Hi, good morning, good afternoon, good evening maybe.

And welcome to this Felix live session on interest rate swaps.

My name is Thomas Krause I'm head of financial products here at Financial Edge, and I have the honor to guide you through this introductory session.

Let's have a quick look at today's agenda.

We're gonna start with an overall introduction to interest rate swaps.

We will look at their general mechanics.

We will talk about some of the important terminology around interest rate swaps.

We are going to discuss the difference in cashflow mechanics between interest rate swaps that are linked to IBOR, because yes, some of them are still around.

And on the other hand, we're also gonna talk about overnight index swaps that are these swaps that are now linked to the new risk rates like SOFR, TONAR, SONIA, ESTR, et cetera.

We will also take an intuitive look at interest rate risk with in interest rate swaps, and then we will see some application examples for these products as well.

Before we start though, couple of quick reminders.

Without further ado, I will now get started.

And the first thing we're gonna talk about is, as I said, the introduction, right? What are interest rate swaps? Well, they are a type of financial swap and like any other financial swap, they are basically the agreement between two counterparties to exchange two streams of cash flows.

And what sets interest rate swaps apart from other sorts like equity swaps or credit default swaps, et cetera, is that both of these cash flows, both of these series of cash flows, which are also referred to as swap lags, are linked to interest rates, right? And this could happen in very different forms.

There could be, for example, and this is by a far, the majority of all interest rate swaps, a structure that's called a fixed for floating swap, which means one leg is fixed, the other one is floating.

i.e. pays a variable rate. That's the vast majority. That's the one we're gonna spend our time on here today. But there are other structures, for example, the basis swap where both legs are floating.

This could be different tenors, like three months versus six months IBOR or this could be across different indices like an IBOR rate versus an overnight rate.

This could also be different rates in different currencies.

For example, sulfur versus ester, et cetera.

So a vast majority of the variety of potential structures, but as I said, the vast majority of swabs traits in the format of fixed for floating, at least in the interest rate swap world.

And so let's have a closer look at this structure.

We see an example here right in front of us on this slide.

There are two counterparties, which in swap world in interest rate swap pollens are referred to as the payer and the receiver.

Now, what's important to remember is that pay and receiver always is determined in reference to the fixed rate, not to the floating.

So when we're talking about a payer swap, what that means here is that the counterparty has agreed to pay the fixed rate to their counterparty.

That means they're receiving the floating lag. But we don't explicitly have to mention that because hopefully it's self-explanatory.

If someone enters into a receiver swap, that then means that they have agreed to receive the fixed rate of interest.

And yes, that agreed they have, or that also means they have agreed to pay the floating rate.

But again, we don't have to explicitly mention that simply because that is how the structure works.

So remember that payer receiver in reference to the fixed rate of interest.

Then of course, you know, we need to determine when we enter into a transaction like that.

A couple of things here and at the bottom you see some of them.

And we're gonna spend some time on the next slide exploring a little bit more about the terminology.

But basically the structure that you can see here is a five year contract, right? So that means the exchange of interest fixed versus floating will happen over the next five years.

So if we traded this swap today, then it will actually begin because interest rate swaps for the most part have a t plus two settlement.

So we're starting this swap on Tuesday.

There's no practical settlement, no exchange or cash versus, uh, security or anything like that.

But that's then basically from the day from which interest rates on both legs will start to accrue. So we're starting that thing on Tuesday, and then five years after the date of next Tuesday, that will be the maturity.

That's the day on which the last payments on this swap will ever be exchanged.

Assuming of course the contract is not canceled or you know before that point in time.

Now what will be the agreement? As we said, the agreement will be to exchange a fixed rate of interest. Here in our example, this was 5% also often referred to as a swap rate. Sometimes the OIS rate, we're gonna learn the distinction between those two later on.

So whenever you hear OIS or swap rate, think about fixed rate on a swap.

And that was set here in this example at 5%.

Now, that is, as for any other instrument in interest rate world, a per annum number.

That means for the whole year the payment is gonna be 5% on whatever the underlying notional amount is. In this case, 10 million whichever currency we're looking at here.

Now, how often the payments are exchanged on the fixed lag, that could vary, right? So the, for the vast majority, we probably have either semi-annual or annual payments, but swaps are OTC instruments.

That means they can be tailored to whatever the specific needs of the counterparties are.

So there could be, in theory, a monthly payment frequency quarterly as well.

All of that can be discussed because this instrument, as I said, can be tailored to individual investors' needs they count can vary as well. That's basically just a set of rules that we need to know in order to transfer the interest rate payment into an actual monetary number.

But let's not go into this topic here today.

Same applies to the floating rack that basically frequency or payment frequency and day count can vary.

There are a few sort of limitations to this though, which we're gonna discuss on the next slide.

But first of all, I just wanted to highlight that there are two main floating or types of floating rates that swaps can be linked to. And we said it already in the beginning we're looking at IBOR structures, but we're also gonna look at OIS.

And this is then basically what the difference between the two is actually the characteristic of the floating leg that they are using to determine payments on the floating leg.

If the floating leg is or determined by an interbank offered rates like EURIBOR for example, then this would be obviously an IBORR linked swap.

If it's determined by a new risk-free rate, like SOFR like SONIA, like ESTR, like TONAR, et cetera, then this would be an overnight index swap because the reference rate is an RFR. Frequency and day count vary in this or can vary in this case as well. We're gonna talk a little bit more about that in due course, but remember, it's an OTC instrument, hence it can be tailored to the bottom line in this.

