, considering hedges or anything like that.

Okay? So that gives us those two.

And then, um, when we're thinking about put options, because so far we've always talked about calls, um, you know, a put option gives you the right to sell.

So, whereas a long call position gives you basically, uh, sort of like synthetic long exposure to the underlying, uh, the put option, the right to sell, the underlying gives you synthetic short exposure, uh, to the underlying, because you have the right to sell at 105 if we're sticking to the same strike for simplicity, um, you wouldn't use this right when the, uh, underlying price at expiry trades above the strike, but you would take advantage of this, right? Once, uh, the, uh, spot price is below the strike at expiry. So here 105 is the same point at which we, um, sort of see a change in the, in the payoff line.

Um, but now to the, to the right hand side of 105, there's this flat profile because above the strike we're not gonna sell.

Um, but we're gonna sell.

If the price is below the strike, break even calculations then changes, it's now strike minus the option premium.

Um, but, you know, uh, that's relatively, um, straightforward.

So this time, if you wish, we had to basically, um, flip the whole payoff chart, horizontal, uh, sorry, vertically, uh, and the, uh, access would be at the 105 price mark because that's where the strike is.

And then we have worked out the long put payoff, and to get the short put payoff, we just have to flip it, uh, horizontally again because buyers profits are sellers, uh, losses and vice versa.

Again, assuming no hedging activity.

But those are just this classic, um, four different or payoff profiles at expiry of the four classic option positions that you can, um, take.

Now, let's, um, talk a little bit about, uh, option mindness.

Um, and that's important simply because when we talk about options and not talking about a specific contract, but rather about a certain group of options, and mindness is often something that we used to, um, basically distinguish different types of options.

And there are three stages of money. This, there's the, in the money option, there's the at the money option and the out of the money option. And I think the easiest way really to remember, uh, what those different types mean is just to think about what the option under current circumstances be exercised, yes or no, or would we just simply be, um, you know, undecisive there.

So if the answer to this would be yes, under normal, uh, under current circumstances, I would exercise the option, then this option is in the money because a strike is favorable, um, in comparison to the current market price.

So example here you see on the slide, you have $105 strike put and the ACE trades at 90, of course, you would use the right to sell at 105.

If the price in the market is 90 at the money, then basically means strike equals current market price.

So you have a hundred strike dollar call and the underlying trades at a price of 105, you're just not, you know, the option is no disadvantage, but no advantage either.

So, uh, that means the option is at the money.

And, uh, then we have an out of the money example here.

And basically think of it as you wouldn't exercise the option under current circumstances because the market price is better than, than the strike.

So example for this 105 strike call and the underlying trades at 90, it would be much better to buy at 90 than at 105.

Again, pretty intuitive.

So the concept of moneys I in itself, I think is really, really, uh, straightforward, simple to understand.

The one thing that I think is important that one is aware of is that moneys can be looked at, uh, in, in, in two different ways, right? One, you can compare the strike with the spot price of an asset.

Two, you can also compare the strike with the forward price, uh, of an asset.

As we know from, uh, introduction to derivative of courses and sessions like that, the forward price and the spot price are not necessarily the same.

In fact, on the, uh, first slide, uh, I told you that when we took that example, the spot price of the asset was a hundred and the 12 months forward price was 105.

So if we would use our 12 months call option was a strike of 105 from earlier to figure out whether this option would be in, at or out of the money.

Um, we see actually the interesting fact that if we compared the strike of our $105, uh, strike call with the spot price, there was a hundred.

As you can see here on the slide, this would be an out of the money, uh, strike.

But if we compare the same option now against the forward strike, uh, sorry, not the forward strike, the, the, the forward price, uh, which was 105, then strike equals forward price, and that would make the option at the money.

So I would advise when you sort of want to use that language, um, make sure that you mention whether you are talking about, uh, the moneys with reference to spot or, uh, always forward.

Don't assume we always look at forward prices in case of whatever type of option and, and spot price and other types.

Um, I would just say this is at the money spot or out of the money forward, right? It's much safer, uh, and avoids potentially a lot of hassle, uh, later on.

