Hi there. Good morning. Good afternoon, potentially. Good evening everyone. And everyone, welcome to this Felix live session, introduction to Derivatives.

Now, my name is Thomas Krause. I'm head of financial products here at Financial Edge, and I have the honor to take you through today's session.

And then, of course, let's first address the question what exactly we're going to cover today.

This is an introductory course, and that means we are going to start with the definition of the term financial derivatives.

We are then going to introduce the three basic types of derivatives.

We will then discuss some of the generic aspects like, for example, cash versus physical settlement, how to use derivatives for hedging versus speculation, et cetera.

And then we're gonna zoom in a little bit and have a more detailed look at forward contracts as a really critical building blocks that are necessary to really understand the dynamics of all the other types of derivatives. And then towards the end of the session, we will have a brief look at options and what makes them so special as well.

But then without further ado, I'd say we start with today's content.

And as I said, we're going to start with a definition.

And I would say that, you know, the, the, the general definition that you find for financial derivatives, because we're not talking about the mathematical type here is somewhere along the lines on the definition that we have included here on the slide in front of us.

And that says that the derivative is a type of financial contract, which means there's two counterparties here, sometimes referred to as buyers and sellers, other times as payers and receivers, et cetera, depends on the type of derivative that we're talking about.

And they form a contract, they agree upon a, a particular contract, and that contract may or may not have a value.

And that value is then going to be dependent on the price of another financial asset, which is then generally referred to as the underline.

So,mwhat underlyings are generally possible here, the answer is a fairly significant range of different types of underlyings are possible.

We see here two sort of groups on the slide.

On the left hand side, we've listed the more traditional asset classes, the traditional underlyings we should say.

So for example, you can have derivatives where the underlying i.e. the value driving component are interest rates.

That could be short-term interest rates, could be long-term interest rate, interest rate swaps, interest rate futures, things of that nature.

The underlying could, rather than being an interest rate, also being the price of a particular bond.

Bond futures come to mind here, but we could also obviously see derivatives on very different underlying that are the equity derivatives based, for example, altogether where the underlying is the price of a single stock of a bespoke basket or of an equity index, we can have credit derivatives where the underlying is a credit spread either on a single company level or as well on an index level.

We have currency derivatives where the underlying will be naturally a currency pair and then commodity derivatives where commodities are e real existing physical goods will be the underlying. And that is probably true to call those sort of derivatives the first generation, because this is where the derivatives business certainly started. However, what we've seen over the last couple of decades is the fact that we had more and more market factors also becoming the underlying. And these are sort of, you know, a little bit more abstract in the sense that these are not real existing financial instruments like a stock or a bond, for example.

But they are sort of more abstract things like, for example, volatility.

And this is where, for example, the VIX comes to mind, which is the volatility index.

And we're trading derivatives on the level of the vix, for example, vix futures.

Then we have derivatives where, you know, the value of the contract is sort of driven by dividends being paid or not being paid, or the actual amount of dividend being paid by specific companies.

We have inflation derivatives where payouts are linked to evolving inflation levels, et cetera, et cetera.

And of course, you know, this is something that's probably still less traded in volume than the traditional asset classes.

But of course we can see a lot of use cases and a lot of people potentially being interested in the derivatives contracts on those sort of market factors.

Now, in general, what I think, and I've been sort of like already leading, leading into that sort of question of the use cases.

I think one thing that becomes obvious when you're looking at the numbers that we have displayed on the slide here at the botto one thing that becomes clear is that certainly there must be a lot of attractiveness or a lot of use cases for derivatives being used. Because if you just kind of compare the numbers here, and we're showing on the left hand side here, the actual market capitalization of global public equity markets at the end of 2022, that was 101 trillion, then the global public debt market volumes in 2020 2, 230 5 trillion.

And then we're looking at derivatives volume.

And the way we're looking at them here is the Underlying notional amounts.

And that was at the year end of 2023, only looking at the OTC market.

So not including exchange traded contracts, 618 trillion dollars.

And then, of course, is not a like for like comparison, simply because, you know, a notional amount doesn't mean that this amount has been completely invested. So what this number here doesn't mean is that $618 trillion of cash have been invested in derivative contracts.

But what it does mean is that contracts with a total notional amount of $618 trillion have been traded. And that points towards the fact that derivatives are extremely popular.

And that will always be the ca or will only be the case if there are some advantages of using those specific type of financial products.

And we're gonna see some of these advantages as we go through the content of today's session.

Right? So this is the general introduction.

Now let's have a quick look at those three basic type of derivatives because one thing that, you know, I always found a little bit dis unsatisfying about this general definition that I started this presentation with is, yes, it's correct.

It's, there's nothing wrong with it, but it is possibly a little bit abstract, right? So if this is the first time you're looking at derivatives, then this definition I gave you, and that's a financial contract. And the value of this contract is linked to some to the price of some financial asset that's not necessarily telling you exactly, you know, you, you're not much more familiar with how derivatives work in particular after I've given you this definition.

So the best way to really get your hands on the concepts of derivatives is then just looking at concrete examples. And that's what we're gonna do right now.

And we have split the slide into three columns here.

And each of these column addresses a certain type of derivatives. And we're starting on the left hand side with forwards and futures. Now, you might argue these are two types of derivatives, but I would say that they are more or less identical in terms of how they work.

The only difference between forwards and futures is that futures are exchange traded contracts, whereas forwards are traded in the over the counter market.

That basically means that in the OTC market, IE forward contracts counterparts can almost freely within obviously legal boundaries determine the details of the trade.