Or, you know, regarding the bottom line here in in this table where it says the PV i.e., the present value, net present value, we should really say of n interest rate swap simply because it has two lags.

One goes out, one comes in.

So the net present value of all these payments a swap would basically represent, or, you know, the contract would represent is usually zero at swap exception.

What does that mean? It means that both parties enter into the interest rate swap without any upfront payment, without the need to pay a premium or getting a discount or anything like that.

You agree on the swap rate.

In this case it was 5%, and the swap rate then is set in a way that the swap is considered to be fair.

And that's basically telling us it needs to have a PV of 0.

What does, or what is the main criteria for a swap being fair for an interest rate swap being fair? And we don't really have to stay within finance to think about this because hopefully it's quite intuitive that a swap can be considered fair when the value of what you're gonna give up is the value is identical to the value of what you're expecting to receive, right? And that's the sort of common principle of a fair swap, regardless of if we're talking about credit default swaps or equity swaps, FX swaps, whatever that is, the general share in combinate principle here that they have at inception, a PV of around zero, not exactly zero maybe, but generally speaking it wouldn't be too far away from that, which effectively, in case of interest rates fixed versus floating means that if you discount all the payments on the fixed lag and you discount all the payments that you would derive from forward rates, for example, on the floating lag and sum up these two, or all the present values of both lags, then they should be identical with opposite signs.

I.e. the value of what you will receive is the value of what you expect to pay or vice versa.

That is the meaning of this line here. But we're gonna talk a little bit more about swap valuation later on.

But bottom line, and I want you to remember this for later, is the moment the swap is traded, this equation typically halts i.e. present value of fixed leg equals present value of loading leg. Now, as soon as a trade has been agreed, interest rates obviously start to move or well continue to move because they never stop just because we're trading interest rates swaps, right? But basically interest rates will change, that could apply for the fixed rate of the swap. That could also apply for the floating legs here or floating rates.

And that means that this equation of, or the, the, the balance between the present value of the fixed cash flow and the floating cash flow is no longer necessarily gonna be zero.

The swap can accrue some mark to market value a little bit more on that, as I said later.

But let's stick with some terminology here.

And I know we covered, uh, quite a few of these points already. Notional value, it's not an amount that is actually gonna be exchanged between the counterparts, right? When we're having a single currency interest rate swap where you pay me a fixed rate on a hundred million dollars and I pay you a floating rate on 100 million dollars, we don't need to exchange this notional amount because that would just mean I give you 100 million dollars, you give me a hundred million dollars, we might as well not do this, right? What the purpose of the notional amount really is, it is the calculation basis for the interest rate payments because interest rates are given us percentage numbers.

And to calculate a percentage rate into an actual monetary payment, you need to have a monetary basis for this.

And this is then the notional value.

Next point, payment frequency, I already said it can be tailored to the individual's needs, right? Usually there's at least a payment once a year could be more frequent though.

It could be semi-annually, quarterly, things of that nature that could be determined almost freely within certain boundaries.

The next point is the reset frequency.

That's something where the payment frequency really can be determined for both fixed and floating lag.

The risk that frequency really is just affecting the floating lag.

So we can put this here fixed and float, right? Wheres reset frequency only affects the floating lag because what it basically means is how frequently is the floating interest rate reset? How often do we take a new benchmark rate into consideration for calculating the payments on the floating lag? Now, in the past when we only really traded were well interest rates swaps for longer tenors, were almost exclusively traded in the IBOR format we had on the floating leg usually a link between the payment frequency and the reset frequency.

So to give you an example, if we had as a floating or as a benchmark rate to determine the floating interest rate payments six months EURIBOR, and in EURIBOR and euros swaps, that still works.

So I'm using that as an example instead of your dollars here. So if the reference rate that determines floating rate payments was in fact six months EURIBOR, we would basically have a six monthly reset frequency.

So every six months we're gonna look at six months EURIBOR, although it's fixed daily, right? But, and then also what this comes with is, is semi-annual payment frequency.

So the thing, and we're gonna have a look at cashflow mechanics in more detail in a minute, but what I want you to remember right from this slide here is that in IBOR world, we typically had the sort of overlap or the same reset and payment frequency on the floating lag on the fixed leg. We don't reset, right? Because we're just having the fixed rate that is set at the point we're entering into the transaction. That never changes. There's no reset on the fixed lag, right? Then next thing, maturity date, which I think is self-explanatory, that is the last date, or that's the date on which the last payment is made usually is the start date T plus two in most markets, plus the tenner.

And then at the bottom here, um, there's something that's worth pointing out or talking about that's netting.

Now, netting is not something we necessarily need to agree on a per swap basis, right? Simply because it's generally part of our regular or regular or legal framework contract here like this, the master agreement, for example.

But what netting refers to, in this case we're talking about payment netting to be precise, is that instead of what or when two point, well two payments on the swap happens at the same day or sort of supposed to happen on the same day, then rather than both counterparties making their payment, we will just agree or we have agreed to net those payments, and then simply the net amount is transverse.

So if we are just kind of for a second putting us in the example that, you know, we have entered into a swap together, so you pay me a fixed rate, I pay you a floating rate, and if then today our both of our payments are due and you're supposed to pay me 4 million, I'm supposed to pay you 5 million, then rather than me paying you five and you paying me four, I'm just gonna make a net payment of $1 million to you.

That basically simplifies things, it reduces counterparty exposure, credit risk, and it also, you know, reduces transaction costs at least holistically.