So just be aware because spot and forward prices can differ, uh, or most of the time actually do differ.

Um, the mons, um, might differ as well when you're looking at different, uh, or you're referring to different prices.

Okay, cool. Um, that's the mindness.

Uh, and now, um, quickly, uh, on some of these, uh, different exercise styles, basically what this refers to, you know, some call it the option geography for obvious reasons.

It's just, um, you know, when can you actually exercise your right of buying or selling the underlying asset? And the sort of, um, there's one extreme, uh, that we can see here on the left, the American option, which is basically an option that can be exercised at any point in time.

I mean, business hours obviously, um, between, um, now I either purchase time of the option and the expiry date of the option. So if you had this 12 months American call and you bought that today, then you can exercise it at any day between today and, you know, uh, whenever the expiry date is.

Um, the important thing to note though, is you can only exercise at once, right? So if you now decide on Monday to exercise that option contract, then the option contract is basically gone.

You don't have, uh, another call option for another, um, you know, 11 months, three weeks, and a couple of days, right? That's then gone. Um, and that also means that if you exercise before expiry, then you will no longer benefit from any future price moves in the underlying asset unless you buy a new contract, right? Um, but what's also worse considering as another, uh, possibility rather than exercising an American option, um, before expiry, you can sell it, right? And you can sell, uh, contracts at any point in time before expiry.

Then we have the other extreme, um, and that's European option, and that is an option contract that can only be exercised at the expiry date.

So 12 months European call cannot be exercised next Monday.

It can only be exercised on the day of expiry that is 12 months from now, right? And so it feels that on first side a lot more flexible than the American option, and I think everybody would conceptually agree this American option should never be cheaper than an otherwise identical European option.

Um, but the one thing that we should also, uh, mention here, um, although you cannot exercise a European option on Monday, you can sell a European option on Monday, even if it has still 12 months, uh, to live.

So it might not be quite as bad as it might look at, uh, on first sight.

And, you know, um, uh, just to kind of make that point that yes, American options are more flexible from an exercise point of view and clearly, uh, have it their advantages, European options might not be that much worse. That's the main point I wanted to make.

And there's a lot of, um, you know, details that we need to go into to really figure out when, uh, which type of option really more beneficial than others. But just as a general, uh, guide, um, they are very often not that different in, in price. Sometimes they are though. So it's worth understanding the differences.

Uh, and then there's, um, the ber mutant option, which sort of is a halfway house between the two, um, don't necessarily exist in any asset class, but in rates, for example, in Swatch world, uh, you do find them.

And so might be useful, know what it is, it's sort of like an option that can be exercised on more than one, uh, day in the future.

So it's, um, possible, for example, to exercise the option every once every year of the next five years, um, but not at any particular, uh, day, but there are, um, or at any day.

But there are specific, um, pre-agreed dates on which we have to exercise, same as the American options.

We can only exercise at once and once we exercise, remaining exercise rights are basically, um, gone and as any other option, we can of course sell it before expiry, right? And now, um, we're gonna focus a little bit more on the option premium.

And I would say the left hand, uh, column here, we have already, uh, discussed, right? We know option payoff profiles are asymmetrical and the premium compensates for this, et cetera.

But now let's kind of focus on the question as to how, how, how, how high, um, should this premium actually be.

And, uh, I think before we even go into the different price components, I think it's, it's useful, um, to get a conceptual understanding as to, you know, what does the option premium actually try to, or what does it represent? And yes, we said it's compensation for the asymmetry, okay, makes sense.

But, um, you know, what is, um, then really feeding, um, the, the option premium? And I think it's, it's quite nice to see that actually, um, to get to the theoretical price of an option, uh, we would have to answer two questions only, right? Uh, and that is question one.

What's the probability that the option we are selling is going to be exercised and, um, if exercised, how much money will we have to pay into the contract? And, um, that's very similar to, you know, pricing credit risk, for example, where you think about probability of default and you think about loss given default, and then you just kind of match this together into a, into a spread.

Um, and an option rac.

Um, basically we're trying to solve these two, or trying to answer these two, these two questions.

