Good morning, good afternoon, maybe good evening for some of you, and very warm welcome, uh, to this Felix live session.

Introduction to Derivatives. My name is Thomas k Crows, and I have the honor to take you through today's session here, uh, today.

Uh, most important question right from at the start is of course, what exactly are we gonna cover here today? Well, it is an introductory course, so we're going to start with a definition of the term financial derivatives, and then we're gonna introduce the three basic type, um, of derivatives just to get a proper understanding of what delivers actually generally, uh, all about.

And then we will discuss some, uh, generic aspects like, for example, cash versus physical settlement. We're gonna think about, you know, use cases more specifically with hedging, uh, versus speculation.

And then we're gonna take a more detailed look at, uh, forward contract as they are, I think pretty critical to understand the dynamics of, uh, any other type of, uh, ative as considered the main building blocks.

And towards the end, we will then take a very, very brief look at options as well. There's gonna be another session on options, uh, later in the year, but at least we wanna sort of point out the key differences between the delta one, uh, and the option.

As I said, we're gonna start with an introduction and a definition of the term financial derivative.

And I would argue that when you Google or use a chat bot or you do an old school and, and, and read textbook about derivative, is one of the first things that you will read is the definitions.

Uh, and, uh, it will look probably very similar to the one that's on the slide here and that says that the financial derivative is a type of financial contract and that contract has a value, but this value basically then depends on the price of another financial instrument, which is referred to as the other one, something.

Now, actually the statement is absolutely correct, um, but if it's the first time you look into financial derivative, it probably doesn't really tell you very much about how they, uh, work and what exactly financial derivatives are.

Um, before we go there, and we will on the next slide, I just wanted to spend a couple of minutes discussing what those typical underlying in the, uh, financial world are for derivatives.

And then on the left hand side on the slide, we can see this, uh, traditional asset classes that I think in the sort of beginning of ative markets have been, um, the, uh, underlying of choice of most market participants.

So here, uh, we see obviously, um, interest rates or, uh, bonds being, uh, underlying. For example, if you're thinking about bond futures contract, then we see that equity derivatives of course, exist, um, in great numbers as well.

So we're thinking for example, about, uh, equity index future or single stock futures, things of that nature.

Then there's credit, uh, ities where the underlying tends to be a credit spread, the currency derivatives, where the underlying, of course is an FX rate.

And then commodity derivatives, which unfortunately receive a lot of attention these days, um, where the underlying could be, for example, an energy ative like oil, uh, and energy, um, underlying like oil or, uh, you know, maybe some agriculture things or precious metals or anything like that.

Um, this is probably where, uh, the derivatives market really starts to develop over the last couple of decades.

But then obviously as markets mature, um, you know, we see changing requirements of of the users and with that a generation of new topic or new new, uh, products that, uh, has come to market that now allow us to not just, um, have traditional asset classes as underlying, but also more and more, um, market factors, which are probably in more difficult to trade directly than the traditional asset class where we're thinking about, for example, volatility being the underlying big futures contracts, right? Are they, are they allow us to trade certain types of volatility.

Then there's dividend, um, contracts where we can sort of have dividends, real dividends actually as, as underlying, uh, or things like inflation, which is not really a tradable asset per se, but of course we can enter derivative contracts, um, and therefore benefit from an increase in inflation or, um, for the decrease in inflation, whichever direction.

Um, we take. So that's obviously just to show the evolution of the market.

So there's more and more underlying that are become tradable in the derivatives space.

Uh, and that together with obviously the fact that there are many, many different use cases is then explaining as to why when we compare just the size of the derivatives market, and we're looking at the OTC market only, so we're ignoring the exchange chain stuff.

It on first side looks so much more bigger than the equity market or the debt market, even with some of the two, right? We're talking about $618 trillion here.

Now, I have to be honest though, um, this is not quite comparing apples with apples because what we are referring to here, as you can see, is the underlying notional amount.

That means this is just the calculation basis for the payouts. It doesn't mean that $618 trillion have been invested in, uh, those derivative products. So we need to, um, at least mention this so that the comparison is not, um, really, um, perfect, but I think it clearly shows that derivatives are used quite extensively.

Therefore, it does make sense to have some general understanding of how this contracts work.

And that brings us back to the dis, right, what we said, it's a financial contract, and the value of this contract is driven, um, by the price of another, uh, underline.

And that is, as I said, factually correct, but it doesn't really tell us much about how they work and to learn about how they work.

I think it's best to have a look at concrete examples.

And what we're gonna do on this slide here is we're just having a look at the three basic type of derivatives.

Um, they are, we're looking at forwards and futures. We're looking at swaps, and we're looking at options now, starting on the left hand side with forwards and futures.

And I said earlier that I believe that forwards and futures are actually the main building blocks of derivatives markets.

So it's really, really critical to have a solid understanding of those contracts before we're moving on into, uh, the other categories.

So what are forwards and futures? Well, they are strictly speaking the agreement to buy or sell the underlying asset.

Um, and of course, the agreement is that the settlement of this transaction will happen at a pre grade point in time, and that time is obviously in the future, um, simply because everything else would be a spot transaction.

And, um, that is then the key difference between forwards and spot transactions.

The settlement is agreed to happen at a point later than spot under the most circumstance, it is three months in the future, six months in the future, 10 years in the future, depending on obviously what the underlying is.

Um, and despite the fact that settlement will happen at a pre um, specified point in the future, the price for this transaction is already agreed upon today.

