Good morning, good afternoon, good evening, uh, wherever you are in this world, and a very, very warm welcome, uh, to this Felix live session.

Introduction to Interest Rate swaps. My name is Thomas Kza. I'm head of financial products here at Financial Action.

I have the honor to talk you through, um, this session here today.

So what are we going to actually talk about over the next, uh, 60 minutes? We are going to start with a quick overall introduction to swaps, followed then by a look of, uh, or at the cashflow mechanics of interest rates swaps, more specifically on the fix to floating interest rate swaps.

Uh, we will then, um, after we have a soer understanding of those, um, have a intuitive look, take an intuitive look at interest rate risk in interest rate swaps.

Uh, we will briefly touch on the fundamentals of interest rate swap valuation.

And then we're gonna wrap this up with a look at some, uh, common application examples, which then really help to explain as to why interest rate swaps are such in large part of the OTC derivatives market.

Um, we have just had the, um, triennial survey from the BIS released, uh, a week or so ago.

Uh, and they're the dev daily average, uh, turnover in interest rate swaps was just below, uh, $7 trillion a day. And that is, of course, a significant, uh, notional amounts that are traded here on a daily basis.

And we wanna understand as to why this is and what these products can be, uh, used for.

And we're gonna see some of the application examples at the end. As I said, I said, we are going to start with a general look at swaps, and more particularly of course on the interest rate, uh, swap range of instruments.

Now, generally, um, interest rate swaps are just in inverted commas, another type of financial swap and what all those financial swaps has have in common.

And what really distinguishes them from, uh, forward contracts, for example, is that they are the agreement between two counterparties to exchange two series of cash flow.

So if you think about forward, usually what they all have in common is that there's a one time exchange between cash and an asset, or there's a cash settlement, whichever way this works.

But after this, um, final or this settlement has been, uh, or this payments have been made, then the contract stops to exist.

That's kind of like the forward contract. However, in case of, uh, swaps, we have usually exchanges of cash flows or off cash versus assets at multiple points, um, in time.

And those series of cash flows, that's what we loosely refer to as the swap lags. And then Of course, in case of interest rate swaps, it kind of makes sense that the cash flows that we are exchanging here, uh, are linked to interest rates.

Uh, and then of course, when you sort of look a little bit further down on the slide here, you see that there are different mechanics, different structures, uh, that we can use to exchange cash flows linked to interest rates. And we're gonna talk about all of them on this slide. However, we are gonna focus for the majority, uh, of this class on the first type here, which we refer to as fixed for floating swaps. And this, I think is by far the most common type of interest rate swap structure that's traded. Single currency here, IE both swap lags are denominated in the same currency, could be US dollar, could be euros, whatever, uh, you'd like to think about.

Uh, and then we are exchanging a fixed rate of interest that is basically agreed upon at trade inception versus a stream of variable cash flows.

The floating lag, as we call this, and the payments on the floating lag, are determined by future fixings of, um, whichever interest rate benchmark we have agreed to use here.

That could be in some cases, for example, in euros, we still have U ior.

So an IB rate, an interbank offered rate that we can use to determine the cash flows on the floating leg.

It most likely nowadays though, in most currencies, will be one of the near risk free rates.

Sulfur, um, Saron, Tona, sulfur, Sonya, uh, Esther, and all those, uh, newly created, uh, rates there that came up and about as a result of, um, us finding out, or the market and regulators were, um, particularly finding out that L-I-B-O-R was not immune, uh, to manipulation.

So, um, as I said, a fixed stream of cash flows versus a variable rate of cash flows.

And now of course, uh, we need to be careful here when we use, or that we use the right terminology in fixed for floating interest rate swaps. Nobody buys anything.

Nobody sells anything, hence there isn't really a buyer or a seller here. The counterparties are referred to as the payer and the receiver, and that is always in reference to the fixed rate. So if you hear someone saying, I'm a payer in 10 years, that could mean that they have just entered into a 10 year payer swap, um, which means they are going to pay the fixed rate for the next 10 years.

And then of course we'll receive in return the variable, the floating rate, um, in return, however, that we don't need to mention assets, sort of, um, you know, a logical consequence of the fact that we are a payer.

If I'm a receiver, then the opposite applies.

I'm receiving the fixed interest rate and I pay, of course, the floating, uh, swap leg.

But again, we don't have to, uh, mention this.

Now, of course, this, um, is only 100% crystal clear, uh, once you have a fixed rate, um, which is not always the case.

As I said, most swaps in the interest rate swap world will have a fixed versus floating, uh, you know, general mechanic, but not all of them.

We have a actually quite a variety of, uh, swaps where both, um, swap legs are actually linked to a variable rates. So both legs are floating where exchanging, uh, floating stream or a variable stream of cash flow, uh, against another variable stream of cash flows. And of course, that only really makes sense if there's some sort of a difference between, uh, the interest rates that we are exchanging here.

Right? Um, so that means we have obviously a book potential range of different, um, basis swaps that we, um, can consider.

The list that you see here is of course not complete. There's maybe some other, uh, types there, but I would suggest that the three that we see here are the most common, uh, type of basis swaps.

So let's just kind of quickly talk through all of them.

There's of course, first of all what we call, or what I would call a reference rate basis swap, meaning we're in the same currency, so single currency swap, both are cash flows are denominated in the same currency.