And in, in, in very simple environments, of course, it's not that difficult to answer this question. And the most simple case you can probably come up with here that does a nice job in visualizing the problem in a way, is a coin to right, where we all know there's, uh, two outcomes.

Actually, there's three, but you know, as, as, uh, people keep pushing back on this, it's, uh, when I say there's, so let's agree, there's, uh, two outcomes, hats and tails.

And if the coin has some sort of like equal weight distribution or, or whatever is relevant there, uh, we can assign a 50% chance of a coin landing on hats or on tails, right? So if I now would invite you to the game where we use a one, let's say Euro coin or a pound coin or any other coin, if you're choosing, um, and I flip this coin and then, um, you guess the outcome, and if you guess the outcome rate, you can keep the, uh, coin. So let's stick with one euro now, uh, for simplicity.

So I flip a one Euro coin, you guess the outcome, right? You keep that coin, how much should I charge you for that game? And that's basically where we can go through answering these two questions.

What's the probability that I will lose that game answers 50%.

I mean, now simplified world here, and if I lose that game, how much will I have to pay out answers one euro.

So I have a 50% chance of losing one euro.

So expected loss is, um, 50 euro cents, right? And that's what I should charge you to play this game with me.

And then if we play this a large number of times, half the time, you will win this game because you guess the outcome rate, that means you keep one euro, but you paid 50 cents to play the game in the first place.

So I'm out of pocket 50 cents, right? The other half of the time, you guess the outcome wrong, I keep the 50 cents that you have given me to play the game.

And that means in the long run, none of us will be better off, right? We had a lot of fun, but we're not sort of gaining financially all that much.

That's the idea of the expected loss. And we can expect or expand that then to the concept of option pricing.

But we run into problems at some point relatively soonish because if you think about equities for example, uh, then it gets relatively clear that the only thing we can really say with a hundred percent certainty about a stock price at any point in time in the future is that it's gonna be somewhere between zero and infinity, right? So this first step of just kind of writing down the potential price outcomes, um, we will never finish to do that, right? So we can't work, uh, with, so okay, these are the price outcomes and we assign probabilities, et cetera, because of the infinity problem, we will never finish.

So what we do in reality, we need some, uh, help by, um, our option pricing models, and they use certain distribution assumptions or modeling techniques to really find the answer to those two questions.

IE what are the chances that the option will be exercised? And if exercised, how much do we have to pay? And so while it is conceptually a fairly simple problem that we're trying to solve here, um, because of the reality, um, or the complexity of reality, um, you know, answering these two questions is really, really, um, not trivial.

And that's then obviously where the pricing models, uh, come into play.

Um, but one doesn't necessarily have to dive really deep into those models to get a conceptual understanding of what is actually, uh, driving the premium.

IE when should an option have a relatively high premium? When should the premium of an option be relatively, uh, low? And I think it really helps with that understanding to think about.

As, you know, literature often, um, it tells you the option premium as a sum of two parts, the intrinsic value and the time value and the intrinsic value is rather intuitive.

And that is sort of, I would just simplify it down to that would be the value that you could extract from the option by exercising it. Right. Now, in the current market circumstances, really, uh, only true if you're looking at an American option, right? So if we're just looking at an American, uh, 12 months call, a strike was 105, and we now have a spot price of the underlying of 110, uh, then, you know, okay, I can buy this, um, particular option right now, I can exercise it immediately, buy the asset at 105 and sell it immediately for 110.

That means the intrinsic value is gonna be, um, $5.

If the spot price wasn't, uh, 105, but it was 95, for example, uh, the intrinsic value wouldn't be negative $10 because yes, we can buy the option, but we certainly wouldn't exercise it immediately.

So, um, the intrinsic value is either zero or positive when the option is in the money.

And so that's the first, uh, well, the left hand, uh, column basically explain.

Now, as I said, in the case of European options, is slightly, um, more complex to calculate the European, uh, sorry, the intrinsic value, but it's possible, right? But the only thing we have to do is we have to compare the strike with the spot, uh, with the forward price because we can only exercise at the expiry date, um, and then we would have to discount that amount back, et cetera. It's possible, but it's, um, you know, a little bit more for a 60 minute session.