Okay? So that is a forward contract in essence. And then the question is, what's the difference between forward and futures contract? That's a really simple thing to answer.

Futures are basically just the exchange trading version of forward contracts.

So forward contracts, ROTC, future contracts are the exchange trade version of those concrete example.

Um, just so that we have a sense of what we're talking about here, transaction wise, um, the trader agrees to buy 10,000 barrels of oil.

Um, the settlement is agreed upon to happen in three months, and the agreed upon forward price, IE the price of the trader is then going to pay for the 10,000 barrels of oil, is $76 and 50 cents per um, barrel.

Okay? So that is an example of a full transaction.

Now, let's move to swaps.

And um, it's a little bit tricky to come up with a one sentence definition that does a good job in really defining, uh, what swabs are. And the reason for this is that there are so many different types of swabs, and while they have some common elements, they're all sort of mechanically ever slightly differently because the underlying is different. And that means there's different use cases and different mechanics, um, that, you know, have been put in place to meet the requirements of the users of the sub.

Um, but what all of these swabs have in common is that they are basically the agreement to exchange to streams of cash flows. And that means unlike in the case of forwards and futures, where we have this one-off settlement.

So on our oil example here, in three months, the trader will receive the oil and will pay, uh, the money, and then the trade is done, it's history, um, because it has been settled, uh, in case of a swap, there tends to be multiple points in time where there is an exchange either between cash flows or between cash versus, uh, oil or whatever that, that we trade here, right? And so there's that common element that they have multiple points in time where there is, um, you know, either payments of cash or whatever.

Uh, and then these, uh, payments tend to happen in regular intervals. So for example, monthly, quarterly, certainly annually. Annually, okay? And what they also most of the time have in common is that the payment, uh, or at least one payment stream, like one of these cashflow streams is not known at the inception of the trade, but instead depends on the future performance of, um, some underly here.

A concrete example for such a transaction would be, uh, a claim, the interest rate swap.

And I've chose that example simply because that is to my knowledge, uh, the most actively traded OTC derivative in in in swap world. There is. And, uh, you know, huge amounts of notion will get transferred there every day or transacted every day.

Uh, decent amount of risk is taken via these contracts, and so it makes sense to look at that.

So how would such a contract typically look like? Um, here, just an example where the trader agrees to pay a fixed interest rate of 4% per annum, and, uh, will do that in exchange for sulfur, um, for a, uh, notional amount of a hundred million and this whole thing has a five year period, that means if I was a trader and you were on the other side, I would now for the next five years, paying you a fixed interest rate of 4% on a hundred million.

I don't invest a hundred million.

Uh, I don't give you a hundred million, you don't give me a hundred million either, which is kind of chosen the notional amount asset calculation basis, IE the 4% refers on a hundred million.

So ignoring day conventions, I'm gonna pay you 4 million, uh, dollars every single year for the next five years.

What do I get in return? I get fr from you, FR is secured. Overnight financing rate is basically a reference rate in money markets that is reset every day.

And so what's gonna happen over the next, uh, year, we're gonna look at where sofa has been fixed every single day, calculated compounded average rate of this and that, and is basically what you're gonna pay me, uh, for the, um, for the first year.

So let's say that compounded average was, uh, calculated to be 3.9%, then I have to pay you 4%, you have to pay me 3.9%. We're of course not doing both transactions, but instead we agree on a net payment, meaning I pay you net 0.1% on a hundred million, and that means I pay you a hundred thousand dollars and that first year's done and then the second year starts and we see what sofa dosing at that point.

That means when I enter into the trade, I know what I'm gonna pay you, but I don't know what you are going to pay me.

That depends on where sofa goes over the next, um, five years.

Just a typical example, uh, that explains the mechanics of one swap.

Okay? Now, um, some people, um, say there's only really two kinds of dividends, right? So they don't think in three categories, but rather than two. And the reason the argument here is that the, uh, forwards and futures and swaps, uh, share really a lot of common elements and that is they are obligations for counterparts to do something, right? Our trader here has to buy the oil in three months time, right? They have to pay the money and they have to take delivery of the 10,000 ballots of oil.

Of course, if both counterparties agree, then you know, we can tear up this contract and say this no longer happens.

But under normal circumstances, one counterparty might have an interest not to go ahead with this contract anymore.

The other counter party, however might, and so they will not let the other counter party out. And if they do, then they might just ask for some financial comp, uh, compensation because most of the time the reason why one counter party wants to get out is that the contract, uh, turns out to be, uh, not as advantageous as they thought it might be.

And so that's why they actions.

So it's possible to terminate these transactions early, as with any contract, but there might be some, uh, payments that are required to get out.

But other than that, they are basically obligations, right? For contractual obligations for both counterparts.

And that changes fundamentally when we go, uh, to the right hand column where we're looking at options. Because what options have, or all options have in common is that they give the buyer of the option the right to do something but not the obligation.

Right? And what, um, rights can the buyer have? Well, that depends on the type of option we generally deter. Uh, distinguish call options from put options here.

Call is the right to buy the underlying asset where the put option is the right to sell. We're gonna come back to that and see, uh, what this means in terms of direction risk later on.

So let's say, uh, we have a trader that buys a three months call option on a stock that trades at a hundred dollars in the spot market and the strike price is $105.

What does that now mean? Well, our trader now has the right to buy the asset at a price of $105 over the next three months.