Whereas when you do use exchange trader derivatives, the offering exchange standardizes the terms of the contract.

So you will just have to accept certain features if you want to use a specific features, um, contract.

But let's look at sort of the specific definition.

What is actually a forward or a futures contract.

It's the agreement to buy or sell the underlying asset. That could be, as I said, a stock, a bond or a currency or whatever.

And, we're having a couple of differences regarding a normal spot transaction because, you know, you could argue the spot transaction is the agreement to buy or sell a financial asset, but the forward differs from spot in the sense that whereas the settlement date is also agreed upon. So we know exactly at which date this transaction is gonna be settled.

The difference between forward and spot then is at the exact point in time when the settlement occurs, because spot transactions settle at spot, that is usually t plus one, T plus two, T plus three, depending on the asset and, and on the jurisdiction you're in.

And, forward contracts have in common that settlement happens at a point in time after this spot settlement debt, it could be three months out, six months out a year, 20 years away from now.

Those are all possible forward settlement debts.

Now the second thing that we need to know about forwards is that not only the settlement is agreed upon at the time of trading, but also the price at which the transaction will take place is determined at the point of trading.

So a three months forward let's have a look at an example here that shows right at the bottom, a three months forward works like this.

Here we have a trader that agreed to buy 10,000 barrels of oil, um, and settlement should be three months, and the agreed upon forward price is $76 and 50 cents per barrel.

So what that basically means, the transaction is made today, we agree on those terms today, and then three months later we're gonna exchange the dollars for the irrelevant amount of barrels of oil.

Now we're gonna use Fords and Futures over the next couple of slides to really delve into some of those kind of general derivatives mechanics.

But before we do that, let's just, um, complete the slide and just have a very quick look at swaps and options as well.

Just giving a quick introduction to those terms here. And we're gonna go right over to swaps. And here's a bit of a challenge because there's many, many different types of swaps. There's interest rate swaps, curse currency swaps, FX swaps, credit defaults, commodity swaps, and so on and so forth.

And they all have different underlyings obviously, and they all work ever so slightly differently.

So it's actually very challenging to come up with a very short definition that does a good job, you know, defining all these sort of swaps in just, you know, one or two sentences.

But there's one thing that all those swaps have in common, and that is that they are agreements to exchange two streams of cash flows.

Now, if you think back to the forward contract we discussed just a minute ago, the contract worked in a, or was actually a, a, a one-off, um, exchange of payment versus goods, right? So the three months oil example here was in three months we're gonna pay $67 and 50 cents per barrel and we're gonna get the barrel of oil.

And then after that, the contract is done, it's been fulfilled, it doesn't no longer exist in case of a swap, we have usually multiple exchanges over a certain time, um, period.

And usually, those payments happen on a regular basis and at least one of these streams of cash flows is usually not known in its entirety at the inception of the trade.

So there's often one payment stream that is known already, but the other one isn't. That then depends on, you know, developments of particular prices of assets, et cetera.

And a good example to look at simply because interest rate swaps are in terms of notional and trading activity, probably the most actively traded type of swap there is in the world.

Let's have a look at one of these, um, type of swaps. And here is the example you find that in the red box at the bottom is that a trader agrees to pay a fixed rate of interest, and this fixed rate is determined at trade inception, and that was 4% at the time.

So our trader will pay a fixed interest rate of 4% per annum to their counterpart.

The notional amount, IE the amount we're calculating the interest rate on was a hundred million dollars.

And this swap was agreed over a five year period.

So that means over the next five years, our trader will pay 4% on a hundred million dollars and this payment is gonna be made as per market convention generally once a year.

So at the end of year one, year, two, year, three, year four, year five.

And if we simplify not take the account con conventions into consideration, then that would be $4 million per year our trader pays to their counterpart.

Now what do they receive in return? The underlying rate here determining the payments of the lack that our trader is going to receive is a floating interest rate that is known as fr secured overnight financing rate. It's an overnight repo linked financing rate in for US dollars that is set every day.

And these contracts work in a way that generally, although the rate is reset every day, we don't have daily payments, but we may have also an annual payment here on the on, on on the floating lag as well as we call this.

And so basically what would be happen is over the next year or so, we're gonna look at where the sulfur generally, um, is, is gonna be fixed, and then we calculate an average more precisely a compounded average rate.

And then we compare that to the 4% fixed. And if, you know, our trader pays 4% fixed and is supposed to receive a 4.1% floating rate, then of course we're gonna net the payments. There's just gonna be a net payment of 0.1% from the counterpart to our trader here.

But the general mechanics are, we know we have to pay as a trader here, 4% IE roughly 4 million every year.

What we're gonna receive will depend on the future fixings of so OFR over the next five year period. And that of course depends on the economic environment, on what the Fed is gonna do with interest rates, et cetera, et cetera. So that is a quick introduction into swaps.

And then I said, um, earlier that in my mind or in my view, there are three types of derivatives. However, if you ask other people they might just say there's two types of derivatives. And the reason why they say this is that they would normally group towards futures and swaps into one category.

Much like I've done it with forwards and futures.

And the reason why they might wanna do this and what obviously forwards futures and swaps have in common in terms of features is that forwards futures and swaps are obligations for all counterparts involved, right? So here in the case of our forward contract, our trader cannot decide not to take the 10,000 barrel of oil delivery and pay $76 and 50 cents in return per barrel just because the oil price has gone down. For example, they are contractually obliged to go through with this trade to pay $76 and 50 cents per barrel in three months time and take the 10,000 barrels of oil as delivery.