Uh, not the best example anyway.

Um, so we have, uh, calculated the intrinsic value of this option $5.

And the good news is now we have identified the lower price boundary of that option, because this option should not be available in the market for anything less than $5. Because imagine you could, uh, you know, you would see the premium for that option be quoted at $3.

You all know what to do, buy the option for $3 exercise immediately, and extract $5 profit from it, ignoring transaction costs and the likes.

And that gives you $2 risk for return.

So we're gonna do this, um, until, you know, the option premium has risen to the price, um, of its intrinsic value, and even then we will probably continue to buy because it's a 12 month option.

And so, you know, while the intrinsic value is five, and so that should be the absolute minimum price boundary under normal circumstances, the price of the option will be higher than five because five is what the, you can immediately extract from the option right now.

But remember, it's a 12 months option.

So this option has still 12 months to go.

You could hang onto this and then hope that over the next 12 months, for example, the price of the asset is going to creep up even more, and you will be able to extract a lot more money at expiry than, um, you would be able to do now with intrinsic value of five, right? So that's obviously, uh, something that the option seller needs to consider, um, as well, and that's where the time value comes in.

And in fact, uh, time value is usually described as a difference between the premium of the option and its intrinsic value.

So we're not calculating it directly, but we can derive it from, uh, the option premium.

Um, and it's conceptually very straightforward, I think, right? It's very intuitive to say, look, if I'm, if I'm thinking of selling a 12 months option that has an intrinsic value of $5, I I don't feel comfortable selling it for $5.

I want price a little bit extra in.

And, uh, the, the intuitive way of thinking about it is that this is compensating for what I just said.

That is, if I'm selling this option, I take the risk that over the next couple of months, the price of the asset keeps rising and I will have to pay a lot more than $5 to the option buyer than what I charged up front.

So let's kind of slap some reserve on top of things, uh, and, and then hope that, uh, this reserve is enough to cover our additional costs.

And as wonderfully intuitive as this argument is, if you stick to this, you run into problems on the next slide to explain a certain behavior of of time value.

So before showing you what this problem is, I would just, excuse me, um, encourage you to start rethinking, um, if that was your understanding of time value, uh, your understanding of time value, and think about, uh, it more like a compensation, uh, that the sell off the option charges for the uncertainty or for taking the uncertainty, uh, whether or not the option will be exercised. Now, that sounds a little bit abstract. What do I mean by this? If the seller of the option knew the option would be exercised, uh, then hedging this option, uh, would be relatively straightforward, very much like hedging, uh, uh, forward is right, because if you think about how, how we hedge it forward, or one way of hedging it forward is buy the asset, fund the purchase amount and receive dividends, and then basically this other cost of carry that drives the difference between spot and forward price.

And the reason why this works is we know in 12 months from now, uh, the wherever is our counterpart will have to buy those assets.

Cash shuttle doesn't really matter, right? But we will, um, unwind this position one way or the other, and we will get the economic benefit or damage pay, uh, to us, right? So we know we're gonna deliver that asset, or we need the hedge.

The problem with an option is we don't know right now, of course, um, we, when we're selling a call, we have the same sort of upside risk than selling a forward, right? So we know the option will be exercised if at expiry the share price is above the strike.

So it might be, uh, a good idea to buy the asset.

Um, and then, uh, if the share price actually rallies and the option gets exercised, we have bought the asset at the lower price and we're not facing, uh, too much p and l pressure as a result of this transaction.

Um, so let's run through this, right? Let's say we sold a hundred calls with a strike of 105, um, and we're buying now a hundred stocks at a hundred.

Uh, let's say the stock doesn't pay dividends, we have to fund it for 12 months and 12 months.

Uh, interest are 5%. So forward price is 105.

So, you know, all wonderful, we've bought our a hundred, um, uh, call, uh, sorry, we bought our a hundred, uh, stocks.

And if now in 12 months from now, uh, the share price is 120, for example, we deliver those stocks into the option, we get $105 for each stock.