And if they don't exercise this option by the end of this three months period, which is also the Expiry day, then we are going to, or the option, option is simply going to expire worthless.

That means, uh, no more rights and also no more obligations.

This price at which we have the right to trade at this 105 is what we call the strike price, uh, in option pollen. So that's really the price from at which we are able, um, to buy.

Um, now one thing that is also, uh, important to mention is that in different to forwards and futures and swaps, um, the buyer of an option has to make what we call a premium payment that is then paying a certain amount of money to the option seller.

And the reason as to why this must happen is that the, uh, say the the the risk reward profile, uh, of an option looks quite different, um, in terms of attractiveness from, uh, an option buyer and option sellers perspective. Because think about the following, how would an option buyer determine whether or not they take advantage of this, right? Whether or not they use this right, that they bought below? Well, that depends clearly on where the spot price is at expired.

So if three months down the line, the spot price of the asset would trade at 120, then of course the option buyer would take advantage of the right to buy the asset at 105, because I can buy the asset at 105 through the option, I immediately sell it at 120 in the spot market and I keep 15 uh, dollars of profit, right? Then. Um, if however, we were trading at a price significantly below the strike, IE this spot, uh, price of the asset now is 80, then the option buyer would clearly walk away, say, I'm not gonna buy this asset through the option at 105.

If I still want the asset, then I'll just go into the spot market and buy it for $25 less, right? So we let the option expire.

Now that's the perspective of the option buyer.

How about the option seller? There's no right for the option seller, right? Other than getting the premium because as soon as the option is sold, the option seller basically has to do what the option buyer wants them to do.

In other words, if the option buyer decides to exercise the option, the option seller has to deliver the asset for a price of 105 no matter where the asset trade.

And if the option buyer decides to walk away, then the option seller cannot deliver any asset and not charge the $105 to the option buyer, right? And now you can combine this and say, when will the option buyer actually exercise when it's financially advantageous for them to do so, which means a disadvantage for the option seller? And when is the option buyer gonna walk away? When it would be financially disadvantageous for them to exercise the option IE when it would actually be an advantage for the option seller? If the option with exercise, that means selling an option, um, without a premium would just mean best case you're losing nothing.

Worst case, you lose a lot and that's not a very attractive, um, position to be in. So nobody would ever take the position.

The option premium actually is there to incentivize, um, almost, uh, option sellers to take that, you know, on, on the face of it at least, um, less, um, you know, attractive, uh, position to be in of being sure it's the option rather than being locked. So that's a conceptual way of thinking about the option premium at least.

And we come back to the option premium when we look at p and l profiles later, but that's, uh, probably an important thing to note at this point.

Okay, so now let's go back to the definition and where we said, okay, there is this link between the value of a derivative and the price of an underlying. And I thought it's worse to think a little bit more about it and visualize this, uh, in some ways.

And so we're going back to our oil example here.

Remember the three, uh, months forward, so that was executed.

We had a a 10,000 oil barrel purchase.

Settlement happens in three months, and the agreed upon forward price was $70, $76 and 50 cents per barrel.

Now let's see, um, how the value of that forward contract will actually, um, develop in two different scenarios. So scenario A here, uh, on the left and scenario B on the right scenario A is oil has, um, risen and is now trading at $80 per barrel, which now means that the forward contract has a positive value because remember, our trader locked in a purchased price of $76 and 50 cents.

Now the oil price is 80 cents.

So the forward price that we agreed upon three months ago is actually $3 50 cheaper than the spot price is now.

And that means we gained $3 50 of economic values through, uh, this forward contract per barrel.

And because it's 10,000 barrels, that adds up to 30 5K.

Simple, right? Then scenario B oil price has dropped and is now trading at $73 a barrel.

We have contracted to buy oil at 76 and a half, meaning we're now paying three and a half dollars over spot that can be seen as a disadvantage and clearly is from an economic point of view.

So the loss that this contract has caused us, or opportunity cost, if you wish, is $3 50 per barrel.

10,000 barrels is a contract size, hence again, 35,000, but this time negative.

So this example clearly shows the rationale of this statement that we made earlier, and that was the financial derivative is a financial contract that derives its value from the price of an underlying your oil price goes up, value of the Ford goes up, oil price goes down, value of the Ford turns negative.

And of course, the further up we go or the fur further down, we drop the bigger the p and l impact in absolute terms is going to be a next question.

Um, then often is, okay, cool, I get this and let's stick with scenario A here and say, fine, we've made 35,000 uh, dollars through the contract, but how will we actually, um, turn this, you know, p and l there into, uh, cash? How's that gonna work? Well, that depends a little bit on the type of, um, settlement that has been, um, chosen or agreed upon here.

And of course, when we're trading OTC derivatives IE over the counter, that can be tailored within obviously the, uh, legal framework here to the, uh, client's need.

Then we can, uh, discuss with our counterparty what type of settlement we want.

If it's an exchange trade derivative like futures, for example, then we have a standardization.

And that means there is a certain, um, well, there, there's on, there's not much flexibility here because the settlement, uh, type is usually determined by exchange set design, the contract.

But in general, we have two possible ways of settling a derivative.

There's physical settlement, and then there is the cash settlement.

Physical settlement really means we're just going through with the originally agreed upon transaction, sticking with our oil forward.

That means the trader actually buys the agreed upon forward price that was 76 and a half dollars per barrel.