We also have what we call the same tenor IE the underlying interest rates that we're using here will refer to the same amount of time, for example, overnight or three months or six months.

Um, but the difference is that we're using different, uh, interest rate benchmarks here that we are referring to.

So for example, in the US we have two overnight rates that are, um, or that have a published or that have a fixing published on a daily basis, for example.

That is the, um, sulfur, of course, the one that secured overnight financing rate from the repo, uh, market.

And then the effective federal funds rate, which is basically looking at the unsecured, uh, lending transactions between prime banks, et cetera.

And, uh, so these rates will of course be very closely linked, but they might not be exactly the same.

There might be, there will be, of course, a difference between both, because one is secured, the other's unsecured, and then of course different market mechanisms will drive the spread higher or lower.

So there's some degree of, um, you know, variability in the spread.

And so if you are, for example, hedging a large interest rate swap book and some of the swaps you've traded with clients against EFFR and others, you've traded against sulfur, you might find yourself running a particular basis risk here on the, uh, swap book, so that you are probably a net payer and EFFR and a net receiver and sulfur, and then you could use such a basis swap to eliminate this basis risk.

Or maybe you have some really specific view on how the difference between EFFR and so FR is gonna, uh, change over time.

And then you could, uh, use this type of swap potentially also as a speculative uh, position.

So that's the, uh, reference rate basis swap, where basically the underlying reference rate is, is, is different.

We then, um, can have what we call a tenor basis swap, which is something, for example, that still is some, uh, would still be found in, uh, euros, where we have still, I os being used as benchmark four or interest rate benchmark for the floating leg of, of many swaps we're trading.

And then of course, we know that there's different 10 for IO or UIO we should pre precise there.

So there's for example, one month UIO, there's a three months UIO, there's a six months UIO, and again, you might have, uh, to hedge, uh, sort of a basis risk that you're, that you have in your portfolio because you've traded some swaps against three months, UIO, others against six months UIO. And then basically you find yourself having a, uh, basis risk, for example, your net payoff of three months and your net receiver of six months, your IO and then of course you're exposed to the spread between the two.

And then this tenor basis swap, as we call it, would be an, uh, instrument that you can use to address this risk.

And so tenor basis swap means nothing else that we're strictly speaking in the same currency.

We're using the same type of benchmark rate, but the two, um, benchmark rates differ by the tenor, uh, that we are, uh, that we're, uh, linking to by determining the cash flows.

And then last but not least, we can also, uh, have something that's called a cross currency basis swap.

And what that means is, in complete difference to what we have, uh, said so far, we are actually having or exchanging two floating rates, but they will be in different currencies.

So for example, you could enter into a SWAT way changing, exchanging sofa versus esta, for example.

So a dollar overnight rate versus a European overnight rate or soya or, uh, sarona, whatever, um, it is that you'd like to, uh, think about here.

And that of course is a slightly different, um, animal, but I still wanted to mention here because it's a, you know, relative important part of the, of the basis swap, uh, market.

And as I said, other combinations probably do exist. You can obviously think about maybe bringing some of these things together, have reference rates that maybe sort of differ by tenor and maybe even in currency.

So there's obviously combinations of all this, but, you know, that should be enough, um, for us now because as I said at the beginning, what we want to focus on here, ladies and gentlemen, is the fixed to float, uh, swap in a single currency.

That, of course, is a pretty, uh, clunky name. So I'm not gonna repeat this, uh, many more times when I say swap from now, uh, going forward, then I refer to the single currency fixed for floating swap.

Keep in mind though, that there's many other structures that do exist as we have just seen.

Now, um, as you know, interest rate swaps are generally considered to be OTC instruments.

Yes, a lot of those swaps are traded or are executed on electronic trading platforms, but that does not make them an exchange traded product, right? Because we can still, um, send, uh, requests for quotes, we can ask market makers or counterparties for specific structures.

We can basically tailor those instruments to our needs. There are some exchange traded swap futures, um, but that is not today's topic.

We're gonna focus on the OTC part, um, of this market.

Now, um, that means obviously when an instrument can be tailored, we need to, in the negotiation process, IE between the two counterparties, agree on a couple of things to make sure that we have all, um, the same understanding about the contract that we are about to enter into.

And here no particular order are some of those, uh, important things that we need to, um, agree upon with our counterparty.

And let's go through those things one by one.

Um, and just sort of see as to why this is important and what the general, uh, con, uh, conventions here probably, um, are.

So first of all, it's a notional amount that we want to, uh, discuss now, um, and of course, I think you probably will be aware of that already, that the notional amount is not in an amount of money that will be exchanged here at the beginning, at least not for single currency swaps.

Cross currency different.

We might or we will see some, um, exchange this of cash flows at the beginning and also at the end of the trade.

Um, but we're talking about single currency, uh, swaps here, meaning there's not gonna be an exchange of notional, because if you and I entered into a swap on a hundred million dollars fixed versus floating, and then at inception I give you a hundred million dollars and you give me a hundred million dollars, uh, we might as well not do this, right? So that's, um, the idea.

But what is the notional amount then for, well, that's quite straightforward because we are exchanging interest rates here and interest rates are given in percentage numbers.

And so we need to transform this percentage number into an actual dollar amount or currency amount.

And for that, we just need a calculation basis.

And that's basically the function of the notional amount.

So that's something we need to, uh, obviously determine, um, pretty much, um, at the start.