And that's exactly the amount we have to repay treasury because we borrowed a hundred, uh, from them at 5% interest.

All is golden, right? No damage done.

Um, but the problem gets obvious when the price has moved the other way.

So what if the underlying asset price has fallen down to 90, for example, right now, the, uh, buy off the option is simply gonna walk away from the contract. They're not going to exercise the option, they're not going to buy the underlying from us at a price of 105.

Um, so, you know, it's not all bad news because we still have a hundred shares.

Problem is the value of these shares has fallen and it's no longer the, uh, 105 that we were aiming for and the treasury wants to, uh, receive back, but now we can sell the shares only for $80.

So we do that, and now we have a $25 loss per share or per option, basically, um, because of the way the market has moved and what was designed as a hedge has actually turned into a loss maker.

And that shows the problem of hedging options.

You cannot, like, you can and forwards just do a static hatch, put it in place and walk away. Of course, you can buy the callback that you've sold, but that's just, you know, hedging back to back.

Um, that's not usually what we end up doing, but if we were thinking about hedging the underlying risk, we would have to do this much more dynamically.

So we start, instead of buying a hundred shares, we can think about what's the likelihood that, uh, the option will be exercised.

And then if that's, say that was 50%, we're gonna buy 50% of the shares, IE 50 shares, and then if the price of the underlying goes up, then the probability of the option to be exercised increases.

We're gradually buying extra shares.

If the price goes down, the, uh, probability decreases, we're gradually selling shares, which sounds, then, you know, it's okay. It's a good approach, it's a dynamic approach.

Um, but obviously it sort of aligns the risk.

The only fundamental issue of that approach is we're always going to buy at high prices and sell at low prices.

And that's of course, uh, not necessarily, uh, a guarantee to be successful in the long run.

But it's also not that bad because remember, as a sell of the option, you get the option premium, and that's as long as you, uh, don't necessarily lose more than the premium you charge upfront by doing this hedge.

Um, then in theory, um, all is good, right? Um, but the point want to come back on this now is that, um, this, um, risk, this, this, uh, sort of uncertainty whether or not you need the shares that creates a need for this dynamic hatching that then creates obviously negative p and l impact.

That's really what time value in my mind is compensating the option seller for.

So that, uh, with that in mind, that's kind of start thinking about what drives time value.

I mean, we, we have, uh, gone through the calculation of intrinsic value was all relatively easy, but what should fundamentally drive time value? And we said, well, it's compensation for uncertainty if the, uh, option will be exercised or not. And then we need to ask conceptually, when, uh, is uncertainty of exercise high? When is it not so high? And of course, uh, you know, first thing that comes to mind immediately given the, the thing is called time value is probably, uh, the time to expire, right? And I think it's absolutely intuitive to say, um, long time to expire means uncertainty increases because, uh, it's generally more difficult to forecast things over a 10 year horizon than one day horizon, right? Um, so that's number one.

Time to expire, uh, increases the time value.

And also what that means is as options, uh, time to expire becomes shorter every day.

Um, the time value all else being equal should go down a tiny amount every day. So that's basically the, uh, options, uh, premium decay, the time value decay that, that, that you might read about.

So time value is driven by time, but not only, but it's also driven by the volatility of the asset.

IE does this, um, asset that we're looking at. Does the underlying behave like a very boring asset, doesn't move up, doesn't move down a lot, or is it something that is, uh, extremely volatile? And of course, the more volatile an asset is, the bigger the uncertainty whether or not the option will be exercised, the bigger the time value, um, should be.

Another, uh, point, although we have already, um, touched upon it, is that time value will be zero when the option approaches expired because then there's no uncertainty left, right? There's, in all factors are known, it's just intrinsic value at that point.

Um, I skipped this because we talked about this conceptually.

I wanted to, uh, come to this, um, point here.

'cause this is a slide that I referred to earlier there where you run into problems when you kind of think of time value as, you know, things could, compensation for things becoming worse. Because what we've done here is we've, uh, looked at the option premium or the value of the option, uh, in different scenarios.

So, uh, differing for different underlying asset prices.