IE in total trader pays 765,000 and in exchange receives 10,000 barrels of oil.

Now if the, um, buyer here in this example doesn't have the need for 10,000 barrels of oil, what they will do to extract this positive p and l is they will sell the 10,000 barrels onto the spot market and realize the current spot price of $80 per barrel.

IE they get 800,000 from selling the oil. They paid 765,000 for it.

That means they have 35,000 left on their account.

We're ignoring transaction costs for simplicity here.

Good, that's physical settlement.

In case of cash settlement, all we do is we just calculate the economic value of the contract, and this value is then being paid or received dependent on which counterpart we're looking at here.

So that means in our example here, scenario A where we said the oil trades at $80 spot, the trader has locked in $76 and 50 cents, three and a half per barrel times 10,000, meaning the buyer has a positive economic value on that forward contract of 30 5K, and the seller is going to transfer that to the buyer, and then the contract is settled.

That arguably is a lot straight, uh, you know, a lot more straightforward, right? So it's a lot simpler.

We don't have to sell the oil and there's no execution risk, et cetera, et cetera.

Um, so one might think that cash settlement actually is a preferred, uh, type of settlement in, in many cases, and I agree with that for most market participants and most derivative users. Obviously cash settlement is certainly the, uh, preferred, um, away, but also, um, it depends a little bit on the, um, original purpose or the use case of der tip. And we're gonna come back to this in a minute, but what I would like to say before we move on is that one thing that we need to make sure when we agree on cash settlement is that we agree with our counterpart, not just that we're gonna cash settle, but we also need to agree at trade inception.

How are we going to determine the economic value? I mean, obviously in our case here is relatively easy to say, well, you know, the, the di the the original forward price was $70, $76 and 50.

But obviously the payout does not just depend on the forward price, but it also depends where the spot price is. And we said loosely that was $80, but where's this $80 coming from, right? So obviously there's not just one oil price a day, there is many, right? I mean, sometimes oil isn't very volatile.

Other days it can actually be extremely volatile. And then the question is, which oil price do we take? Do we take the oil price at 12 o'clock and then which data vendor are we going to use, et cetera. So we need to have absolute clarity, and this is an obviously where benchmarks and fixings and all these kind of things, uh, really come into play and we need to make sure that we have agreement, uh, on those things.

How do we determine the settlement value of which price are we going to use? And that saves a lot of time and potentially a lot of negotiation and, and, and, and things of that nature.

Okay? So that, um, is done.

Now let's move to use cases and explore as to why someone might actually prefer physical settlement. Because you know, arguably cash settlement is easier, um, from a a, a transactional point of view, but it's not always, um, actually the desired settlement type.

So, um, as financial instruments, um, of the normal kind, IE um, you know, many other positions, uh, that we do take, um, derivatives can be used for two reasons, right? For speculative purposes, uh, and then also for hedging.

Now, um, on the speculative side, the idea is obviously that we use derivatives to create or increase existing, uh, positions and with a view obviously of, uh, creating a positive p and l when the price of something moves as expected.

So we're buying or selling financial instruments depending on our, um, view on price.

That's a speculative angle.

And if you use derivatives for speculative purposes, then of course cash settlement is really the easier, uh, option for you.

Um, then we have the, uh, second use case that's hedging.

And the idea of hedging is the opposite, right? We don't wanna create risk positions or, you know, but we're instead trying to reduce or mitigate existing risk, right? And the idea here is that we're taking a position in the market that's the opposite from a directional point of view, um, to an existing position that we want to hedge.

And if you think about our oil, uh, example, uh, then, you know, it's very easy to come up with a, a potential use case here where physical settlement would be, um, preferred.

And that is when you think about, for example, the, um, trader not being, uh, an employee or a portfolio manager of a macro hedge fund, but instead maybe working for an oil refiner.

And so basically what the traders trying to achieve here is actually locking in the future purchase price for oil, which the refiner actually needs to purchase because it's the starting point of their production, um, process, and that's what they need to buy and produce, uh, and, and, and refine into all the higher value components like jet fuel, gasoline, et cetera, et cetera.

So, um, they not only look to lock in the price, but they also need the oil anyway.

So in this specific circumstances, actually physical settlement might be the preferred choice, simply because they don't just want to have a cash payment and then have to go into the spot market and buy the oil.

They actually want to get the oil, they want to use it, and uh, also they want to lock in the price for this future purchase right now.

So in there are clearly, uh, cases in which physical settlement is actually, um, the preferred choice.

Most of these cases, uh, I would say, um, are happening in, in, in a under circumstances where the use case of this derivative trade actually is, uh, a hedging transaction, okay, halfway point.

So time to, um, switch from the generic part to looking, uh, at forwards in a little bit more detail because, uh, as I said earlier, I believe that, you know, it's really important to have a solid understanding of forward contracts as they are the building block, um, for or a building block, um, for anything else.

And so we're now going to revisit, um, the, uh, forward contract. We're going a little bit deeper into the definition. It's the mechanics. Uh, and then we're actually gonna think a little bit about pricing as well.

So here's the definition, we're clear on that, right? It's an agreement to buy, and that is a long position on a forward basis or to sell, that's a short position on a forward basis.

Uh, the underlying, and we agree, um, that there is settlement at a specific date in the future, which we call the forward date.

And then we also agree the price at which we're gonna, um, settle the transaction, and that is, uh, what we call the forward price.