In our swap example, our trader can also not decide to no longer make this 4% interest rate payment.

They are contractually oblige to pay a 4% fixed at the end of every year to the counterpart on an amount of a hundred million dollars.

Now, that doesn't of course mean that both counterparties cannot agree on terminating this contract earlier.

That is an entire different topic.

But if the other counterpart doesn't agree, then you know, every counterpart has to go through with their contractual obligations.

And that's what those three types of derivatives certainly have in common.

And this is also where options fundamentally differ.

And if you look at the definition here of options, then what what says is that an option gives the buyer of the option the right to buy or to sell depends on if you are having a call option or a put option.

The underlying right, and this is the fundamental difference, the forward gives you the obligation to buy the underlying.

Um, if you are buying on a forward basis, if you buy a call option that gives you the right to buy, the underlying.

And of course we need to also have a little bit more, um, things to be discussed around this option.

So an option doesn't just give you the right to buy something, but, but it needs to also set the price at which you are having the right to buy it. That's what we call the strike price.

And also options usually have a sort of specific expiry date. That means the right when you then buy it will only be yours for a specific period of time.

And that is the expiry date, as I said, or the time to expiry of the option.

And now if we're looking at the simple example here at the bottom, what we see is that we have a trailer here who bought a three months call option on a stock that currently trades at a hundred dollars in the spot market.

The strike of this option was $105.

So what precisely does this mean? Our trader here now has bought the right to buy the underlying at a price of $105 over the next three months.

If they don't use this right in the next three months, this right will expire worthless and just stops to exist.

Now, of course, um, having the right to do something generally very intuitively feels better than having the obligation to do something right? And this is why options are fundamentally different because when would we use this, right? When would our trader use their right? Well think about a couple of scenarios, right? What if the underlying price in three months trades at $110? Naturally, I would then use my right to buy the asset at 105 because that allows me to buy the asset at $5 less than where it currently trades. So the economic value of this contract at that point will be $5.

If however, the asset had,gone down in price and now trades at let's say $90, I will not use my right to buy it at 105 series the option.

I would just simply walk away, let the option X expire a worth list, and if I still want to buy the asset at the price of 90, then I can do that in the spot market.

If that was a forward transaction though, I would have to buy the asset at 105.

And this is where obviously the option has some extra value over a forward contract because it allows you to step away.

And that's where we are already seeing that something must be fundamentally different between forward and future contracts when it comes to the price and et cetera.

Simply because they are very different from a risk reward, um, perspective.

And also we can just think about this difference, um, by looking at the option seller because where's the option buyer has the right to do something, the right to buy. In this particular example here, the option seller doesn't have the right, they have the obligation to sell the asset if the, um, option buyer wants to buy, right? So in case the asset trades at 110, the option by our exercise is the option buys the stocks at 105, the option seller has to deliver the stocks for 105.

If however, then the price of the asset had declined and the option buyer walks away, then the option seller doesn't have the right to claim $105, for, you know, the stock, simply because they have only given the right to the option buyer to exercise the option, not the obligation. And then when you look at this, um, then it's, it's immediately clear that being long, the option IE buying it on the face of it in direct comparison feels a little bit more, um, attractive than selling the option, right? Simply because if you're buying the option, you have the right and you decide whatever is best for you, if you're selling the option, it will be decided for you.

And then obviously as we've said, you most likely you know, to have the option exercised against you if it is a disadvantage for you.

So if there wasn't any adjustment, then I would argue there would be a lot of interest to buy options, not so much interest in selling options, right? And that would mean there wouldn't be any option markets simply because if there's only buyers and no sellers, then no transaction would ever happen.

So how can we incentivize people to sell options to take this on the face of it at least less attractive side of, of the trade? And that is done by something we call the option premium.

So other than forwards, futures and swaps, when you buy an option, you will have to make an upfront premium payment. Sometimes you pay at expired, but generally speaking, you will have to make a specific premium payment that is a price you pay for having this right for a specific period of time.

That's a payment you're making right now and that you're not gonna, reco or get back. This is not a deposit, this is actually the price you pay, um, for the option.

So if that option was costing, for example, $7 and 90, then that's what we need to put on the table to get this option.

And then after three months, if we haven't used it, it's just gonna expire worthless and we have lost our option premium of $7 and 90 cents.

And then of course the option seller is or can keep this option premium as a reward of having sold, the option more on that at the end of the session.

So what I wanna do next is I want to just go quickly through those couple of important mechanics and just highlight, um, using our forward example from earlier, how derivatives work from a a structural point of view.

And the first thing I want to highlight is just how intu or the intuitive link between the underlying price and the value of a derivative.

And you know, remember that was basically slide one, the initial definition of a derivative.

So, but how can we understand the link between the value of a derivative contract and the price of the underlying? And we're using, again, our forward example here.

We're looking at our three months, um, forward contract on oil.

We are the trader now we agreed to purchase 10,000 barrels of oil at a price of $76 and 50 cents delivery will take place in three months from now.

That's at inception. Now let's fast forward three months.

So we're now at expiry date and let's have a look at three scenarios.

Scenario one market price of oil now is at $80 per barrel.

We are feeling good because we have locked in, um, lower oil price.

We are gonna buy our 10,000 barrels of oil at 76 and a half dollars per barrel.

That compares to a market price of $80 per barrel right now.

So we're $3 50 better off, um, per barrel.

And because we have a contract volume of 10,000 barrels, we have a gain or a market value of positive value here of 35,000, um, dollars right now.