And also from a market maker's point of view, you wanna know roughly what's the volume that the client is looking, uh, to trade.

Um, and the reason for this is you wanna see, um, how, you know, big the volume is in comparison to the average daily trading volume to see how long it will probably take you to hedge this position, how much, um, execution risk, market risk you're basically, uh, taking there.

And that should then inform the size of the bit of a spread, um, that you might wanna, wanna quote.

But that's, you know, the usual sort of things.

None of that is specific to, uh, interest rate swaps.

The important thing is obviously the trade size for many, many, uh, other asset classes as well for interest rate swaps, though, it's not only the trade size, uh, that matters from a risk point of view, but it's also the tenor.

And that is very similar to the argument here that you might know from, uh, the bond world, right? Because there you've learned that obviously, uh, a bond that has a longer time to maturity, and we're talking about fixed coupon bonds here, and ignoring the coupon for a while, uh, has obviously, uh, or the, the, the sensitivity of such an instrument increases with increasing time, uh, to maturity, right? And that is the same here for interest rate swaps.

So, you know, um, a hundred million one year swap fixed versus floating will have a very, very different overall interest rate risk than, for example, a hundred million 30 year, uh, fixed versus floating swaps. So it's a combination of trade size and the maturity or tenor, or basically if you want to call it duration, uh, here in general, uh, then that's fine for me as well.

So those are, uh, certainly components and not only obviously do we want to know the maturity, um, to get a better sense of the interest rate sensitivity we're taking, but also because there's a term structure of interest rates, right? And that means under normal circumstances, the one year rate and the third year rate, um, in the swap on the swap curve will not necessarily be the same.

Hence that's a, you know, for us information that we need to find the appropriate point on the yield curve or swap curve, uh, that, uh, we're, we're actually, uh, gonna trade here.

Okay? So these are then, um, I'd say very important risk related points.

Now we're coming to some that are, you know, maybe not quite as critical, but still, uh, certainly important.

And I skipped the fixed rate for now, I'll come back to this in a minute, but I wanted to talk about the reference rate, um, briefly and the other two components that you see here as well.

First of all, when we're entering into a swap, um, you know, in addition to the factors we have discussed, uh, so far already, we need to discuss which type of reference rate are we going to use here to determine the payments on the floating lag.

And of course, you know, the reason as to why we have to do this is they might differ and the expected cash flows will differ, and then the SWAT rate might differ.

Um, so we need to have clear understanding of what is gonna be paid here on the floating lag, because as you can sort of conceptually, I think very easily, um, probably capture is that a three months arrival and a six months arrival probably won't be, uh, the same all the time, right? And so if I'm entering into a swap where I receive fix and pay six months, uh, rate versus, and, and I pay enter into the swap where I receive fix and pay at three months rate, then the fixed rate will not necessarily, uh, be, uh, identical, right? So this is important information for coming up with the fair price, uh, of this, uh, particular product.

So that's why it's important to determine the reference rate, um, at the beginning of the negotiation process as well.

Then we need to, um, discuss what we call the reset frequency.

IE how often do we reset the fixing on the floating leg? Because so far we have just sort of, you know, colloquially said, yeah, okay, we're going, we we're having a fixed rate of interest versus a variable, and that's changing every now and then.

Well, how often, how frequently does the rate change, right? That's what we call the reset frequency, um, under normal circumstances.

Um, so pretty much also, if Ive ever come across the reset frequency is determined by the tenor of the underlying reference rate. What does that mean? If the reference rate, for example, was a three months IBOR or a six months IBOR, then we would reset this floating payment every three respectively, six months.

If it's one of the overnight rates like SFR, then that is basically a one day an overnight rate, meaning that we actually are gonna see a daily reset of the floating rate.

So that's, these two things normally go hand in hand.

There are of course variations, but that's probably more of an exotic, uh, type of instrument where you have a six months IB reset every day, things of that nature.

But that's, um, I wouldn't say, uh, a fairly common, um, thing to do.

So usually these two are aligned.

And then before we saw this, um, move away from I bor in many currencies to the OIS world, and we're gonna talk about all this, uh, in a, a little bit more detail, but, um, you know, OIS overnight index swaps, which are sort of like those swaps that are against overnight rates.

Um, we also had almost always, um, a perfect match between the reset frequency on the floating lag and the payment frequency on the floating lack. Meaning if the underlying reference rate was three months, IBOR, we would reset this every three months.

And then at the end of the three months period, there would also be a payment on the floating lack.

IE If we had three months IBOR, then this would be a quarterly payment on the floating lag under normal circumstances.

Again, variations did exist, but the vast majority of swaps would've worked this way.

And then on the fixed lag, um, there were different, uh, sort of standard conventions. There were some currencies that per market standard were paying, um, semi-annually, others were paying annually.

And so, very easily you could come across a situation as it's shown here on the slide, and by the way, that still is the case in Euros, where the standard convention in, in IBO swaps is annual, uh, fixed payment versus six months, your IBOR, um, for everything above one year, uh, in, in swap terms.

So you will have a situation where there's a mismatch or, or sort of like, uh, where, where payments on the fixed leg and floating leg are not perfectly aligned like we have laid out here.

Let's say this is a five year swap, right? Uh, with annual, um, fixed payments.

So that means after one year, there's gonna be the first after two, there's gonna be the second, et cetera, et cetera, against six months, um, UIOR, right? And that means we're gonna see semi-annual floating, um, fixings.