Okay? Now, because we have looked at oil for, um, you know, quite some time, and we want to just make sure everybody's aware that, um, you know, forwards are traded not just on oil.

Uh, here's different examples. So now we're moving into the world of FX because, um, obviously there's a pretty, uh, robust and liquid market, um, for forwards and, and, and swaps and related instruments in the fx, uh, space.

And here, the example is that a trader agrees to buy a hundred million dollars against Euro at an agreed upon price of 1 10 29 for settlement in three months.

First question for those who are not really, uh, have a lot of experience with FX is what does this price actually mean? Euro dollar 1 10 29, uh, that just basically means one euro equals $1 and 10 29 US cents. So that's how you just read the, uh, foreign exchange quote here.

Uh, then the next question is settlement in three months, when exactly does this settlement occur? So let's have a look at this.

And, uh, transaction date shall be today, which is the, uh, 20th of March, 2026, right? Um, now FX transactions, euro dollar for example, still, um, ha settle on a t plus two basis, right? So we haven't moved to t plus one there.

Uh, you know, um, there might be currency pairs that settle on a t plus one basis, but euro dollar still, to my knowledge at least settles on a t plus two basis, meaning that this transaction we agreed upon right now will settle, uh, well, or the spot date at least, uh, for, for a transaction that we do today will be on Tuesday next week, which brings us to the 24th of, uh, March, if I'm not mistaken.

Um, so spot date should be the 24th of March, 2026.

Why is that relevant? Well, because in FX markets and most other forward contracts, it works as follows, the forward period IE the three months timeframe we're referring here to starts counting not from the trade date or the transaction date, but actually from the spot date.

And that means that a three months euro dollar for a transaction traded on the twenties of March, 2026 doesn't settle on the 20th of June, uh, 2026, but instead on the 24th of June, um, simply because the spot date was the 24th as well, then of course assumes that the 24th of June is not a, uh, bank holiday or a, uh, weekend.

Um, so that otherwise we would have to make some sort of, uh, adjustment for that.

But, you know, for simplicity, let's just assume it is, right? And then what would happen at this three month point? Well, this is a physically, uh, settled, um, derivative.

So that means that our trader will receive a hundred million dollars and then will pay the equivalent amount in euros. That's determined by the firm, an exchange rate of 1 10 29.

And that in this case was 90.67.

Now, of course, um, you know, today the dollar is not trading at one 10, it's one 15 ish.

But, you know, um, just for purpose of illustration, that example still works.

Okay? So that is some of the mechanics, some of the cash flows, the timings, et cetera, et cetera.

Now, let's have a look at the forward, um, payoff simply because, you know, we touched upon it before, but it's, it's good to visualize that.

Uh, and here we now move into the probably most, um, uh, intuitive asset class. So we're looking at equities now because that's the easiest way to interpret price moves in my mind.

So, um, let's say we have someone who went long, a thousand shares on a forward basis, 12 months forward to be precise, and the forward price was $75.

Right? Now, we can simply, uh, calculate the p and l, um, for different scenarios at, uh, the, um, forward expiry or at the, you know, forward date.

So assuming the spot price in 12 months is actually $75, then the economic value of this contract will be exactly zero because we have the forward contract where we're buying the asset of $75 per share, and we could buy them in the spot market for the same price as well.

So this forward contract has zero economic value, nothing positive, nothing negative.

So, uh, let's have a look at the scenario where the stock price has risen to $85.

Now, we, uh, are going to buy the stock for $75 through the forward contract, and we could sell it immediately at $85 in the market.

That means $10 per share profit ignoring transaction costs.

And that means because we transacted thousand shares, uh, we have $10,000 profit.

If however, the price had fallen to $60 per share, now we're buying at 75, we're selling in the market at 60.

That means we have a $15 loss per share adding to $15,000 on a thousand share contract, uh, volume.

And of course, you know, if we would increase the scenario to 90 or a hundred or, you know, lower the, uh, price here from 60 to 50 40, and we can easily calculate, um, those sort of numbers.

But we do see that the p and l profile off of Ford is actually this linear, uh, line.

And that obviously means what we said earlier, that they're sort of like pretty symmetrical risk and, um, you know, risk and, and, and, um, and well, uh, reward, uh, profile here for this type of contract and not just for the person that buys forwards or that is long on a forward basis, but also for the counterpart that would be assured in this case, right? This p and l profiles basically all assume no hedging has been done, right? So this is just, um, we, in case of this, uh, profile here, we have sold a thousand shares short and we haven't bought anything back, and then we're just basically writing the short position until the end of the forward, uh, period.

And then we're calculating our p and l based on the scenarios.

And what is, uh, relatively, uh, clear here is that, and this is hopefully not coming as a surprise, that the um, short position here is basically just in p and l terms always the exact opposite of the long position because clearly the seller's, uh, or the bias, uh, profits must be the seller's losses and vice versa, right? It's a zero sum game if we're assuming nobody has hatched anything, nobody has done anything else, uh, to offset.

So then hopefully the p and l uh, profile is very clear, which then leaves us with one last question to answer, which I think probably is the most important one anyway.

And that is where's the forward price coming from? Okay? Because now obviously we're saying so far we have agreed upon a forward price, but what is the forward price and what, where should it be? Should it be where the spot price is? Should there be, uh, you know, should it be somewhere else? Does it depend on expectations? What's going on? And I think it's best to approach that sort of questions through storytelling and, and basically just thinking about a concrete scenario.