Scenario number two is that oil price has dropped and we're not trading at $80, but we're trading at $73 per barrel and that is $3 50 cheaper per barrel than the price we locked in our forward contract.

So now in comparison to the spot market, we're worse off 'cause we locked in a purchase price of $76 and 50 cents, whereas the market price is $73.

And that means we're losing in comparison to the spot market, three and a half dollars per barrel times 10,000.

So now we have a loss of 35,000 dollars and that's at least a zero theoretical value of our trade.

So basically we entered into the trade, then the market price of the underlying has changed and we have calculated the value of our full port contract for two different scenarios had expired.

Now prior to expiry, then of course the calculation might be a little bit more complex, but generally you can see how the value of a derivative, the final pay if you wish, is linked in this case to the price change of the underlying which was the barrel of, right? So next question then is how can we, if we have this positive or negative value, how can this value then be extracted or realized? Right? And that's sort of then brings us to the question of how derivatives generally can be settled.

And there's two types of settlement.

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

And one thing, um, just before we go into each type a little bit further is that of course when in the OTC market, then generally, as I said, within legal, within the existing legal framework counterparties can pretty much decide, um, which terms they want to agree on.

And so in OTC there is often you can sort of, at least within certain, um, boundaries choose between physical and cash settlement.

However, when you're thinking about exchange trade derivatives, then the type of settlement is generally standardized by the exchange.

But, that, just as a side note, now let's have a look at physical versus versus cash settlement, physical settlement. What did we mean by that? It just basically means that we're going through with the originally agreed upon transaction.

Going back to our forward example one more time.

Trader agrees to buy 10,000 barrels of oil, add an agreed upon forward price.

That means at expiry, three months after the trade has been initiated, our trader will actually take 10 delivery of 10,000 barrels of oil and we'll pay $76 and 50 cents per barrel in return for it.

So this is really the physical exchange of cash and, um, purchased goods.

Now of course then the question is if I want to, um, realize my profits of $35,000 that I made as a trader, how can I do this? Well, you bought oil at $76 and 50 cents.

It currently trades at $80 in the spot market.

So why don't you just sell the 10,000 barrels that you bought at a lower price for the higher price And if you managed to sell all 10,000 barrels of oil at $80, you bought them at 76 50, you now get 80 per barrel.

So you get 800,000 for selling your oil, you paid 765,000 to buy it in the first place.

That means you have now realized the profit of $35,000 we're ignoring transaction costs and, and slippage and all these sort of things for simplicity here.

Alright, so that's the physical settlement. How would cash settlement work? Cash settlement is just basically, um, exchanging the economic value of the contract.

And you know, on the previous slide we've done the economic value calculation.

We looked at the value this contract has for the buyer and um, you know, this is then basically just in cash case of cash settlement. All that would happen at expiry is the exchange of this economic value.

So in our example, and we're looking at the $80 scenario here, um, that means the forward contract had an economic value of plus 35,000 for the buyer.

And that's then basically gonna settle by a payment from the seller to the buyer equaling $35,000 because that was the economic value at that point.

If we look at the other scenario, oil now being at $73 per barrel, then $35,000 would have to be paid from the buyer to the seller.

So this works in both wakes.

Alright then let's think a moment about the question.

What would I prefer, right? If I can choose between physical and cash settlement, which one would I use? Is one better than the other? And the answer of course is depends, and it depends a little bit on what your use case is.

So you can think of maybe someone that is using a derivative to hedge, um, and that would basically mean they want to reduce in existing risk or mitigated away.

And the general concept of hedging is you know, defined here or even described at the bottom of slide here is you, you build a position that is basically having the opposite directional risk, then an existing position and then, you know, profits in the hedge transaction should offset losses on the, you know, general existing risk and so on and so forth.

So that's a general hedge for you.

But you know, let's bring this back to our thought example.

When could this transaction our trader did, for example, be a hedge? Now think about this trader may be working for as a commodity straight as for a refiner, for example.

So a company that is going to buy oil and then take this oil, put it in the refining process and crack it up into this higher value components, jet fuel, you know, gasoline, et cetera, et cetera.

And of course, you know, then oil is one of the main input factors into their production process.

And so they have obviously an exposure to oil and will be potentially damaging to their margins if oil prices were going up.

So they might consider, um, you know, hedging this risk against rising oil prices by buying oil on a forward basis.

So instead of hoping that oil prices gonna stay where it is, and then buying it at whatever market price available in three months, they can lock in these purchase price for oil in three months already today, did that at $76 and 50 cents.

Now let's fast forward to three months.

Do they want the oil is the question? And in case of a refiner, the answer could be yes, they want the oil because they need the oil anyway to start their production process.

So then if it was a hatching transaction, like we have just discussed, you could see as to why sometimes, you know, in those transactions, the clients or the users are looking for physical delivery simply because they need the underlying, um, and they want to have it anyway.

So then physical delivery for them might be the best choice.

If, however, that trade was done from a speculative point of view.

So now we're not a trader working at a, you know for a refining company.

But let's say we are an oil trader, we're a commodities trader working for a macro, um, you know, portfolio manager, then of course we're not buying the oil, um, because we're planning to, you know, refine it into other components.

But we are buying the oil because we have the view that oil prices are going up and if our view turns out to be correct, we want to extract positive p and l from that transaction.

And of course, when this is the scenario we're looking at here, then hopefully it's intuitive to see that this sort of, I guess motives would generally lead to cash settlement being preferred simply because we don't have the infrastructure maybe or the necessary experience to deal with taking delivery of 10,000 barrels of oil. Because remember, we're not talking about financial assets here. We're talking about real existing physical goods that needs to be transported, stored, et cetera, et cetera.