Um, and by the way, we've changed, um, and I need to change that at some point, uh, to be consistent. But the strike of this option was a hundred, uh, dollars, because here you see, uh, a change in line behavior.

But anyway, a hundred dollars strike and we're looking at this, uh, three months, uh, option at, uh, four different points in its life.

Uh, here the green line shows us three months option. So basically we just bought the option, it's now three months, uh, left to expiry.

The red line shows, uh, one months later when it has two months to expiry dark blue, one month to expiry, and the light blue is at expiry. And then we see this, uh, hockey stick that we've looked at earlier because now we're only looking at intrinsic value because the option has already expired.

Uh, and then if you, um, look at this set of lines here, the difference between, uh, the green line and the light blue line, that's basically the three months time value here, right? Because the option when we bought it was x, uh, yeah, was a $4 probably, uh, more expensive than, uh, at expiry when it was zero.

And that was then the time value we paid for is the three months, um, optionality.

And as one would expect as time goes by, IE as we're sort of traveling through time, uh, the difference between the option premium and the intrinsic value just goes down to zero.

And that was this sort of time decay effect.

I alluded earlier, so far everything is cool because we said, okay, shorter time to expire leads to smaller time value. That's perfectly in line with what we said.

Volatility doesn't play a role here, by the way.

We kept it constant artificially, but you know, we, we wanted to sort of eliminate, uh, that other factor here.

Um, but what I want to point your attention to is the, in the money and out of the money scenarios.

Because as we move, uh, as these options move deep in the money IE the underlying price increases significantly.

Something very interesting happens.

And that is that all the lines seem to converge.

And if the difference in line basically defines time value, uh, then what that would mean is if the option goes in the money, then the time value disappears.

And that is something we cannot explain.

If we're thinking of time value as the compensation, that the intrinsic value might go up just because we're at 120, um, it doesn't mean we cannot go to 121 or 122, right? So that would be, uh, not co really conceptually sound. So that doesn't seem to, um, work all that well.

But if we're thinking about this, um, uncertainty argument, then I think it makes sense because especially when you think about real extreme cases, right? Let's say we have this, um, a hundred dollars call, right? Expires in, you know, uh, three months from now, but the underlying asset price is a hundred thousand dollars, right? Uh, so we have the right to buy at a hundred, and right now the underlying trade's at a hundred thousand.

Um, so legally speaking, we have an option.

We have the right to buy the asset in three months time. Practically speaking, we have the obligation, right? Because if you don't exercise that option in three months time, um, or sell it now or whatever you wanna do, um, you know, there's significant problem.

Um, so from a hedges point of view, that would mean they will already own all the stocks.

Um, and that would not change really very much for the remaining time.

So they have hedged all their exposure, and if now the market keeps rallying, they have bought the shares and they're gonna deliver to us. So it's basically more like a forward contract from a, um, behavioral point of view rather than an option, which is legally still is.

But uh, practically speaking, it's a forward contract.

And so as forwards don't have time value, um, it's, um, perfectly sensible that when the options go towards in the money, um, they are sort of, um, losing, uh, time value, at least if you look at this, um, in, in the way we have done it here and out of the money, same thing, right? If you have, uh, a hundred dollars strike, um, call, but the underlying price is uh, 2 cents, um, it feels very unlikely that this is gonna be exercised.

So no uncertainty, no time value, alright? Uh, that's that then.

Um, and, um, now we can obviously start to derive, um, a simple sort of, um, price driver overview, um, saying what determines if the option premium should be high or low.

Uh, I really just kind of see this as a, um, preview for, you know, us moving into, uh, the Greeks at some point, uh, next year.

But generally speaking, um, you know, what we have discovered, uh, right now is that obviously time to expire, apologies, time to expiry and, um, volatility, um, are influencing the time value.

And time value is sort of, um, you know, a concept that applies to cult and puts in the same way.

So the longer, uh, the option has to live and the more un uh, volatile the underlying is, the more the time value or the higher the time value will be. And that's regardless if there's a call or a put. So you have some of these variables, time to expiry volatility affecting prices for calls and puts in the same way, but you also have other variables like the spot price, um, affecting, uh, calls and puts in opposite ways. And that is sensible because we're talking about directional exposure now.