That's the idea of netting. Cool.

Now let's have a bit of a more detailed look on those mechanics that apply on swap cash flows. We've touched upon this already in the IBOR world.

I'm gonna go through this one more time just to make sure everybody's crystal clear.

And then we're gonna move into the OIS space where things are, pretty fundamentally different, right? So here what we can see is our five year swap, and we have an annual fixed payment frequency, and we have a semi-annual floating payment frequency, right? So here's our 5% paid at the end of every year, and then we have a range of floating payments.

Now, the question is, how exactly will these floating payments be determined? Now remember, we're starting with an IBOR example, and that reference rate here in this example is six months EURIOBR.

So let's assume we traded this swap today, right? Then, as I said, the interest on both legs fixed and floating will typically start to accrue Tuesday next week, t plus two, right Now, what we know is the fixed rate 5%, and the question is, what is the first floating payment going to be that we know is gonna happen six months after the swap start date? But what determines this payment? The answer is, and let me just tidy this slide up a little bit.

It's today's six months EURIBOR fixing. Why is that? Well, EURIOBR is a term rate, six months.

EURIBOR is a six months term rate.

i.e. basically refers to a six months investment period that starts two days or two business days after the fixing date.

So when we're trading this swap today, let's put the number and that's T zero, that's today.

Then a t plus two interest rates starts to accrue.

And if we take today's six months arrival of fixing that basically is a six months rate that applies for a period that starts at the T plus two point, and then last for six months.

So today, six months EURIBOR will basically determine the first floating payment, six months later, six months and two days later.

And then six months from today, we're gonna look at six months arrival o again, which then is the rate that will determine the interest rate payment on the floating lag six months after that, et cetera, et cetera, et cetera. So that's gonna repeat every six months.

We're gonna have a new fixing and the payment will be made six months later.

That is how interest rates swaps for longer tenors used to work for many, many, many decades.

And that's kind of a mechanism that we call set in advance paid in arrears, because at the beginning of the interest rate period, we determine the interest rate, and that means the moment the period of or the interest rate period starts, we already know how much interest, how much money has to be paid by the counterparty that's supposed to pay the floating rate at the end of the interest rate period.

And that, as I say here, is for IBOR rate linked swaps still the general mechanism, let's not focus too much on the term RFR, we're gonna have a brief mention of them on the next slide.

So now I want to actually come to the next swap type.

And now we're gonna have a look at the OIS example.

So now let's assume we traded a five year OIS, which basically stands for overnight interest rate or interest overnight index swap, excuse me.

And basically what fundamentally differs here is that the benchmark rate is not, or the reference rate for determining floating lag payments is not an IBOR rate, but now is an RFR a nearly risk-free rate like SOFR et cetera. And let's just take sulfur as an example here because it is obviously the best known of them all, I believe.

And so now we have a swap where two counterparts have agreed to exchange over a five year period, a fixed rate of 5% versus, SOFR over the next five years.

Now remember, SOFR is an overnight rate, which means it only really applies for an investment period from today to the next business day. In this case, it's, you know, kind of a three day rate because we're doing this session here on Friday.

But generally speaking, if we would do it on Monday, then it would be a truly one day overnight rate, simply because it's from Monday to Tuesday, that's SOFR for you, right? So, generally speaking if we now would stick to the IBOR principle that the payment frequency and the reset frequency should be aligned, we would find a contract where we basically had to make daily transfers of small amounts of interest rates, right? Simply because today's, SOFR only applies from today to tomorrow, then we're gonna reset.

SOFR we're using the new, SOFR fixing for the next day and so on.

So effectively we would have to transfer small amounts of money, every single day, which of course, from an operational point of view, as an absolute nightmare, and it's really, really inefficient.

So the market has you know, developed a more efficient way of doing this, and we have basically decided to move away from this payment frequency equals reset frequency environment to this an environment where fairly regular the payment frequency is smaller or lower number or, you know, let's say we have less regular payments than we have or less frequent payments, then we have the reset.

So in this particular example we're staying with a six months payment frequency on floating.

So that's a little bit unusual, it just works better here in our example graphically.

But, um, in general, the interbank standard or convention is usually that we make annual interest rate payments on the floating lag as well. But let's stick with semi-annual because it just, you know, fits better into this example.

So now we have a swap where the floating lag or the floating rate, the variable rate is indeed reset every day, every day we have a new SOFR fixing that will have to be used to calculate the interest rate payment on the floating lag, but we don't make daily payments, right? So the idea here is that every day over the next six months period, we now record the SOFR fixing and all of the SOFR fixings will then basically contribute to the actual rate that needs to be paid the problem or not the problem.

But, you know, the, the one thing to be aware of when you're switching to this approach is obviously that now we no longer know at the beginning of the period how much money, you know, has to be paid on the floating, like at the end, but we will pretty much know it only as soon, or we will only know it once the last sofa fixing is known, which is basically the day the interest rate period ends.

So no longer we're setting an interest rate in advance and then pay an arres.

We still pay an arrears because we still pay at the end of the interest rate period, but we now also only know the, uh, applicable rate at the end of the period.

And that is of course, an operational challenge for some, not so much for financial investors because we're managing cash flows and, and we're very efficient in liquidity management, et cetera.

But if you think about the non-financial community, if you think about corporates that use these instruments, for example, to hedge Loan payments, et cetera, or loan contracts, then having such a short notice or advanced notice for the payment amount could actually operational probably provide a little bit, of a challenge.