So in this case, cash settlement might just be the preferred choice because then we get the economic value, no need to deliver or take delivery of the oil and then sell it to someone instead. We're just getting the $35,000.

So both, um, you know, physical and cash settlement are generally possible.

Sometimes physical settlement is not really working if the underlying, for example, is one of those market values we have, um, discussed earlier.

So for example you know, the VIX coming back to that is, um, you know, just a mathematically derived number that's gonna be impossible to physically deliver.

So VIX futures will by nature be cash settled and inflation contract, um, as well.

But you know, if we're thinking about the traditional asset classes for example, then physical delivery of a bond of a stock are entirely possible.

Um, but it really depends on what the use cases are, which type of settlement is generally, um, being referred.

Okay, so now, um, let's dive a little bit deeper and have a look at the forward contract in more detail.

But now we are gonna, you know as I said, have a closer look at the mechanics.

So we already know what a forward contract is, right? Agreement to buy, and then we're long or to sell, then we're short the underlying at a specified date in the future, which is called the forward date and the price that we agreed upon, add trade inception and that's what we call the forward price.

You know, or if it was a future, the the futures price example.

Now we're moving away from commodities, we're looking at foreign exchange here in this particular, on this particular slide.

So we had trader here that agrees to buy a hundred million dollars against Euro.

So they are selling euros, buying dollars, add an agreed upon a forward exchange rate of 1 10 29.

That's one euro is $1 and 10 29 cents.

And this is a three months forward contract.

And the first question is, when exactly will this forward contract be settled Three months from today, IE 21st of June, 2025, assuming this is a good business day.

And the answer is most likely not because forward periods IE three months are usually then added to the spot date, not to the transaction date.

This transaction date is today spot, however, and euro dollar settles at a t plus two convention.

So settlement for a transaction done today in the spot market will be Tuesday next week.

And whatever date that is, we then add three months to that and that will be the settlement date of our three months forward transaction.

Assuming once again, that's a good business day.

So basically trade agree today, price agree today, but then Tuesday plus three months, we're gonna deliver a certain amount of dollars here as, oh, sorry, of euros.

And that's driven by the exchange rate. We've done the calculation here for you, it's 90.67 million euros.

And then we're gonna receive our a hundred million dollars that we, um, were planning to buy, and that's the general mechanics, um, and date conventions of a forward contract here. Then have a very quick look at the p and l profiles, um, of a forward contract.

And we're now switching to equity simply because it's the most intuitive asset class when it comes to p and l calculations.

So just want to be able to focus really on the lines rather than having to think, am I long dollar, short dollar? And what does the exchange rate mean? So let's go to equities.

And the scenario here is that we had a client who entered into an equity forward contract and they bought the shares forward and in total a thousand shares, although that's not entirely relevant here. For our example, the forward price agreed upon was $75 and the forward period was one year.

Now, what we're doing on the graphic here is we're just looking at different scenarios and looking at the p and l here that our client would, um, realize under certain scenarios. So $75, what is the p and l if in 12 months now from now, the price of the underlying is $75? Well, the answer is the p and l is gonna be exactly zero because they are, they have locked in a purchase price of $75.

If in 12 months the price still is at $75, then the economic value of the forward contract is zero.

However, if the underlying share has gone up in price to $85, then of course now the economic value of the, um, contract is positive because they're buying the shares at 75.

They could sell them immediately at 85, which means they have made a profit of $10.

And if we're looking at the other scenario here, decline of the asset two $60, then of course this would have been a loss because now the economic value of the contract is negative, they are buying at 75, but the asset they're getting is only worth 60 in the market.

So minus 15 here as a loss. And then of course, we can calculate this for many other different scenarios.

And the result is we can connect all these dots and that gives us this linear line.

And that's why, you know, sometimes these products are referred to as linear derivatives, sometimes delta one, et cetera, basically because it means there's that linear line that we can use to extrapolate p and l for different types of scenarios.

Okay? So that's the perspective from a long position in forwards.

Um, but of course we cannot only take long positions in forwards. Short positions are entirely possible as well.

And here we're just looking at the con counterparty of this transaction that let's say was a bank selling those shares on a forward basis at $75 with a 12 months forward settlement.

And if they have done no hedging whatsoever, then of course their p and l would be the exact opposite of what we've seen from the buyer side, because obviously the buyer's profits are the sellers losses and therefore we have at 75 a p and l of zero at 85 a p and L of minus 10, and at 60 a p and L of 15 because that's the exact opposite of, um, what we've seen, um, in the long, um, position.

And here's then maybe already just one example, one, um, benefit of using derivatives.

And we've seen obviously a couple of things already, but one I want to highlight at this point is that when you, for example, think about forwards, they probably make it a little bit more convenient to take short positions because if you think about taking a short position in a stock for example, then yes, of course you can borrow the stock through securities lending and then sell the stock pay securities lending fees, et cetera.

However, that may consider, or you know, that may not necessarily be an extremely convenient way of doing this. However, if you are selling a stock on a 12 months forward basis, for example, you don't need to borrow the stock right now because you have 12 months until you have to deliver the stock.

And if now the next 12 months the stock price is falling, you could buy the stocks back at a cheaper level and that gets you around the need to for example, borrow securities, pay securities, lending fees, et cetera.

So this might just be a little easier way, um, to take a short position, um, for example.

Um, but now to something that's really, really critical and that is where does the forward price come from? And of course, we all know the answer, it comes from supply and demand, right? People buying, people selling on a forward basis that drives the price.