And that's obviously the opposite between a call and the put call gives you long position, and if you're long, you benefit from the price moving up put gives you a short position, and when you are, um, short, you lose when the underlying price um, goes up relatively, uh, straightforward.

But I wanted to use the last 10 minutes of this, uh, session, um, to, um, move over to, uh, having a look at why people, uh, use options.

And I think there's many, many different, uh, use cases, right? And, uh, different investors use options, uh, in different ways and they might have different, uh, reasons to do so.

But if I had to come up with, uh, two sort of main, uh, reasons as to why we would do this, um, I'd say you can classify, um, these use cases in, in two main cams.

One is, um, you want to build a certain directional exposure that is, um, you know, coming with a payoff profile that's somehow different than a straightforward, long position or short position.

So you are thinking about, for example, um, using this benefit that options have, that the loss is limited to the option premium you paid initially.

If you are longer call or, um, you know, longer put for example.

Um, and, and that you cannot lose more than the premium.

Um, or you might wanna, uh, monetize certain price targets. It's an example. We're gonna have a look in a minute at, um, so that's camp number one, or that's, that's the main, um, area of use cases, uh, that that is, is there the other, um, reason as to why options are used, and that's, I think, um, more often, uh, uh, or, or, you know, a very, very important reason as well is that options give you exposure to, um, a volatility, which all the delta one zeros that we've looked at, uh, don't, right? Because that component of volatility of prices, that's only really, uh, used in, in pricing, um, of options not in Fords swaps and, and, um, and futures. And now of course, um, know there's other volatility products like, you know, VIX futures just come up as an example here, variance swaps, volatility swaps, et cetera.

But they will all be somewhat linked to, um, underlying option contracts.

So, um, you know, if you want to trade volatility, then options are still a very useful, uh, tool for that. So that's what we're gonna do. We're gonna have a look at how we can use options, um, to, um, create more efficient, uh, long exposures, for example, with the, uh, call overriding example.

And then we're gonna have a look at the straddle as an intro example to, um, getting a volatility exposure.

With that, let's have a look at the covered call.

And the idea here is, and that's why it's called a covered call, is that somebody sells a call to increase the potential return of a position, um, by selling away upside that they don't think is really, uh, worth having example here we have an investor that is long stock, they bought it at $50.

Their expectation is generally the price will go up, but it will not increase more than $4 over the next three months.

So they expect, uh, that, uh, price to stay, um, at or below $54 over the next three months horizon.

And if we hit that target before, they are happy to sell, uh, at those, um, $54 and then, um, move on.

So they can either now just kind of sit on their long position, wait for 54 to print, and then sell, uh, the stocks there, or they can, uh, sell the upside away, um, beyond 54, uh, and exchange it in, you know, return for some upfront premium.

And that would be done by, for example, selling a three months call with a strike of $54.

In our example, that gives them a premium of $1 30. They now sell the option, they get the premium.

And what does it mean? They have sold the right to buy the shares at 54 to someone else.

So if now in three months we're trading above $54, then uh, they will have made $4 profit on the shares because they bought at 50.

Now they are, uh, trading at, um, well they're selling at 54. They won't benefit beyond that very much simply because the option will be exercised and they have to sell the share, say bought at 50 into the option at 54.

So $4 profit on the share, that's profit is kept, but in exchange for that cap, they get also an upfront of $1 30, which immediately, uh, improves their performance or well, basically increases their return.

Um, and so, um, in exchange, obviously for the capped upside benefits, they are generating income through premium.

Um, and because they're selling at an out of the money strike, they have some, um, degree of upside participation things to consider.

No downside protection really, because, you know, you're along the stock of the market will fall, that leads to a loss.

Now it's not quite without protection because at least you got the $1 30 from the premium, uh, of the option that now expires worthless.

Um, and then you obviously have also the opportunity cost if there was a significant, um, rally.

But for anybody who has a limited view on upside, that might be a strategy, um, worse considering.