And we're gonna talk a little bit more about this on the next slide, but for now, what I hope everybody has taken away from here is that the moment you move from the IBOR world into the OIS space and you use that daily reset frequency of sulfur, et cetera, you are in an environment where you basically know the interest rate in arrear is it's paid in arrears. And we therefore referring to those RFR rates as backward looking because strictly speaking, and I'm just tidying this up here, at this point, we will know all previous sulfur fixings and that basically this rate will then be retroactively applied to the previous six months period, right? So that is the key difference.

And as I said, this difference could provide some operational issues for some market participants.

And that's then when you look at the transition data, because remember this OS was a switch from IBOR swaps to swaps versus SOFR as the SONIA, TONAR et cetera, is not too long ago, right? So this started obviously around 2018 when we had clarity around which rates we would use going forward, et cetera. And then there was a transition what we saw in pretty much any currency more or less than of course, you know, some were more proactive than others.

It was a relatively slow uptake in the transition.

i.e. we knew there was a deadline on which we can no longer really trade IBOR linked swaps simply because the regulator would announce they have lost representativeness and then we shouldn't really be using those sort of rates.

But as time was gone by, there wasn't really a lot of uptick in, in the overnight index swaps that were sort of developed in a way as an alternative.

And of course, you know, you could argue that's a liquidity problem simply because if there's no transactions happening in a particular market, liquidity is low, but offers are relatively wide. And then why would you, you know, without being forced switch into a market which is less liquid when you can still trade what you need to, or you know, what you need to manage your interest rate risk in a fairly liquid market.

But part of the transition might, or, you know, let's say, I won't call it issue because the transition actually works smoothly, but you know, part of the relatively low uptake maybe in the transition at the beginning was maybe due to this issue that we have already described, that some users really had concerns about knowing the interest rate at the end of the period and to address those concerns or to really address those potential operational issues.

Then term rates or term RFR rates had been developed like term, so RFR term, SONIA term as their, et cetera, et cetera, which basically are mimicking the mechanism of the IBOR rates in which they are forward looking term rates.

And the idea is that we use derivative prices, for example, futures on these rfr overnight index swap data to calculate theoretical term rates on a daily basis.

i.e. today we would've calculated a one month term sulfur, for example, it's three months, a six months term sulfur, which is then basically derived from the swap market.

And those would have been published as sort of very similar, to, you know, LIBOR slash EURIBOR used to be.

And then obviously if we now have contracts where we say, well, we're not referring to SOFR but instead to three months term SOFR or six months term SOFR, for example, then basically we would be back in the old world.

And that is interest rates set at the beginning of the period and then basically paid at the end.

The one thing that is important to understand though, is that regulators are really limiting the use of these term RFR rates in contracts to, you know, really some fairly limited cases, and they are all around corporate lending.

For example, corporate loans possibly can use term SOFR as an interest rate to reference or to to link the payments to.

And then interest rate swaps, for example, can be linked to these terms software rates, but only if they are transacted by clients simply for the requirement because they have the requirement to hedge and actually underlying lending transaction that is linked to terms of rates as well.

So it's a pretty restrictive way, but of course, remember if our clients come to us with that request, we can, if these circumstances are, or if, if the conditions are fulfilled then of course these contracts can be designed.

And with that just a final look at the terminology here.

Simply because in swap world, like, you know, any other, part of the market, we are using a lot of acronyms just to make our communication much more efficient.

And what you will see when you're kind of looking at interest rate swaps is very often IRS and OIS.

Now, what's the difference between the two? I would argue that in many, many cases people start using them probably already as synonyms.

However, in many cases, also there's a distinction between those two.

So both of them are actually types of interest rate swaps, hence it's quite sort of attempting to assume IRS just stands for interest rate swap, which means everything, it does stand for interest rate swap, but when we're using it as an acronym IRS, then usually what we're referring to is, the make the first type of, so that we discussed, i.e. the, and I'm put it in ver commas old way of you know, doing it where we have a single reset of the reference rate at the beginning of the period, and then we have the payment at the end, i.e. payment frequency equals reset frequency, all those things we have already talked about.

So the EURIBOR or swaps, for example, they would be still referred to as IRS in many market statistics that, you will see. And we're actually gonna have a look at one or two in a minute.

Now what does OIS then basically represent? You would've guessed this, right? That stands for the overnight index swap market, and those are the general swaps that have, as we discussed, the inner rear setting of the interest rate or determination of the interest rate, we should say.

And then also the payment fairly, fairly close to this particular point.

One question remains then, and we haven't addressed this, but we will do in due course, is how exactly do we then transform all those daily, SOFR or reference rate fixings into the actual, you know, semi-annually or annually paid floating rate.

And we're gonna come to that in a minute, but generally speaking, we use something that is called a compounded average rate.

More on this, as I said, to come.

I just wanted to point out one more thing, whilst being on this slide, and that is that sometimes, you know, the impression is that the concept of an overnight index swap is in fact new was only really developed.

you know, when LIBOR transition became, became a thing, I just wanted to remind you that the mechanics of overnight index swaps have been around for much, much longer.

For example, there was a, okay in terms of liquidity market for, you know, overnight index swaps in Euros, for example, the reference rate wasn't ESTR, it was EONIA, which was the predecessor of ESTR.

But that was already available in the early 2000s, right? So the mechanism of these swaps isn't exactly new, but what was different back then was that these were more or less money market derivatives.

i.e. the liquidity was fairly okay up to maybe two years out in terms of maturity.

After that, it got relatively thin.