But the question I want us to think about is, is there maybe a theoretical way or is there theoretically fair forward price that we can calculate? And that gives sort of like an anchor point that determines where roughly forward prices that are driven by supply and demand then finally will roughly trade at.

And so for this, I'm want to use a scenario here.

And the scenario is that we work as a market maker in some equities trading division, and we've been asked to quote a 12 months forward price on a particular asset here. And let's say that is a stock just for simplicity, um, purposes.

And, um, what I also wanna um, point out is that, um, we assume that no forward market exists.

So we cannot cheat here. We cannot just look at our screens and see where's the market for 12 months forward contracts trading. That market doesn't exist yet.

We're tasked with basically trading the first ever forward on this particular asset.

What we have though is a bunch of numbers here and a pieces of information that have been given to us.

The first one is we know that the spot price of the asset is a hundred dollars.

That's one piece of information.

Second piece is that our in-house analyst has a 12 months price target on that particular stock of $107.

We are a little bit more bullish.

We're expecting the asset to trade at a price of $109 in 12 months time, wherever that view comes from.

Then our client has told us that their view is that the asset price should reach $115 within 12 months.

And we've been given a 12 months interest rate of 5% and we have been told that the asset pays no dividend.

Now, if it's a first time ever, you look at derivatives and you have never thought about um, forward prices, et cetera, then it might be tempting to say, okay, um, basically what I will look at to determine my forward price is my own expectation and price.

And then I look at the client expectation and I might come up with a scenario, say if I quote a forward price of 110, right, then I'm okay because I think I can buy the stocks at 109 and 12 months, then I'm selling them for 110 to my client.

So basically I'm there with $1 in my pocket because I buy at 109, I sell at 110 and my client is happy because they think the price is going to be going to go at 115.

So they like the price of 110.

That's a, you know, a starting point for this.

However, it's not quite how we should do things and that is basically, you know, we can, um, approach this in, in, in a couple of different ways.

But I just want to remind us that our role in this example is that we are a market maker and the role of a market maker, the way I understand it at least is that a market maker should provide liquidity.

IE we should facilitate the trade of the client here.

Client is asking for a 12 months forward contract. We want to give them the 12 months forward contract, but we don't necessarily want to expose our firm to a significant amount of market risk. And that's exactly what we would do here if we just quote a forward price of 110 and then hope that our view of 109 in 12 months proves to be correct.

Because what if we're wrong? What if in 12 months the actual underlying price is not 109, but let's say it's 150, then we need to buy the stocks at 150, we're selling them onto 110 to the client.

And there you can see there's obviously a problem here now, so that approach doesn't necessarily work.

Now let's think, is there a way maybe how we can give the client what they're looking for IEA 12 months forward price without exposing the firm we work for to market risk at all? Um, and for this we have to think about, okay, what price do I know, right? And the information we've given is one price, one price that we know was absolute certainty, and that is right now the asset trades in the spot market at a hundred.

So the first thing we're going to do here, um, and by the way, this is not a legal requirement to do this, but I'm just building a model, um, that allows us to hedge this transactional and therefore not expose the firm to market risk would be buy the asset spot and the price of that would be a hundred dollars because that's where the asset trades right now, right here, problem with that transaction in one, two or three business days from now settlement, right? Which means we have to deliver a hundred dollars and we get the stocks.

Now taking delivery of the stocks, that's necessarily the problem.

It's you know, basically database entry anyway, but we don't necessarily have the money.

So what we have to do is we have to borrow those a hundred dollars that we are going to spend on the stock purchase and then the is for how long? Well, the client wants a 12 month forward contract, so they're gonna pay us the money for the shares in 12 months time.

That means we need to borrow these a hundred dollars for the next 12 months period.

And of course we can use we can borrow for a day and then borrow again tomorrow. But that would introduce some sort of interest rate risk here because what if interest rates go up, et cetera.

So instead we're taking a 12 months borrow and that's why you have given the interest rate of 5% for 12 months.

So basically we borrow a hundred dollars now with those a hundred dollars we buy the stock and then in 12 months the client is gonna pay us.

And with that money, we want to be able obviously to repay the a hundred dollars we borrowed plus the interest that we have to pay for our borrow.

And that if we're ignoring day count conventions, et cetera, means in 12 months just drawing a timeline here, now we need to, um, pay $105 back to whoever lend us the money.

And then that is of course what the client should pay us.

Because if the client pays us 105, then remember at the spot we have a hundred dollars leaving the company, we have the stocks coming in, um, and then we have a hundred dollars borrowed.

So cash wise we're neutral at spot.

And then at the 12 months point, we will have to return the a hundred borrowed plus $5 interest.

If we now get 105 from the client, then all those cash flows basically, um, neutralize each other.

And what we have achieved is the client has bought the shares on a 12 months forward basis at a price agreed upon right now.

And the fair forward price in that example would be 105.

Now that of course means no profit for us.

So what we're gonna do realistically is we're gonna put a bit of spread around this, but that's a fair forward price giving the market data that we have given you here.

Alright, now let's change this ever so slightly and say the asset now pays a dividend.

And let's say that the future value of this dividends over the next 12 months is actually $6.

Meaning it doesn't really matter when the dividend is paid because in 12 months from now, the value of all dividends received, um, over the 12 months period, that's gonna be $6.

And who receives the dividends here in this case? Remember we bought the stock right now at Spott, we're then gonna deliver to the client in 12 months, but for the next 12 months we are physical holders of the stock. That means any dividend paid over that 12 months period that is gonna be paid to us.