So this is what we have in front of us now, um, we ask you to assume that you work as a market maker and uh, you've been asked to quote a 12 months forward price.

Um, it's not on the slide, but I'm telling you right now that the assumption also is there is no forward market to this particular instrument.

So you cannot cheat and look at the screen and, and figure out what the price should be.

Um, instead we have to come up with our own price and we have to think about how one would conceptually do this.

And for that, we have given you a bunch of, um, numbers here.

So you can see that the spot price, uh, of the asset was a hundred dollars.

Uh, our in-house analysts are people that are analyzing stocks, for example, uh, have a forecast that this, um, stock should go to a price of 107 on a 12 months horizon.

Uh, we are the trader in the stock, so we actually have our own views and we are a little bit more bullish than our in-house analysts. So we expect the price of that asset to go up to 109 in 12 months time.

And the client kindly has told us that they are looking to buy this asset on a forward basis because they believe that the price is going all the way up to 115, then we know 12 months interest rates are 5% and the asset pays zero dividends.

Okay? Now, some of you might already know how this works.

Um, others that take a look at derivatives for the first time ever today, um, probably sort of would start to think somewhere along the lines of needs to have something to do with those numbers.

In fact, actually, you know, we might be just saying I trust myself my own skills more than, um, of my in-house analysts. So it needs to have something to do with my own expectation, right? So if we believe now that the asset will trade at around $109 in 12 months time and the client believes that it's going to trade at 115, then it's very tempting to say, well, why don't we just use a forward price of let's say 111, okay? And, uh, that should be still of interest for the client because they believe the asset is going to trade at 115.

So if they buy it at 111 and they sell it at 115, it's still $4 profit.

Also, we believe that the asset is going to go to 109, and that means we believe we can buy the asset in 12 months at 109 and then sell it to the client for 111.

So we make $2 a client is heavy because they're making $4 and everybody's happy, right? And that's fine as long as our prediction really comes, uh, true.

And that is that the asset trades at $109 in the future.

But what if we're wrong? What if we have just, uh, forecast it wrong? We didn't see a scenario, um, you know, happening. And obviously the stock price is not just driven by, you know, the company and it's, you know, idiosyncratic sort of drivers, but it depends on the macro economic environment, right? So, um, maybe there's a risk of, uh, environment suddenly and the stock price drops quite conservatively.

Maybe, um, you know, we we're seeing a a, a huge melt up in equity markets because a lot of asset, uh, you know, money gets distributed across the share market and so prices are, are are going up.

Um, you know, plenty of reasons why our forecast may not turn out to be correct.

And the problem with the strategy that we have taken here is just like, okay, we, we believe we buy at 109, what if we don't buy at 109? What if we actually see that in 12 months the actual spot price has gone up to 120, right? Now we have sold the shares at 111 to our client and we now have to buy them at 120.

That's clearly, uh, not, um, profitable.

Um, then of course we might have the other scenario, right? And that is the spot price has declined and let's say the, um, as it is now trading at 80, which now of course means accidentally we've made quite a large profit because we haven't bought the shares, right? We can now buy them at 80 and we sold them at 111 to our client.

But that's an accidental profit.

That is not a very sustainable trading model, right? And remember we said you are the role of, in the role of a market maker and what is the market maker's role? The market maker should provide liquidity, right? Client wants to get a 12 months forward done.

We are there to provide the client with a solution, but what we shouldn't necessarily do is take a huge amount of market risk, right? That's not, uh, the role.

In fact, we provide liquidity, but we don't do that by taking crazy amounts of market risk that may or may not work out.

So I would say we should, before we quote the price, at least think about how could I hedge this position, right? How could I, even in the absence of a forward market, how could I, um, fulfill my role here? And that is give the client what they're looking for, IE at 12 months forward price, but without exposing the firm I work for to a crazy amount of market risk.

That's really what the question comes down to.

And this is actually surprisingly simple, and I'm not saying this is what traders do all day, right? But it's the mental model that one could use that's very intuitive to explain where the fair forward price actually should be.

And it all starts with a simple question, when is the only point in time where I know where spot price is or where, where, where the price of this asset is? And the answer is right here, right now, because I know that the spot price of the asset is a hundred.

I can see it on my screen, I know I can buy it.

You, let's say we see the order book, there's enough liquidity.

I can buy this asset at a hundred dollars right here, right now, and that's one thing I could do, right? To hedge my risk. Now I know where the price is.

So the first thing I do is I buy the stock at a hundred.

And that's a spot transaction, right? Meaning depending on, you know, your jurisdiction t plus one or T plus two, something happens and that it's a settlement of this spot transaction.

So let's say t plus one, right? And uh, that means we buy today and on Monday we get the stock, but we also have to deliver a hundred dollars.

And that brings us into the question, do we have a hundred dollars lying around answers? Of course not. Money's always working hard generating profits.

So what we can assume here, in order for us to be able to pay a hundred dollars, we need to borrow a hundred dollars.

That's, you know, maybe not externally, maybe from other parts of the bank, but you know, we borrow money and that means we have to pay interest.

And which interest do we have to pay? Well, that depends on for how long we're gonna borrow the money.

Now, if we're looking at this from a timeline point of view, this is today and this is the 12 months point.

Now, if we're entering into this transaction, uh, uh, you know, by stock at the spot, we have the stock coming in, uh, on Monday, and we then have to pay a hundred dollars.