Then when we had the whole regulatory overhaul of swap market and the whole idea of central clearing, et cetera liquidity extended out the curve.

But you know, what really has changed in sort of the OIS market that we're looking at nowadays what sort of makes them new is that the reference rates for most currencies haven't been around that long.

So we're using SOFR now in the United States, we're using ESTR in Europe, both you know, OIS markets in those currency use different reference rates.

Many, many moons ago there was, for example, the effective federal fund rates in the US and as I said, EONIA in Europe.

But the concept of mechanics isn't exactly new.

Okay, with that, uh, let's have a look at the actual mechanics. And this addresses the question, how do we turn all these single, um, reference or single resets, IE all these observed interest rate fixings into the actual floating rate? Because what is the aim here is remember, we wanna increase operational efficiency.

We don't wanna have daily payments on the floating lack. That's way too costly.

Uh, and therefore we have decided, okay, let's make these things annually or semi-annually. And as I said, this can be discussed, it's an OTC market, but the standard interbank convention is at least an annual payment on the fixed leg or at maturity, whatever happens first, right? So we're looking at a seven day example here. We just wanted to keep, uh, things nice and, and, and easy and to put on a slide here.

So it's a seven day interest rate swap, right? Over a seven day period, the counterparties have agreed to exchange a fixed rate versus a floating rate.

The floating rate here is, so OFR, it's reset daily, but the interest rate payment should happen at the end in one net payment.

So seven days after the swap has started, we calculate the net amount between fixed and floating interest rate or payment or, you know, uh, swap legs and the net payment will then be transferred.

The fixed leg isn't the problem.

We have agreed on the OIS rate at the start, we know what the payment on the fixed leg is gonna be, but we need to wait until all sofa fixings are known in order to calculate the effective floating rate.

But how exactly is this done? Now, of course, um, there's different ways on how one could address this.

The easiest way probably would be to just calculate the normal average, right? So the arithmetic average of all those sofa fixings, just, you know, remember all the sofa fixings across the seven days, some of them up divide by seven, that's then basically the software rate we're gonna use, nice and simple, however, it comes with a problem.

And that is that strictly speaking, it is a disadvantage for the receiver of the floating leg.

Why am I saying this? Well, generally think about how interest rates are usually paid.

If you put your money in a savings account or in a deposit certificate of deposit, whatever, uh, let's say it's a three months investment, when would you normally expect to get interest? Most investments pay interest, as I said, at least on an annual basis.

But in a three months investment, in most cases, you will get your money in three months when you get your money back.

It's a simple interest rate payment made at the end of the investment period.

And that's usually what all investments have in common.

If they are interest linked interest rate linked at at least do you do get the interest that is applicable or that that's a reward for having the invested the money for a certain period at the end of this period.

What this means, SOFR is that within SOFR, there's a conve, or there's a, there's you know, basically baked in that today's rate, this SOFR rate applies from today to the next business day, which in our case, given that Friday again is is gonna be Monday.

But generally speaking, if this was as I said earlier on Monday, then SOFR would apply for Monday to Tuesday.

On Tuesday, you get the money back that you have invested, plus you get the interest.

If we are now not getting the interest on Tuesday, um, but instead we're gonna get it a week later, we are losing out, right? Simply because if we would've gotten the interest already on Tuesday, we could have reinvested it on Tuesday and then we would've earned interest on interest.

So a simple arithmetic average here would just ignore the fact that there is time value of money and that's not quite accurate.

So the way this is handled in reality is that we're using a compounding averaging method, which effectively means the following, right? So let's look at the example.

So on day one we're starting this example here, and let's say the notion of the swap is one could be a hundred million, could be a million, could be just $1.

It doesn't really matter for our example here, but we're starting with small numbers. So let's say we start with a notion of one, then the first SOFR fixing that applies here is the fixing for Monday i.e from Monday to Tuesday.

Actually, that fixing comes out on Tuesday.

But let's not worry too much about those mechanics here right now.

So the rate applicable from Monday to Tuesday was actually 5.25%.

That is now effectively, or what we do now is effectively apply this interest rate on the notion of one times 1 over 360. Because the day count convention of SOFR is actual 360.

It's for one day a 5.25% rate over 360 days a year.

And then we basically have a certain amount of interest that technically should have been paid on Tuesday.

Now it isn't paid on Tuesday, remember it's paid on Monday, of the next week because that's when the swap ends.

But we use this interest rate or this amount of interest and basically put it on the original notional.

So that means the following the interest rate from Tuesday to Wednesday, which was set at 5 26, is not just paid on the original notional amount of one, but is paid on the original amount of one plus the one day accrued interest from Monday.

So we're taking this amount that we've just calculated and then apply the 5.26 interest rate for another day.

And that gives us then another interest rate payment, which again, is added on top of this.

So here you see basically what the campaign compounding average does, it is including interest on interest.

And that continues then throughout the, life of the swap.

The only thing worth mentioning is that on Friday the day weight changes, it was one day throughout the life of the swap here, simply because from Monday to Tuesday, one day from Tuesday to Wednesday, one day, et cetera. However, from Friday, even though we're technically talking about overnight rates here, when you lend money to someone on Friday overnight, that means you get your money back on Monday.

That's three days simply because payment systems aren't operative on, you know, set days and Sundays. So effectively the rate you should get for three days because your money is away for three days.

And that's what the waiting factor then basically does here.

It adjusts the investment period for the weekend three, and then you end up with a total amount of you know, in theory of the crude floating lag.