And I mean, this is just, you know, in a way it's just how those cash flows work on those instruments.

But I think this is something that you look at and you think, well, um, okay, this is probably not a huge problem given that we're now in the world of central clearing, et cetera.

But, you know, if that was something we didn't have, if that wasn't margining, then obviously this would've been a little bit of a credit risk, uh, consideration here, because whoever pays the floating rate here, we'll have to make a payment after six months of the accrued interest for the first half of the year.

Um, but we'll receive the accrued interest for the fixed lag six months after that.

So once we made the payment, now we really kind of need the, um, counterparty to be around after 12 months as well to pay us, um, not just the first six months, but also the second six months. So there was a bit of a misalignment, but that was, uh, something that was just, um, uh, you know, dealt with.

Um, and we had very often, as I said, mismatch between, uh, the fixed and the floating lag payment frequency.

Nowadays, this is different when we're looking into the OIS market.

And that's what we're gonna do, uh, in a minute, and I'll just kind of leave this as a cliffhanger here before, uh, going there.

Um, I want to just briefly touch on a terminology that sometimes needs to be taken with a pinch of salt, and we have to be a little bit, uh, careful, because very often when you look at sort of statistics there, um, or, you know, trading systems or, or something like that, you see, uh, three, uh, three letter acronyms.

Um, like IRS and OIS, now, IRS stands for interest rate swap, OIS stands for overnight index swap, which is arguably a type of interest rate swap.

So sometimes then probably the most logical way to think about this would be IRS stands for all interest rate swaps together.

OIS is just a specific category.

Um, and while this makes perfect sense, what I've found is that in many cases, when you see IRS, um, in, in a chart and OIS in a chart, um, what this actually means is that the IRS is sort of like the, in inverted commas, old way, the classic way the eyeball linked, uh, swap.

Um, and OIS refers to the sort of, well, not so new, um, but the new way of trading swaps here versus overnight reds.

Why did I say not so new? Um, because, you know, the interesting, um, point to make here is maybe, um, that, um, the structure of an O-I-S-I-E overnight versus, you know, overnight floating versus fixed that's been around for much longer than actually the demise of L-I-B-O-R, right? So L-I-B-O-R, you know, this whole transition happened from 2018 to 2020.

I don't know what, but, um, you know, that is not the starting point of the OIS market.

In fact, we had overnight index swaps, uh, trading, um, in many currencies, you know, um, much, much earlier.

So I remember in my practitioner days, and that was sort of like the early two thousands that I was very, very actively trading Ionia swaps, for example, right? So this instrument was already around.

Now, what has changed since then is obviously a lot of the benchmarks are now different.

IE ionia is no more, that's now esta, it's been, uh, revised. And the same happened in other currencies.

Um, but also, uh, in the early two thousands, this used to be more like a money market instrument.

IE the liquidity of the swap curve was fairly limited, uh, beyond two years.

Um, and that has since then increased in terms of maturity quite significantly.

And now we have obviously absolutely liquid curve out to, uh, you know, at least 30 years in most currencies. And, and obviously, um, beyond that in, in cases as well.

So, um, I would say, um, safe assumption at the moment is when people talk about IRS in a, uh, graph, and there's also IRS versus OIS, uh, then this refers to IOR swaps versus, um, you know, OIS, uh, link contracts.

And so the fundamental difference here is that obviously these IRS structures have one single reset or one single fixing of the floating lag.

Um, and that's usually done in advance, and we're gonna see the mechanism in a minute.

And then OIS is versus overnight rates.

And this means we're, um, seeing multiple, uh, resets over a specific period.

And again, we're gonna, um, look at this in a, um, bit more detail, um, right now starting with the IRS and now we're using these, um, abbreviations there, um, way of, uh, operation, right? So this is, as I said, for many currencies, no longer really the way we're trading this, but for others it still is the predominant way.

So we need to know this right here is an example, and we're looking at a two year payer, IRS, um, where the fixed lag is paid annually, and the floating lag is linked to six months U ior, meaning that we will have a semi-annual reset of the floating leg, and we also have semi-annual payment of the floating leg.

Um, but you know, what we now want to investigate is when exactly are these resets happening and when exactly are the payments happening, and how exactly is the whole payment thing working anyway? So first of all, let's put dates to this.

And let's say we are today, the transaction date is the 10th of October, 2025. That's when we're trading this thing swaps in euros usually settle with a T plus two, um, settlement convention, meaning spot t plus two would bring us not to the twelves because that Sunday, but we are in this case actually on the 14th of, uh, October, 2025.

And now we said this is a two year swap.

So to determine the, um, maturity date of this swap, we have to just add two years to the spot date, meaning that the last day or the day on which the last interest rate is paid is the 14th of October, 2027.

Okay? Then, as it's standard for many, many other, uh, instruments, um, we are rolling the annual and also semi-annual payments on both legs over the maturity date, meaning that there's gonna be an interest rate payment on the 14th of October, uh, 2026, there's a second fixed payment on the 14th of October, 2027, and then the floating payments will happen semi-annually.

First one will be on the 14th of April 26th, um, then on the 14th of October, and then again on the 14th of April, 2027, and the last one on the 14th of October, 2027.

So now we know the dates, and of course, we're making the assumption here that none of the dates that we have on our screen here is a bank holiday or a weekend.