Now, when are we gonna get the money? Well, when the client pays for that at the 12 month point.

So they pay us a certain amount of money that we need to determine, and then we're giving the stock to the client.

So here we have the stock and we pay it out there.

So stock is neutral, and then we have a hundred dollars going out on Monday, and we now need to solve the question how much money needs to come in at the 12 month point, right? We can calculate that because we now obviously have to borrow the money for a 12 month period because we need to pay on Monday and we will get paid 12 months later.

That means we need to borrow the money for a whole one year period.

And that's why we have given you a 12 months interest rate here.

So step two, borrow a hundred at uh, 5% and then for a whole year.

So again, we're ignoring Daycom convention and all that kind of jazz.

That means in 12 months we have to pay the money back, that's a hundred and we have to pay 5% interest for a whole year.

That means we have to repay in total $105.

And that means the fair forward price should really be $105 because if we now get $105 in 12 months from the client, then we are perfectly hedged. We have not incurred any costs because we bought spot, we borrowed the money and we need to repay the money plus interest at the 12 month point, and that is equaling $105.

And if the client pays at this, we have facilitated the for trade at zero cost for ourselves, we pass the cost of borrowing the money that was required here onto the client, and therefore the client is happily paying 105.

Now, of course this means if we quote 105 flat, we haven't made any, um, money here.

In reality, of course we're gonna put a bit of a spread around it. So a hundred four fifty, two hundred, five fifty for example.

And that is then of course, meaning we're sort of extracting, uh, some compensation here for our services.

So that means in this case, fair forward price would be 105.

And interestingly, you kind of start to realize that it has a lot to do with the 12 months interest rate. And if we put this in this example, not at 5%, but let's say at 7%, then the fair forward price would be 107.

If it was 10%, it would be 110 if it was 2%, 102.

So you start to see that obviously the fair forward price is pretty dependent on the level of interest rates, but at no point in this calculation have we actually considered anyone's expectations, right? So bottom line forward prices are not driven by expectations.

They are basically the result of what we call a cost of carry adjustment.

So we are basically thinking how much does it cost to take a position and then carry this position for the forward period.

And that's why the whole thing is called cost of carry approach.

Now, before we see this on the next slide as a sort of conclusion, um, I want to introduce one more thing and that is what happens to the forward price if now, uh, one of the um, uh, assumptions changes and that is that the asset pays no dividend and instead we say the asset pays a $6 dividend, right? So how does that change our, um, fair forward price? Well, basically the first step is still buy this stock, right? And we're buying this at a hundred.

Then the second step is borrow 100 for 12 months.

And the third step, and this is sort of assuming, you know, for simplicity, I'll just make the assumption here that this is 12 months and then literally the day before we get the $6 dividend, right? So, uh, it's a nice simplification here.

So basically what happens then is we are borrow a hundred for 12 months at 5%, meaning after 12 months we still have to repay 105, but we also receive, uh, $6 dividend.

And that now means that the client doesn't have to pay us 105, um, because the client has to now pay us only $99 because well, we borrowed a hundred to start with, then we have to repay 105, but we get $6 from holding the stock that pays a $6 dividend.

And so to get from, uh, six to 105, all the client needs to pay is 99.

And sometimes it's a bit kind of surprising and, and, and people struggle with this and saying, why do I pass on this dividend, uh, to the client? Why do we not just keep it? Well, you know, of course, fair question, but um, think about it as follows, right? We're not the only one that gets asked for a price.

So, um, yes, we can try to keep the dividend and quote at 105, but of course if some of our competitors quote 99, then um, you know, we have a, uh, we have some relationship fixing to do, right? Because that's not, uh, really good practice.

And um, so we need to factor these things in accurately.

And as we've seen, right? If we're passing on our funding costs to the client, then it's just fair that we're also passing on any benefits This, uh, holding this position gives to the client.

And that is bringing us back to the concept of the cost of carry.

So forward prices are not primarily driven by expectations, but instead they're just spot prices adjusted by the net cost of carry.

And we've seen that in our equity example here.

There are components that increase the forward price relatively to the spot.

This is the interest rate we've been talking about.

And then there are components that decrease the forward price relatively to spot.

And this is the asset yield, which in case of stocks is a dividend.

If we do not talk about equity forwards, but instead we're looking at forwards on a bond, for example, while we still have to buy the bond, we still have to borrow the money, we still pay interest.

But now the asset yield is different because it's no longer a dividend.

But now we're talking about coupons or accrued interest.

So that brings a forward price down.

Then we have currency forwards, right? FX forwards, uh, where we can, uh, start by buying a currency that the client wants to have delivered 12 months out, for example, today.

Um, meaning that we have a currency amount that we don't need, so we're gonna invest it in the money markets for 12 months. That generates interest income, but we also have sold the currency, which most likely we have to borrow.

So we are paying interest on that, and that is then obviously the funding cost.

Uh, commodities is always a little bit special here because, um, they're physical, uh, existing goods. So if we go back to our oil example here and we wanna facilitate that trade, we could of course buy the 10,000 barrels of oil in the spot market. That means we need to pay interest on the amount of money we need to borrow.

We also need to store the oil somewhere.

So we have to actually pay storage costs.

We need to then transport the oil from where we get it to where we wanna store it and back.

And that's then basically transportation costs.

We might wanna ensure the whole thing.

Um, and so more than one, uh, price easing, uh, price increasing component, but actually no yield, uh, that is produced simply because you put 10,000 barrels of oil in storage.