And you could transform that of course, into the effective interest rate here because you know, the starting value, it was 1, you know, the end value, it's 1.001022, et cetera.

And you know that this has been a seven day over 360 investment period and you can solve that for the interest rate and that would give you the effective floating leg or floating rate on a compounded average basis.

Now, that's the theory behind this formula, ladies and gentlemen, because this formula is basically the official formula that is to suggest for making these calculations.

But basically it is what we have just done expressed in a smart looking formula.

So that's explaining the OIS mechanics.

And with that, let's just have a quick look at the size of the swap market.

And the number two, you know, look at here is the one there at the bottom.

And that is that in 2023 across the full year, the notional of interest rate swaps, and I don't mean IRS, I just mean the concept of interest rate swaps. Now IRS and OIS was 300.

You know, let's round it up to 25 trillion $325 trillion worth of notional being traded in a single year that suggests that it's a fairly popular instrument.

And of course, the question is as to why that is.

Well first of all, I think, you know it is, an instrument which can be used to take views on interest rates.

I.e. enter into specific interest rate risk positions to benefit from expected moves in interest rates, but it's also a very, very convenient tool to hedge existing interest rate exposures a way.

And that obviously explains the attractiveness.

It's OTC, remember.

So it can be tailored to specific needs that again, adds to popularity.

And then of course, look at the size of the market that suggests it's fairly liquid, so it should be relatively, you know, easy to trade, large amounts, add relatively tight bit of a spread.

So there's a liquidity argument then of course, as well.

So as I said, this number basically refers to IRS and OIS and a couple of others here we can look at the right hand side.

So there's actually four groups of or four types of subs that are included here. There's the fix for floating IRS.

So here you see IRS being used as the IBOR principle.

Then we have OIS as swaps against the new overnight index swap rate. Then there's something called FA stands for forward rate agreements.

Technically speaking, they are one period interest rate swaps. So basically you're exchanging a six months fixed rate for six months floating rate, but that usually starts at some point in the future.

So for example, a fixed rate is determined today and the floating rate that you're gonna receive is the six months, rate in three months time or anything like that.

So it's forward starting one period.

Interest rate swaps, call forward rate agreements, hence they are in the interest rate swap statistics and others.

What do we find here? Typically things like basis swaps, i.e. floating versus floating, and also the cross currency examplesthat I put that I mentioned already earlier.

So another bit of market statistics here.

And I think it's interesting to point out that 75% of or approximately we should say, of course, of all swaps are either, and I say single currency swaps here are either denominated in US dollars or Euros. And then what we can do here, or about we can see on this slide is a breakdown across the different currencies here. So you see the colors at the bottom on the different product groups, and when we just look at, you know, the different points in time and we're comparing fourth quarter, 2022 was fourth quarter 2023, and we're looking at the IRS traded in US dollars, we can see that it was 7.7 trillion back in fourth quarter 2022.

This has gone to zero on the fourth quarter of 2023.

And the question here on the slide is why did the USD IRS trading disappear over that period? And I think we all know the answer of that.

That was a LIBOR transition because US dollar LIBOR was officially declared you know, non-representative on the 30th of June, 2023, which means we were technically no longer allowed to use, dollar LIBOR as a reference rate.

Hence there's no trading volume.

And what has this volume been replaced with? We can see over the same period the meaningful uptake in the OIS and notional being traded in used dollars, which indicates that the volume shifted from IRS to OIS if we're looking at Euros.

The second big part of interest rates swap markets globally.

So we're now looking at the green color here. We can see we started in our in in fourth quarter, 2022. We had 4.3 trillion in IRS at the end of the observation period here, fourth quarter 2023, we actually had increased the notional to 5.9 trillion.

Now that doesn't mean we have actually increased, we have, taken market share from the OIS market or anything like that, that will just be the result of different levels of trading activity.

Also, we are looking at notional here.

So the thing with notional is obviously that it isn't equivalent to risk because you can have fairly short dated interest rate swaps being traded and a large notional, which then obviously will inflate somewhat the notional statistics.

But the amount of risk traded through these contracts actually will be fairly, fairly limited.

Going back to our seven day example from earlier, that swap will have a seven day duration, right? And of course, a, you could trade that in fairly significant notional amounts until you see a reasonable, Do one here in comparison to, for example, a 30 year interest rate swap, which will have a much, much longer duration.

So we can see what I basically told you right from the start.

The, European interest rate swap market is still alive or IRS market, we should say meaning swaps against EURIBOR or still alive and kicking.

But there also is a meaningful overnight index swap market in Euros as well.

Okay? So, when we were looking for reasons as to why interest rate swaps are so popular, I said that, you know, one of the drivers behind that is probably that they are very convenient and very flexible and also very liquid tools to exchange interest rate or existing interest rate risk exposures, but either increasing it or decreasing it i.e. using swaps to build speculative positions or hedge existing interest rate risk positions.

So we now wanna have a quick look at the interest rate risk in interest rate swaps.

And we do this from an intuitive perspective because we don't have a sufficient amount of time to look into this from a mathematical point of view. But I want you to think about the question here on this slide.

Assuming that you entered into a two year US dollar overnight index swap and you're receiving a fixed rate of 4.05% versus SOFR, and let's stick with the standard convention that is annual payments compounded average, we now know what this means, and that's thing we've entered into today.

Now think about in which direction would you now, after the trade has been agreed would you prefer sulfur to move? So I'll just visualize this, that always helps, right? This is us, this is our counterparty here, and we have agreed to receive 4.05% in exchange for SOFR.