So we're just ignoring this for simplicity, right? If there was, um, a non-business day, we would have to apply the equivalent, uh, role conventions.

Um, but you know, that goes a little bit beyond what we want to discuss here today.

But generally, you now have the good understanding of when payments will be made, uh, and though what we can see here is that there's two points in time, uh, on which there is actually a payment on the fixed leg and on the floating leg.

And then there's two points in time when there's only a payment on the floating leg.

Now, uh, leaving the credit considerations aside here, um, what is, of course, you know, good to know is that, um, usually when we have two payments happening, IE one payment on each swap leg, we're gonna apply something called payment netting.

Meaning we're just, instead of you paying me something and I pay you something, we'll just make the net amount, uh, in a single transfer.

So if I owe you 1 million, uh, dollars for the period, and you owe me 300,000 for the period, then I'm gonna just send you $700,000.

And then that's the net payment, right? That's, uh, efficient.

That's, uh, obviously reducing amount of transactions, that's reducing, uh, settlement risk if you wish.

Uh, so it's the right way, uh, of doing this. Okay? So with that, now we are, uh, familiar with the timing of cash flows. We have discussed payment nettings. What we haven't discussed yet is which arrival rate exactly applies for which period.

Now, of course, we're trading this swap today.

That means interest rate starts to accrue on Tuesday, because that's really what a swap start date mean. This is not where we're exchanging, uh, the notional amounts because that doesn't happen.

But that's basically the start date from which interest starts to accrue on both swap legs, right? So next Tuesday, 14th of October, 2025, that then raises the question, which arrive or fixing does apply, um, for this period from 14th of October.

Um, sorry, yes, it is 14th of October, um, 2025 to the 14th of April, 2026.

Is it today's I or is it Monday's I, or is it Tuesday's IO? Now, for this, we have to know how your IO conceptually works and your IOR basically, you know, if you are not familiar with it, is if fixing for a term deposit, IE unsecured, uh, deposit, uh, given to banks for six months.

Uh, and the usual deposit market, with exception obviously of overnight also works on a t plus two basis, meaning the six months UI were fixing that was made available, uh, today at 11 o'clock Frankfurt time, if I'm not mistaken, that is actually a six months rate that applies for a six months unsecured deposit starting t plus two IE Tuesday, 14th of October, 2026 to, um, the 14th of April, 2026.

So covers perfectly, uh, our first six months interest rate period.

So takeaway is today six months arrival will actually apply for the first six months, um, period.

And then six months into the trade, we will obviously receive the first or make the first payment on the floating lag.

And again, we will also have fixed the next six months UIO that will then be responsible for the, uh, coming, uh, fixing, uh, or coming, uh, floating rate payment two days before that.

So we have a regular fixing, which then is applied, uh, for the, uh, period that starts two business days later.

And that means the last floating rate here on this swap will be known.

Um, basically if the 12th of April is a good business day, and the 13th is a business day as well, then it will be the 12th of April, 2027.

That's the point in time in which all cash flows on the swap will be known.

And we know exactly how much did we pay, how much did we, uh, receive.

So we can almost calculate, no, not almost, we can calculate what is the final net cash flow on this swap gonna look like for us.

Okay? Uh, so that is, um, the IRS.

Now, let's switch to OIS. And there's one important, uh, thing to note.

Um, and this is quite a significant difference because so far we have only looked at swaps where the reset frequency and payment frequency was aligned.

Um, now the good news is in OIS what we have aligned in most cases is actually the payment frequency on fixed and floating lag.

So what you very rarely see these days is an annual payment on fixed and a semi-annual payment on the, um, sofa lag. That's, you know of, of course can be arranged, but the market standard is annual fixed and annual floating.

But that raises a question because when I'd say overnight index swaps, OIS, and the most common, um, reference rate there in the US for example, will be sulfur, and sulfur is an overnight rate, which applies from one day to the next.

Um, you kind of start wondering, okay, if we are just paying the floating rate once a year, but the interest rate is reset every day, then there's now a mismatch between the payment frequency, which is annual and the reset frequency, which is daily.

And so then there should be automatically the question popping up, does that have any implications? And of course it does, and we're gonna discuss that, um, in a short moment.

But let's stick with our example here. Let's just map out the cash flows. Generally, we are sticking with the 10.

We have a two year, um, pay OIS annual versus, well, annual fixed payments versus annual esta.

So we're staying in Europe.

Um, but you know, this could be software, this could be Sonia, any of those rates, and they will work in exactly the same way.

Um, so that's the starting point.

Fixed versus floating annual versus annual.

But you know, we have a daily reset of the underlying reference rate, which is as of the European or the European short term, uh, rate, right? So same idea, we are trading today on the 10th of October, right? That's t and we're starting at t plus two, which brings us to the 14th of October.

And then we see again, uh, the interest rate payments rolling over the 14th of October.

Uh, so 27 is the final payment, 26 is the first payment.

And because now both slacks are paying annually, there will always be, um, payment netting applied.

So wonderfully efficient, no sort of mismatches and payment here, we can always net the cash flows very, very nice, um, very smooth and, and, and, and clean, right? But as I said, this comes with a bit of a problem.

Uh, and that is basically what the question at the bottom of the slide here refers to. What factors make the cashflow mechanics of OAS more complex, uh, compared to IRS? It's certainly not the mismatch of payments here on fixed and floating because that's been taken care of, but there's a problem in the mechanic, right? So how do interest rates generally work? When is interest rate paid normally at the end of the investment period, right? So if you would, um, place a deposit with the bank for three months today, right? Or well in T plus two, then may, let's, let's, uh, stay in that one.