Now of course the question is how does that impact the forward price? Well, think about it.

We buy the stock at spot for a hundred dollars, we then borrow those a hundred dollars at 5%, meaning we need to have $105 cash.

Um, at the 12 months point to repay borrowing plus interest.

We're getting $6 out of the interest sorry, out of the dividends already.

And that means we have in 12 months, $6.

So the client will only have to give us $99 because then $99 from the client plus a $6 dividend that gives us the 105 that we need to repay the cash.

That's relatively straightforward mass.

But some might now say, well, you know, that's okay, but why don't I sell the contract to 105 to the client because, you know, make some $6 on the side from dividend income.

And of course you can try to get away with this, but realistically we're not gonna be the only one in this market.

So some of our competitors will obviously pass the dividends on to, you know, the client and then we will quote a price of 105 others, quote a price of 99.

And then of course we're not gonna see any of this flow here because our price is too high and we all, we might just actually get arbitrage on the other side.

But generally speaking, it's then obviously the competition that makes the market here being, um, fairly priced. But basically, and you know, um, hopefully we can all agree that the fair value or the fair forward price would be in this scenario be $99.

And so basically what we can see here is we have the same underlying stock, the same forward period, the same interest rates.

All that has changed is in one case we're paying a dividend. In the other case we're not.

And the fair value of the forward contracts or the fair price of the forward is very different in both cases.

One time the forward price is higher than the spot at 105, the other time it's lower than the spot that's 99 forward price in a hundred spot.

And this has nothing to do with anyone's expectations.

This is just the result of interest rates and dividends.

And that is a concept that we call the cost of carry concept.

So basically the idea is to get from the spot price to the forward price, all you have to do is you have to adjust the spot price by what we call the cost of carry.

And that is what we can take literally that's just the cost of taking a position at spot and then carrying it over the forward period.

In our example, this was 12 months and then as we've seen interest rates increase the forward price and then if interest rates would've been 6% for example, the fair forward would've been 106 and 107 by 7%, et cetera.

And then we saw for equities, at least dividends decreasing the forward price because the moment we added the $6 dividend in on the previous slide, the forward price, um, changed from 105 to 99.

Now that's generally the, the principle here.

Spot price plus net cost of carry, and that is then the general approach.

However, the specific components differ of course, depending on what is the underlying that we're looking at.

If this was a bond, for example, we still need to borrow the money to buy the bond, but now we're not getting dividends, but we're getting accrued interest or coupons.

If this was a currency, then we borrow money to, um, sorry, we need to borrow one currency and then we get another currency at spot, which we then can invest.

So there's two interest rates here involve.

If we're thinking about commodities and we want to hatch this transaction, we would have to borrow the money by the commodity.

But because commodities are physically existing goods, we then have to store it. We might have to ensure transport, et cetera. So other costs are to be considered there.

And one thing that commodities don't do is reproduce themselves. Maybe life catalyst being the exception here, but generally speaking, you put 10,000 barrels of oil in storage, you get 10,000 barrels of not 5% more or anything like that.

So there is no price decreasing, um, component.

So that's the general mechanics of, um, forward pricing.

Remember, forward prices don't necessarily, um, reflect it's the expectation where asset prices will be at a certain point in the future.

It's just the spot price tidied up by the cost of care.

And with that, now let's spend the last five minutes just, um, you know, having a bit of a closer look at options and I wanted to um, bring in the option premium because we have looked at the p and l profile of a forward contract.

Now I want us to look at the p and l um, profile of an option contract as well, including this option premium.

And um, what we're gonna do is we're gonna have a look at a concrete example here.

We know what an option is. We've defined it earlier to now we're just looking at a concrete example and we're looking at a 12 month call option.

We're looking at $105 strike price and the premium of the option is $7 and 90 cents.

So we have the right to buy the asset at 105 over the next 12 months, and then we pay an initial premium of $7 and 90 cents for this option in the first place.

Now, fast forward to expiry, let's analyze the value of this position, the p and l of this position for different scenarios. And we're starting here with the price of 105 or the asset price being at 105 because that's the strike price, that's the option. So we have the right to buy the asset at 105.

The price of the asset now trades at 105.

Easy to see that the economic value of this option is zero because the price we can buy it through the option is identical to the price where we can buy it in the market.

Zero value of the option.

However, it's not a zero p and l because remember we paid $7 90 to get the option in the first place.

These $7 90 premium are now lost because the option has expired. Worthless. That means p and l is negative $7 and 90 cents.

If however, the asset price has gone up and now trades at 110, then the economic value of the option is positive simply because we have the right to buy at 105.

The asset trades at 110.

That means the option is $5 better in a way, or the strike is $5, $5 better.

Then um, the actual market price, economic value of the option is $5.

P and l though isn't $5 because remember we paid $7 90 to get the option in the first place.

So if we're ignoring time, value of money here, 'cause the option is paid, you know, at the beginning and and so on and so forth, but we're simplifying life here a little bit, then the negative, p and l would now be $2 $97 90 premium five we've gained from the option that still means we're $2 and 90 cents down. That means also we are reaching breakeven at a hundred and um, $12 and 90 cents.

That's a breakeven point because at that point the option will be worth $7 90. That's exactly what we paid for the premium.

Anything north of that will lead to profits.

There's excuse me, I just kind of got a question popping up here.

Anything else of that will lead to profit.

Yes, there will be a link to watch the recording.

Um, that I'm not sure when exactly this is gonna be sent out probably at some point on Monday, but there will, this session definitely is recorded.

So you can watch it, uh, later on as well.