What would we like to happen to SOFR? Remember, what we're gonna receive has already been determined.

That's never ever gonna change over the next two years.

We are gonna receive a fixed rate of 4.05%.

The only rate that can change is obviously SOFR.

What would you like SOFR to do? i.e. what would you like the rate that you are paying to do, you would prefer going down over time, right? So that intuitively makes sense.

What you receive is set in stone, that's not gonna change what you pay to get this fixed stream of cash flows would be nice if this would go down, right? So you would prefer SOFR to go down in this particular case, and therefore we can draw a simplified conclusion here.

And that is that fixed rate receivers generally would benefit from a decline in floating rates, whereas fixed rate payers, they are on the other side would benefit from an increase in floating rates.

Now, while this is wonderfully intuitive, we'd have to caveat this a little bit because it matters where SOFR is to start with, right? So let's imagine SOFR today was at 5%, it's not anymore, but you know, let's imagine for a second it was.

So that's today's SOFR fixing, right? If now over the next two years, or let's say, you know, a couple of days from now SOFR drops to 4.25, so a 75 basis point drop in SOFR and then stays there for the next, you know, let's say 23 months and two weeks time, right? Then yes, we've seen a remarkable drop in SOFR that it still would lead to a net negative cash flow for us on the swap because we are getting 4.05% every year and we're paying a rate of that's never gonna be below 4.25 in return.

So it's not necessarily a hundred percent true that as a fixed rate receiver, we will benefit from a decline in floating rates.

That depends a little bit on the structure of yield curve, et cetera, et cetera. But as I said, we don't want to go into too much detail on this.

But as remember, we need to caveat this a little bit, but it's a good starting point.

Now, what we can say though is that a decline in interest rates generally should be at least easing the pain and, and be beneficial for the fixed rate receiver.

But the point is that, or, or what, what we wanna do next is to develop a bit of an understanding about what interest rate actually has to decline for us to build a positive mark to market value on a swap.

And that brings us into the valuation environment because, you know this is an intuitive example I'm gonna show you that really answers the question.

How can we calculate the current value of an OIS or interest rate swap, whatever at a specific point in time? Now, that's obviously a very important exercise simply because we need to be able to assign a mark to market value to all our, at least liquidly traded products on our portfolios at any given point in time.

And this idea here of, you know, thinking, okay, whether or not this swap was a good idea, we know in two years from now, once the last sofa fixing is known, that simply isn't good enough, right? Because we cannot wait two years until we know what the value of the swap is. And remember what I said, the moment you have entered the transaction at a PV of zero, when interest rates starts to change, then the swap will build potentially, at least it's not guaranteed, right? If interest rates do change in very weird circumstantial ways, then of course, you know, the PV of the swap might not move at all, but more likely than not, it is gonna move.

And the question is how can we calculate the present value of a swap? Before it's time to maturity? Again, we're taking the intuitive approach mathematically, it can be done much more accurately than what we're gonna see here, but I just want to share the general thoughts behind this with you.

And now we're using a slightly different example.

And that's here on the slide in front of you.

So it says here that five years ago we entered into a payer swap where we paid a fixed rate of 2.2% on 100 million US dollars, and the floating rate, no, or the floating lag was referenced to SOFR.

So if I just draw this up here, this is us, this is our counterparty, and we have agreed to pay them 2.2% and we're gonna get SOFR from them in return annual payment.

But you know, we know what this means now.

So that's the current position.

Now remember, this is no longer a 10 year swap because five years half passed since then.

From today's point of view, we are in a five year swap where we pay 2.2% and we receive SOFR annually in return.

So if we isolate this position, if we assume for a second this is the only trade we have in our portfolio, then we can identify the risk that we have, right? And that is that SOFR will go down because we are receiving SOFR, we know what we're gonna pay for it, 2.2%, but you know, when sulfur starts to go down, then of course our payments that we receive will start to decrease. So that's sort of like the, the market risk in a way that we're having, at least according to the previous slide.

How could we eliminate any uncertainty around how much money we're gonna get from this particular swap? It won't work by just looking at the swap alone.

But the general kind of approach to do that is you can think about, okay, what do I have to do to offset the risk? To eliminate all uncertainty? Currently we're in a position where we're paying a fixed rate and we're receiving sulfur to have no uncertainty.

We need to do the exact opposite of that.

So we need to go out to the same or another counterpart really doesn't matter.

And enter into, now what's a receiver swap? Because remember the swap we entered five years ago was a payer swap.

Now we need to receive and then of course we need to look at whatever the five year swap rate is at that time, and coincidentally that's a lot higher.

So it's 4.2%.

So if we would enter into that swap, we would now receive 4.2% fixed in exchange for SOFR and then you would hopefully agree that these two cash flows will cancel each other out. If sofa goes to 10%, we get 10% here, we pay 10% there.

If SOFR goes to zero, we get zero here, we get a pay zero there. If sofa would go negative, we pay money here, we get money there.

You know, hopefully it's not gonna happen again, but it would work.

Okay? So then these SOFR payments basically are eliminated in a way. They cancel each other out. So what's left is we have 4.2% coming in every year, right, per annum.

And we have 2.2% going out every year, which means we have a net cash flow of 2% per annum over the next five years.

Now that should, you know, without or was completely ignoring time value of money, that puts us in the ballpark of around 10%.

value of the notion, no but of course we need to include time, value of money. And what we've done here is we've given you what's called the five year PV01, which is basically the present value of one basis point over a five year period.