So you start then with your, or your money is basically invested with the bank from the 14th of October, 2025.

It's a fixed three months deposit.

You have, uh, locked in a certain interest rate.

That interest rate normally will be paid to you in full at the end of the three month period.

So on the third 14th of January, uh, 2026, assuming that's a good business day, that's when you get paid, right? If you instead choose an overnight deposit, then your money will be only invested from today to next business day, which from today's perspective will be Monday.

But let's say we're starting next Tuesday, then it will be from Tuesday to Wednesday.

Um, and if that was an equivalent deposit, then when should you get your money back? Well, you invested on Tuesday, you should get it back on Wednesday, and that's also when you should get your interest.

Now in the OIS um, what we've done is we said, look, you know, we don't really want to exchange small interest rate payments on a daily basis.

I don't wanna transact $2 50 to you, and you don't want to monitor if I have transferred my $2 50 on a daily basis, right? This is way too inefficient.

So what we're instead gonna do is we are, um, making payments less frequent.

And so let's agree we're doing this once a year because it's nice and clean as we said.

But that also means, um, if put yourself in, in, in this situation that, you know, you and I are entering into the OIS and I tell you, okay, I'm gonna pay you floating.

You pay me fixed, so I receive fixed and I pay.

Um, so r but you know, we both agree it's fairly, um, inefficient for me to make you these daily small payments.

So instead, I'll just pay you everything after 12 months.

And you hear this, and then you remember that at some point in your career, you have been told about the time value of money, and you remember that someone told you the earlier you get paid, the better, because then at least when interest rates are positive, uh, then you can reinvest it and you can get interest on interest.

And so when I just tell you, okay, you know what, to be more efficient, let me just pay you all of the floating interest at the end of the year, you'd say, well, I, I agree with the efficiency argument, but it kind of means you pay me later, right? And because you pay me later than you should, at least for many, many, uh, instances, I think I should receive some compensation to sort of, um, make me, make me be at ease and, and, and sort of not giving up the time value of money argument here earlier.

So we cannot just say, I'll pay you, uh, the, the, you know, uh, complete, uh, floating rate at the end of the swap period, because that wouldn't be fair to you.

And so you wouldn't agree.

So how do we actually solve this in reality? Um, most of the OIS um, instruments work that the settlement at the annual basis is then done, uh, called or based on something called the compounded average of all, um, you know, overnight fixings.

So instead of just memorizing and basically just adding up the interest that I should have paid you in the different days, um, and then paying to you this after, or paying this to you in one go after 12 months, not only do you get the, you know, interest add up, but you also get the interest on interest as an additional return.

So how does that then work? And of course, there's a formula on the left hand side that is applied in reality.

So, um, you know, you can either look at this or you can look at the, um, table here, um, which I'm gonna use to talk you conceptually through this.

But the formula is the official, um, formula that's used by market participants to calculate this compounded average.

But basically what happens there in the table is the underlying logic.

So let's say we entered into a seven day swap, um, and you know, here the, the notional amount, you, you can think about it as $1, $1 million, 1 billion.

It doesn't really, uh, change anything.

Um, we just kind of say, okay, the the notional is one, okay? Um, then it's a seven day fixed versus floating swap, meaning a week from, uh, now this whole thing will be over and we're gonna have one net exchange.

That's the other thing I wanted to say.

Uh, of course, there's not always annual payments.

The payment happens either at the end of the first year or at maturity of the swap, whatever happens first, okay? So here we have a seven day swap, meaning at the end there will be this net exchange of cash flows.

Fixed rate is irrelevant. We just want to, um, showcase here how those, um, how the compounded average is actually calculating.

So we're just entirely focusing on the floating lag. Okay? So we're starting the swap on a Monday, that's when interest rate starts to accrue.

Uh, and let's say on that day, uh, we had a sofa, or for that day, we need to say we had a sofa fixing for, uh, of 5, 2 5.

Why for that day? Well, because the way sofa works we'll know this, most likely, um, is it's gonna be published on the business day following the day for which it actually applies.

So basically the rate from Monday to Tuesday will be known to morning, um, New York time, okay? So that was then published at 5 25.

And now we can use this to calculate, okay, what's the accrued interest on the floating lag for this one day that has gone by? So basically that is $1, $1 million, $1 billion times 5.25% times days over basis, uh, which is one day from Monday to Tuesday divided by 360 because sofa works on an actual 360 basis or day con con rich.

Okay? So this gives us in the accrued interest for the day one, which we now add to the original notional. So our notional has now increased by a tiny amount, but it's now 1.0 0 0 1 4 5 8, 3 3, and now what happens on day two? Now on day two, we have another, um, fixing available.

So now we know from Tuesday to Wednesday, the applicable interest rate was 5 26, but we're not calculating the accrued interest on one, but instead we're calculating it on this slightly higher amount of 1.0 0 0 1 4 5 and so on, meaning the second sulfur interest rate is not gonna be paid just on the notion of, but on the notional plus the already accrued interest, and that ladies and gentlemen means nothing else, that you basically, as the person that receives SU OFR at the end will receive interest on interest.

It's begged in automatically into the structure.

So yes, you don't get paid this couple of cents here, uh, on that, uh, Tuesday, but instead we're paying you next Monday.