Best case you get 10,000 barrels of oil out.

So that means dependent on the asset we have, um, certainly sort of specific mechanics we have to consider specific, um, components, but what they all have in common, we need to think about funding costs and then think about the benefit that holding the position gives us over time.

And with that, we come to the final part where I said, as you know, as I mentioned earlier, we're gonna have a brief look at options just as a transition, um, away from those linear derivatives, forward swaps to the world of options. And we are gonna have a whole session on options, uh, later in the year.

So we know what an option is, we have defined it, we know what a call is, we know what a put is, we know the risk asymetry, but here's a payoff profile that visualize that very nicely and this time, mm, we have actually given you the premium as well.

So this is our 12 month call option, $105 strike price, and the premium is $7 90.

Meaning if in 12 months time, uh, the asset trades at a price of 105, we are in indifferent whether we should exercise the option or whether we should just walk away.

So let's just say we're gonna walk away, uh, let's the option expire.

And then you might argue, well, this doesn't cost us money, but that's not entirely correct because the option premium is not a safety deposit or anything like that.

It's a price you pay for getting the option in the first place for getting the right.

And when the option then expires, the premium is gone.

So 105 is a price in 12 months from now. That means we walk away, we let the option expire, but we're not getting our premium back. That means we have lost $7 and 90 cents.

We ignoring time value of money here for simplicity, right? If however, the op uh, the underlying price is going up to 110 for example, that's when we start exercising the option because it has a a positive economic value for us.

So we have the right to buy at 105, we can sell at 110 in the market. That means we're making five bucks per share.

Problem is we paid $7 90 per option and that means we're still down, but now we're only down $2 90.

And then at 112 90 we're reaching breakeven because in that scenario, the option is gonna pay us $7 90 economic value and that's exactly what we paid for the premium.

So we're breaking even and everything beyond that, we are in positive territory.

And then, um, if we compare this with a Ford that was struck at 105, that will have also positive, uh, zero value at um, 105, but this time we didn't pay a premium for it. So the p and l of a forward contract will in fact be zero.

At 110, it will po positive five at a hundred and um, 15 it will be positive 10.

And you see this linear line that we've drawn earlier.

And so it does, you know, um, look like the, uh, forward contract actually is, uh, very, very, um, or is outperforming the option, um, in these scenarios. And that's true, right? Because we haven't paid the premium in case of the asset price rallying.

Um, we will be better off with the forward contract.

Um, but of course, you know, that's only one side of the coin because what we haven't looked at is what happens value wise, um, in case of a price decline or a price being below the forward, um, price.

So what happens at a scenario of a hundred, for example, well, the forward is having now a negative value of $5.

The option still has a lower um, value because we are losing $7 and 90 because of the option premium.

So yes, still the forward outperforms, uh, the option, but we then also see that once we fall below a specific price, and that is 105 minus $7 90, we sort of reach the point where the forward starts to underperform the option.

So there are market scenarios in which it would've been better to choose the forward contract.

There are market scenarios where it would've been better to choose the option.

And I think here is really, uh, the obvious point.

The nice thing about an option in comparison to the forward contract here, at least, that the way we look at it at this moment is that when you go along a call option and you pay the premium of $7 90, that's the maximum loss that you can occur.

Always assuming obviously we haven't done anything else.

So worst case we walk away, we let the option expire, the premium is gone, but we won't lose more if we go along the forward.

And then let's use a real extreme example and the, the asset crashes to a price of zero.

We've lost $105.

If we bought a call option paid $7 90 for it, the same scenario happens.

We have only lost $7 90.

So obviously it really depends, uh, on what you think is gonna happen and on what scenario is going to play out.

And then just to complete this overview, this is a long call we have just looked at.

Uh, and then obviously if we're, um, doing the send that we did before when we were looking at forward contracts, we wanna know how does the p and l profile of the counterpart looks like IE the person selling this call.

And again, we're assuming no hedging, nothing has been done.

Then of course it's just the flip side of um, the long call simply because also here applies that the buyer's losses needs to be the seller. Us, um, as the bias profits need to be seller US losses and vice versa.

So best case seller office call option can earn $7 90.

Worst case they can lose a lot of money, right? And then, um, because we've just looked at calls so far, now let's, uh, look at the put side of things.

Remember, puts are the right to sell the asset.

And that means now we're just having the complete opposite directional risk.

And when a call gives you, um, you know, profits when the asset price moves up, a put will give you profits when the asset price goes down because we're having the right to sell.

So if the asset trades at a hundred, for example, we are gonna exercise our put with a strike of 105 because that gives us the right to sell at 105, we can buy the asset back at a hundred and we're extracting $5.

So this is why the, uh, put basically starts to generate positive economic value.

Um, when we are falling below the strike price, it's not positive p and l straight away because again, we're paid a premium for it.

Um, but at some point we're reaching breakeven as before.

And then last but not least, the fourth box here.

Short put again, just the flip side of long put under the assumption, no hedging, nothing else has been done.

And with that, we've reached the end of today's session. That's all I wanted to share with you here today.

Thank you so much for your participation. Hope you found it beneficial.

Remember in the feedback form you can ask follow up questions. All questions that have come up here in the q and a have answered as we went along.

Uh, thanks for those by the way, and have a great Friday, a great weekend, and I hope to see you again or have you on board and one of our, uh, following sessions very, very soon.

Take care. Bye.