And that was 4.43. How to do you read this? Basically what this number says is adding one basis point of payments over the next five years is having a present value of 4.43 basis points today.

And that means because 2% is 200 basis points, right? And basis points on the notional amount that we originally traded, 100 million.

So we say here, okay, 100 million times 2, which is 200 basis points, then times 4.43 because each basis point is worse, 4.43 basis points from a prev perspective, one basis point over five years, that is, and if you do the math, then that gives you a present value of or net present value of 8.86 million.

Now that's a, a sort of introduction into swap valuation.

The one caveat and I'm just gonna be upfront about this is that this only really works if you have a comparable market swap.

So it works nice if we have a swap that has exactly five years to live. However, if that swap, if we look at the swap now two weeks later and it's no longer a five year swap, but a four year, 11 months and two week swap, then you know, we might have to take a little bit of a different approaches to make sure we're accurate.

But the concept is what I wanted to bring across.

And then very briefly, let's just have a look at a couple of or two common application examples here.

And the first one is that we have a corporate borrower and they have taken out a loan and we're using EURIBOR here as an example.

So European example, and they have borrowed money and the interest they're having to pay on this loan agreement is arrival o plus 1.5%, let's say six months arrival doesn't really matter.

But every six months reset.

And then obviously add 1.5% to the set, to the ref or to the fixing rate.

And that determines a payment.

Six months from now, they are either corporate borrower would like to turn this floating liability synthetically into a fixed rate loan, and they can of course use an interest rate swap for that.

They are paying, floating on the loan they would love to receive floating from the swap for that reason.

And that means they have to pay fixed into the swap.

So they are entering into a payer swap that is having the same time to maturity than the existing loan agreement.

And the market maker did quote a swap rate of 3.7% at the time, which basically in return for EURIBOR and you can see again, assuming reset and, and, and fixing dates, et cetera, are falling on the same day, then these arrival payments will cancel each other out. What's left is 3.7% on the swap and 1.5% to pay on the loan as a spread over EURIBOR.

And that means a total payment of 5.2%, and that will be 5.2% regardless of where EURIBOR goes in the future.

If EURIBOR goes to 10%, yes, we still, or the borrower still has to pay 11.5% into the loan, but they also get 10% out of the swap and they will have paid 3.7% on top of it or to get this.

So that would, net out to 5.2%.

And if EURIBOR goes to zero, then one point a half percent on the loan and zero comes from the swap, which means, again, a total payment of 5.2%.

So we have fixed the level of interest rate that we're paying on our funding if we are the corporate here.

This could also be then just be used in the complete opposite way.

So we have now an example that looks at a bond issuer that is looking or to swap a fixed coupon bond they have just issued, right? So they issued a bond that pays a fixed coupon of 4.5 percent just this morning.

And they issued that bond at par which means the yield they are paying on this bond is 4.5 percent.

And this issuer, for whatever reason, wants to turn this fixed rate liability synthetically into a floating rate liability.

So let's think about what's happening currently, the borrower pays a fixed rate to the bond investors.

So they would now like to turn this into floating.

They want to pay a floating rate. That means on the swap they have to start with receiving a fixed rate.

i.e. they enter into a receiver swap where they receive the fixed rate and then pay a floating rate. In this case, we're using USD as an example.

So SOFR as a return.

Now, the time this example was taken, the market maker quoted you know, four point or you know, 4.04 to 4.06.

That is the normal bid offer spread bid asked, right? And because the client is looking to receive the fixed rate, the lower one applies.

So in theory, the fixed rate should have been 4.04% and then they would've paid a sulfur.

Now, let's assume the client doesn't want this mismatch here because you can see there's a mismatch. If they receive 4.04 from the swap, but they pay 4.5% into the bond, then it's not as simple as taking the payment from the swap and pass that on to the bond investors.

You will have to add 46 basis points there, which technically probably isn't a big deal. But let's assume here that the client wanted to have absolute you know, over a hundred percent match here.

So they don't wanna receive 4.04, they wanna receive 4.5%.

That's what they, they want because then they can pass it on right into the bond perfect match.

So just take the money from the swap, put it into the bond done.

Now of course, the market maker has quoted 4.04.

They don't want to pay a 4.5% i.e. 46 basis points extra right? Per annum without receiving an adequate return because that would be an off market swap, right? That would make the PV of the swap no longer being zero right? Now, two ways in which this could be settled, right? The market maker could pay 4.5% to the borrower and then get whatever the resulting present value of that swap.

Now is because 4.5 is no longer the same PV then sold for flat there could be an upfront payment from the borrower to the market maker to compensate for that.

Or as it has been done in this case where basically saying, okay, if the market maker adds 46 basis points here on the fixed lag and we're having a same payment frequency on both fixed and floating lags, then that should be equivalent to the borrower adding 46 basis points on the SOFR lag because the market maker pays 46 basis points extra.

If then the borrower pays 46 basis points extra on their lag, that should work out to be again, then a swap, which has a present value of zero.

So in this example, X will then be calculated roughly being, 46 basis points per annum.

So now what's the situation? The borrower receives 4.5 percent from the swap, pays a 4.5 percent to the bond investors, and then has to make a payment of sofa plus 46 per, 46 basis points per annum.

And that, ladies and gentlemen, is all I wanted to share with you today.

Thank you so much for being our guest here today. Hope you found it beneficial.

Have a great remaining Friday, a fabulous week and a ahead, and I hope to see you again very, very soon.

Goodbye for now.