But don't worry, you get interest on interest for the money that you are basically owed already, and therefore it's automatically reinvested for you at, uh, so FR so there we have the solution to the problem.

We have basically moved away from having the same payment and reset frequency, but it's done fairly in the way that we're using compounding here.

And that's in basically how the market operates in most, most cases.

And as I said, we're using the formula and then you can automate it very nicely.

The only thing that I would like to point out here and, and some might wonder as to why, uh, there is, uh, the number three here.

That's just because the interest that is set on Friday will apply from Friday to, uh, Monday, which is three business days, because in most, uh, countries, payment systems aren't operating on Saturday and Sunday.

Hence, we have a three day period.

And so this sofa rate of 5 25 will apply for three days of accrued interest. That's it. So then we have done this and we calculate basically what the accrued, um, or what the, um, uh, notional, um, amount of the floating leg has grown to, and it's now known as gonna be 1.001, whatever.

And so basically we know we started with one, we're ending with 1.001 something, and now we know the present value.

We know the future value.

And so what we can do is we can calculate what's the implied interest rate there.

So we can rearrange the formula of time, value of money, solve for the interest rate, um, and then we get basically what is the compounded average one week solve for fixing, um, using those values.

And that's gonna be 5 25 7, 6 9.

And then we're comparing that with the originally agreed upon fixed rate, and we can calculate a net payment.

If that fixed rate was 5 25, then whoever, um, paid, uh, the fixed rate will now receive the difference here, the 0.00769% on the notional, um, for the time, uh, of the swap.

And that is basically how we're getting around this phenomenon.

Now, very briefly, as I said, we're just gonna, uh, highlight the general principles here on the interest rate risk and also on the valuation.

And then we're gonna look at one or two application examples, and then we're already, uh, at the end.

So, uh, let's look at interest rate risk, and let's take this intuitive look because I think that's always very good to start with. What would I expect, what's my preference here? So here's a situation I would like you to imagine, uh, assume we entered into this two year OIS, um, and we're receiving a fixed rate of 3.75 versus sulfur, which is paid annually.

We now know how compounding averaging works, and we've done this this morning.

So now the question is, in which direction would we prefer sulfur to move in the future? And I think the answer is relatively obvious because we are in a receiver swap, meaning we know what we're gonna get paid over the next two years.

What we don't know is what we are going to pay on the floating leg.

So that will depend on where sulfur goes.

And so I think it's clear, uh, to say that we would prefer sulfur to actually decline, um, over time, because then what we receive is fixed and what we have to pay will go down, um, over time.

And that can sort of be then, uh, drawn into a conclusion, um, where we say fixed rate receivers benefit from a decline in interest rates, fixed rate payers benefit from a rise in interest rates.

And I think conceptually this is clear to everyone, um, and it's a very nice and intuitive way of looking at the interest rate, um, risk.

When it comes to valuation, though, we need to think a little bit, um, uh, differently though, because here you would say, okay, um, cool.

So if I enter into this two year swap today, and then, um, basically I have to wait two years, um, until the last sofa fixing has been made, then I know exactly what I will pay on the on, on on, or what I will receive on the fixed leg.

And I know also completely what I will pay on the floating leg so I can figure out what my final net cashflow on the swap, uh, was.

So I can basically determine my financial success on this one particular instrument once I know the last sofa fixing.

But while this is intuitively very nice, um, it cannot how we value swaps in reality, right? Because we need to be able to assign a value, a mark to market valuation to this, uh, swap that we have traded at any point, uh, during the day, any day over the next two years.

We cannot say, well, you know, we've entered into the swap here and I know I'm gonna get 3 75, and I know I pay fr but I don't know where slf r's gonna be.

So I don't know really if the swap is, uh, having a positive or negative value and how much that's not possible, right? So we need to think about how can we, um, value, uh, those instruments at literally any point in time.

And so we're taking a conceptual look, and of course reality is more complex, but I think this helps the general, uh, to understand the general idea.

So same assumption here, uh, we entered into this two year, uh, US dollar OIS we are receiving the fixed rate of 3 75, um, versus sofa paid annually.

And we did this this morning.

We're ignoring bid offers here for simplicity right now.

We did this this morning and now in the afternoon, um, you know, we, we look at our screens and we see that the market rate for two year OIS is now 3.73%, and that's obviously the fixed rate that we can see on the screens, right? So then the question is, does that help me? Can I somehow now calculate the current mark to market, um, of my position? Um, and the answer to that is yes, we can simply because we're still on the trade date, meaning this was a two year swap this morning and it still is a two year swap.

So what is the interest rate risk we got ourself into by trading the first swap, receive fixed pay floating, remembering the i we've just been through that means we are now benefiting when interest rates go down.

Okay? Um, now the question is have they gone down? And then the answer is, well, it depends which interest rate you're looking at. Because yes, the two year OIS rate has gone down, sulfur hasn't changed.

We don't even know su r for today yet, right? There's a daily fixing of su o sulfur that has not changed because it's still not known where today's sulfur is gonna be. We will know this tomorrow morning.

So there has not been a change in the floating rate.

So if we follow the intuition, then we're kind of saying, well, that should not have a value this swap, but in reality it has.

Okay? And that's basically just the common sort of replacement cost approach or whatever you would like to call this.