So then that's the upside.

And now let's have a quick look at, um, you know, how this would change when we're looking at the other side.

IE the asset price declining. And let's look at the extreme example here of 80, um, dollars, asset price add option expiry.

But remember, we have the right to buy the asset at 105.

And of course, if the underlying trades at 80 in the spot market, none of us is going to exercise this, right? We're all gonna walk away from the option.

If we still want the asset, we buy it in the spot market, but for $80 rather than 105, and that means the option expires worthless.

Our p and l is $7 and 90 cents negative.

And that's where the fundamental advantage is of a call option over the Ford contract, for example. Because if we bought this share on a forward basis 12 months out at a forward price of 105, then we would have to take delivery off the asset at 105 now at that point, and we would pay 105 for an asset that now is worth 80 bucks in the spot market, which means we would've lost $25 market value per share here. And that's of course the clear advantage of the option over the forward contract.

Remember though, we have to pay the premium to get the option in the first place.

So that's the long call profile.

And then, I said before that, you know, the buyer's losses, or sorry, the buyer's profits are the seller's losses.

And so if you want to look at the short call, p and l profile, that's just the exact opposite of our long call position.

And of course we're assuming no hedging has been done here.

So the seller of the call, how would their p and l profile look like? Well, simple. They will earn $7 90 premium whenever the option expires worthless, and then they will start losing money when, um, or start seeing a decrease of their premium when the asset trade above 105 because that's when the buyer's gonna start exercising.

The breakeven will be at 112 90 and after that, they will start experiencing losses because the amount of money they have to pay into the option for the exercise is larger than what they have received upfront as the option, um, premium.

And then the last thing on this slide here is just kind of to look at the right hand side because so far we've looked at call options that gave us the right to buy from a, um, put options perspective that now gives us the right to sell.

So that basically means the directional risk is completely flipped.

And that means we are now as a buyer of a put gonna benefit when the underlying traits below the strike price.

So here, if we're looking at $105 strike, but it's a put now, then of course we're gonna exercise the option as soon as the price of the underlying drops below 105, then we're selling at 105 into the option.

And then we're getting advantage here through our long put position.

And the break even here will of course be $7.90 lower than 105, and then we're gonna start seeing a net positive p and l.

And then once again, the seller of the put will have the exact opposite, p and l profile.

And these are then the four general standard option positions that you can take.

You can buy a call, you can sell a call, you can buy a put, you can sell a put.

And then of course you can combine these things in many, many different ways using all sorts of option strategies.

And then there's one last thing I wanted to share with you, and that's the option moneys because when we talk about options in general, not about specific contracts, but we're generally sort of talking about the option market, then very often instead of using specific numbers for strikes, we're using some sort of descriptive terms to define or to describe a specific category of options.

And this is what I mean by the option money is, and that are terms like in the money, at the money out of the money.

Now what does it all mean? Generally an option is considered in the money when undercurrent circumstances it makes sense to exercise.

IE the strike price is favorable in comparison to the current market price of the underline example, you have $105 strike put.

So you have the right to sell the asset at 105 and the current price of the underlying is 90.

You would much rather sell through the put than selling at 105 than selling in the market at 90.

That's an in the money option.

Um, at the money is when you're basically indifferent.

The offer the exercise of the option isn't advantageous.

It's not having a disadvantage either.

It's just sort of, you know, your, your your, um, ambivalent there.

So basically what this means is, for example, you have situation where the strike is identical to the market price.

Meaning do you have $105 strike call and the underlying trades at 105 in the market, then no advantage, no disadvantage.

That's an at the money.

Um, strike out of the money then is when it currently doesn't make sense to exercise the option.

So when the market price is actually favorable, in comparison to the strike, and that would be the case for example, when you have $105 strike call option and the underlying trades at at 90.

So then you would much rather buy in the market at 90 than through the call at a strike of 105.

That's then the out of the money option.

So on the face of it, this is relatively straightforward. There's just one caveat and that is that moneys can be determined, um, by either looking, I'll call comparing the strike with the spot price or comparing the strike with the forward price.

If you have a 12 months option, for example then the question is should you compare the strike with the spot price or maybe with the 12 months forward price? Right? And as we've seen spot prices and forward prices can differ quite meaningfully.

So in our previous example, we had a spot price of a hundred.

We have a 12 months forward price of 105 assuming no dividend payments.

And if we're using that example, now we see where the problem is and why we need to be more precise in our communication.

So maybe saying I looking at in the money, um, spot or in the money forward.

And that basically then indicates if the money, this is determined with related to the spot price or with the forward price. Because here's the deal, if we have an option, 12 months option, 12 months call option here to be precise with the strike price of 105 and we're comparing the strike against the spot, that would make it an out of the money call option, right? Because the strike price is higher than the spot.

However, if we compare it against the forward price and the forward price was 105, then this is an at the money strike simply because the forward price was 105 and the strike price is 105, which means this is an at the money strike.

So if you really wanna avoid all confusion, make sure that you determine or that you mention in your conversation if you are comparing against spot or if you're looking at this on a forward basis.

So the right terminology to use here would be out of the money spot, or add the money forward.

And that ladies and gentlemen, is all I wanted to share with you here today. Thank you so much for attending this session. Hope you found it beneficial. Thank you so much once again and I hope to see you again very, very soon on one of our following sessions.

Please also remember to let us know which other topics would be of interest, any feedback, greatly appreciated.

Thank you so much. I haven't received any questions, so I'm gonna wrap this up now.

Take good care of yourselves. See you soon. Bye-bye.