So that's the, uh, covered call example, just one out of many examples, how options could be used to, um, create more efficient or more tailored p and l profiles rather than, uh, outright long and short.

Uh, and then the other example, as I said, I wanted to run through, uh, the straddles, um, which is basically a, a fairly, uh, common, um, strategy to trade, um, volatility.

And what volatility trading generally means is that we're generating returns, uh, not through calling the direction of a move.

IE is the price of the share going up or down.

But rather than, um, calling, um, the magnitude of the move IE we create a position where we get rewarded if we are right in the view that the price of the underlying is going to move, uh, a lot either up or down direction, doesn't really matter.

We get paid in, in both, uh, scenarios.

Uh, or we can also take the view, um, where we then get paid that the, um, in case the market doesn't move at all.

And that would be, um, just the opposite of a long straddle IEA short straddle, um, position.

Strangles are conceptually fairly similar.

You know, it's, it's, it's explained on the slide here in case you want to read, but let's have a look at the long straddle IEA, um, general position here that benefits, um, if a trader is right in their, um, view that the price of an asset is gonna move, um, a lot, um, and doesn't necessarily have a clear view on the direction.

So this is exactly the scenario we, we have mapped out here.

Try to expect a significant move in a stock, uh, to happen over the next three months.

They are not sure about the direction at the moment.

Spot price is, uh, $50.

How can we, uh, position ourselves not through classic long and short positions? Because we would need a long position to benefit from the up move.

Uh, we would need a short position to benefit from the down move and both positions would then simply cancel each other out.

But through the asymmetry of payoff profiles, adoptions, uh, generate, we can actually create a trade here using options that would benefit, uh, regardless if the move is higher or lower as uh, long as it's large enough.

So how can we do this? We buy a $50 call and at the same time we're also buying a $50.

Put those three months, let's assume both have the same premium, $2 80.

That means we're buying two options, $2 80 each.

That means total premium of outlay, $5 and 60 cents.

The beauty is we're now long two options.

We're longer call option, we're longer put option. Now.

Um, let's have a look at what is the, uh, p and l profile at expiry rate.

So worst case is in three months from now, we're still stuck at a price of 50.

Uh, either price hasn't really moved on a three months, uh, horizon, our call was disastrous.

We, um, believe there was a big move coming and effectively no move occurred.

At least at that three months point.

We're still stuck at 50.

That means both options now expire worthless.

Uh, and we have paid $5 60.

So this is not gonna be recovered. We have a five 60, uh, negative uh, p and l. However, as soon as we move away from 50, either up or down, one of the two options will be exercised, right? If we're looking at, uh, 60 here for example, we are gonna let the put option expire, but we're exercising our call.

We have the right to buy at, um, at 50, but now the asset trades at a hundred that, uh, sorry, at at 60, that's a $10.

Uh, economic value on the option.

We paid $5 60 to get the two options in the first place.

So we're up now $4 and 40.

And if now we have seen the price drop to 40, uh, then we're gonna let the call expire.

But we're exercising the put extracting $10 economic value.

We paid $5 60 for it.

So again, we're up $4 and um, 40 cents.

So what we can conclude here now, we have built a position that will benefit as soon as the price in at the three months point will have moved out of a certain range.

We can even calculate that range because we know that one of the two options must earn us at least $5 60, meaning the price either needs to go above $55 and 60 cents or below $44 and 40 cents, and then we're in the money with that strategy.

So what we have is now a position that will benefit from a move up, from a move down and that will suffer if there was no move at all.

Of course, there's many other different ways to trade volatility, you know, and very different types of volatility.

We could trade implied vol, realized volatil kind of stuff.

But, um, now we have seen as to why options allow us conceptually to trade vol.

And, uh, with that, um, I'm at the end of what I wanted to share with you today. Thank you so much for your participation. I hope you found it, Uh, beneficial.

Have a great rest, uh, of your Friday. Fantastic weekend ahead and of course, um, you know, as I won't be speaking you before, uh, the new year, have a great, um, holiday season.

Hope it quietens down for you.

Um, try to get some rest and I look forward to, um, you know, meeting you again in the next year.

Take care for now. Bye-bye.