But remember, we entered into this swap and we're now basically exposed to interest rates going up, right? Where we will benefit when rates go down, but we exposed to rates going up if we do not want to have this risk anymore.

So let's say we entered into this swap this morning, believing interest rates will go down.

Now a new piece of information has, uh, come out, you know, some macro data or whatever, and we now changed our view. We said, okay, from here, interest rates will go up for the next couple of days, then maybe we don't want that swap anymore because the risk that we, that we, uh, got ourselves into is not really fitting our market view anymore.

So how can we get out one way? And there's obviously multiple ways of doing this, but one way and the most straightforward conceptually is we're just doing the opposite swap, right? So remember in the original swap here with our counterpart one, and by the way, this could be the same counterparty that this, uh, obviously is, is entirely possible.

But on the original swap, we received 3 75 and we agreed to pay solf r on an annual basis.

Now we are entering into the offsetting swap where we're paying a fixed rate, but, and here's the sweetener that is gonna be lower.

Now it's because the market is 3.73 and we're receiving sulfur on an annual basis.

And because we're trading both swaps on the same day, it means that these payments here, the fixed payments and the floating payments will not only happen on the same day, but it also means that these two floating payments will cancel each other out.

Exactly right? Because we're having a 12 months compounded average coming in, and we're having the same 12 months compounded average coming out. If we have traded the swap, same notional and same, uh, tenor, then of course these two cash flows will cancel each other out, uh, perfectly.

So if we're going to the table here, we can basically just eliminate these two columns.

And so what's left is we receive 3 75 and we pay 3.73, and that means we have a net, um, income here of 0.02% per annum over the two year period.

And now of course, what is left for us to be done, these are percentages.

So we now need to multiply that with the notional amount and we need to multiply that with the, uh, days over basis, right? Uh, and then we do this for the payment after year one and the payment after year two, and then we're still not done simply because these are payments that will be made in the future.

We want to look at things from a present value point of view.

So what we have to do is we have to multiply this with the one year discount factor, basically discounting the one year payment with a one year rate and discounting the two year payment with a two year rate, sum up the present values, and that's gonna be our mark to market value.

So conceptually, that is how interest rate swaps can be, um, valued, how we can calculate a mark to market.

Now, of course, this works perfectly here in our example, simply because we said it's the same date tomorrow.

This is no longer a two year swap.

It's one year, 11 months, three weeks and six days.

So cash flows won't match perfectly. Things become a little bit less elegant, but you get the idea.

And so the interesting thing here is that this swap has now a value that we can calculate despite the fact that sulfur has not changed, because the only thing that has changed is a two year swap rate. And so that's really where the interest rate on the two year swap, um, fixed versus floating then sits.

And that's almost it.

Now, just one more, um, application example, because obviously you kind of look at the volumes and you think, whoa, this is huge.

What are people using these swaps for? Now, the first thing we have just basically seen, it's when you want to take a directional view on interest rates, right? If you think rates will go down, you enter into receiver swap.

If you think rates will go up, you might enter into a payer swap.

And then when the move has occurred, you can either unwind it or you can just, um, you know, eliminate the risk by doing the opposite swab.

Uh, whichever way you're locking in some of the, um, p and l there, or you're basically front loading it, you know, different ways of of, of doing this, right? But that could be just a directional risk, an expression of taking a direction risk.

Um, it can, it could also be, uh, a hedge, right? And that means that you want to, for example, um, alter the interest rate, um, risk profile that you have.

So here, for example, we have a corporate, uh, or a borrower that has, uh, taken out money from a corporate bank via a corporate loan.

Those are usually, um, floating, um, rate instruments, right? So the, uh, Bora pays a variable rate here.

We're using a Euro example of Europe arrival plus, uh, a credit spread of one point a 5%, uh, in return for the loan that they have received.

And then, um, what we have here is a corporate that doesn't like the uncertainty, for example, or they expect rates to go up or whatever.

And they therefore want to turn this variable float, uh, variable, um, borrowing into a fixed borrowing. And they do this via interest rate swap. And what they do is they contact the market maker and they will ask for a price in the, let's say this is a five year loan, in the five year, um, swap rate.

And they get a quote here of 3.7 again, ignoring bid offer for simplicity.

And that means they will enter into the swap paying a fixed rate of 3.7, then get out U IOR from the swap and the UIO that they receive from the swap, if they've managed, uh, the contract, um, in the right way should cancel each other or should cancel out the UIO payment they have to make into the loan perfectly.

And so basically the net payment will be 3.7%, the fixed swap rate plus the 1.5% credit spread.

And that then basically leads to a net payment of 5.2% regardless of where or independently from where you arrive or is, uh, set at, you know, over the next five years, this corporate will not pay more than 5.2% all in yes.

If, um, LIBO goes, or UIO goes to 10%, of course they're gonna pay more than 5.2% on the loan because there they pay UIO plus one and a half, but they get your I bor, um, of 10% from this swap.

And so these two payments, um, offset each other.

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

I hope you found it beneficial.

Um, I still have a minute or two, so if anybody wants to take the opportunity and ask questions, do so now.

And please, as I said, uh, use the, uh, q and A function, um, uh, to do so.

If, uh, you wanna drop off, you have to drop off.

Um, have a great rest of your Friday, a perfect weekend ahead, and I hope to see you again or have you, uh, here, uh, on one of our sessions again in the near future.

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Thank you so much. Have a great weekend and let me know if there's any questions.

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