 Hi guys, it's MJ and in this video, we're going to be looking at interest rate derivatives. Remember, this is me studying out loud. It's very opinionated. It's unscripted. So always consult your notes before taking what I say as gospel. But in this video, we're going to be looking at interest rate derivatives and these possibly are one of the most difficult instruments in order to value because what you're basically doing is we're going to be having call and put options. But instead of it on a commodity or a share, we're now going to be doing it with interest rates. And this makes it very difficult. Why does it make it very difficult? Well, that's what we're going to be talking about in this video. So with a normal, maybe let's back it up quickly and just give a quick little background is how a derivative works. Let's say I have a share or I have some gold. Okay. And there is the price today and there is the price tomorrow. We know what the price is today, but we don't know what it is going to be tomorrow. We can use a derivative in order to lock in the price tomorrow. So if I have a share and I want to have the option to sell it, I will purchase a put option, which gives me the right but not the obligation to sell. And if I have some or if I want to buy some gold tomorrow and I want to lock in the price today, I'm going to use a call option. However, I do assume that you guys are quite comfortable finance. So that is as far as derivative introduction is going to go. Let's get straight into the nitty gritty of interest rates derivatives. Okay. So the behavior of an individual interest rate is more complicated than that of a stock price. Why is that? Well, remember what we were talking about in earlier videos. Interest rates are made up. Okay. There's something that someone thinks, okay, today the interest rate is going to be 10% in another country. Someone must say, okay, the interest is going to be 5% and in another country, someone might say the interest rate is minus 2%. Okay. And why that happens is because interest rates are made up. They're not just made up arbitrarily. You know, there is some thought behind it and how it will impact the economy. But the fact of the matter is that the government or the central banks, they very much set the interest rates in their territory. Now, why is this making it more complicated than say shares or gold? Because interest rates are two-dimensional. Okay. And what I mean by that is when we look at say a share or gold, we're just looking at the price. When we look at an interest rate, we're actually looking at a curve. Okay. And this is known as the interest rate curve because what interest rates do is they tend to vary with time. Okay. So this is time and this is the interest rates. And I mean, these things can vary for a lot of reasons. They could be, you know, because of inflation, expectations, market demand and supply, all these various things. I mean, liquidity as well, short-term, you know, more liquid than long-term, all these various things. So before when we came to price, say shares and gold, we were developing an instrument or a formula or a model that needed to output one thing. So it was one-dimensional. And this you're quite familiar with, you know, black skulls model and all that type of stuff. We're predicting, you know, what is going to be the price of the forward price, one-dimensional. But when it comes to interest rates, it's an entire curve. We need to model what the interest rate is going to be throughout time and create some sort of curve. Now, what makes this tricky, okay, is that the volatility at different points in the yield curve are different. So this might be more volatile, and this might be less volatile, which means when it comes to modeling this, the mathematics does get very complicated. Another thing that makes interest rate derivatives quite tricky is that not only is the interest rate going to determine the discounting value, but it's also going to be determining the payoff. So we use interest rates for both discounting and for payoffs. Remember, when we looked at the one-dimensional or the traditional derivatives with, say, shares or commodities, we would take the price in the future and we would discount it, move it back according to the time value of money with an interest rate. Okay, what interest rate was used? Well, that was a lot of discussion, but normally the risk-free interest rate was used. Although, like I said in the very first video, that risk-free interest rate is hypothetical and it doesn't actually exist in practice. So already that causes quite a bit of issues in normal standard or what we call vanilla derivatives. But now when we come to, say, interest rates, not only is this interest rate going to be used for discounting, so we have that problem, but it's also going to be used in the payoffs. In the fact that if the interest rate goes up, then a payoff might happen. If interest rate goes down, a payoff might happen to some of the various parties. So because of all this complexity, I mean, we kind of still take the black skulls model, but we make it even more complicated. I mean, when you look at the mathematics behind this stuff, it is quite crazy and a lot of the proofs behind these formulas are beyond the syllabus. I mean, you're going away from, say, actuarial science and more into something like financial mathematics or what's that fancy word that they use? They call them short-quants. That's what the piece is called. I'm trying to think, what is that short for? Basically, these guys are really, it's more mathematics in the finance and it's the way to deal with all these various things that are all these dynamic links between the derivatives. So I mean, what more can we say about interest rate derivatives? Well, let's maybe talk about the floors and the ceilings and the colors. Okay, so let's use a different color. Okay, you can get a ceiling or a cap. And what this does is you could maybe say you're buying out a house and your payments are dependent on the interest rate. So if interest rates go up too much, then your house repayments become also quite high and you could get yourself bankrupt. So what you could do is you could purchase a ceiling, which means that if interest rates, interest rates move around like that, if they go above a determined ceiling, it then makes a payout to you. Okay, and you would want that because that would then protect you from interest rates going really high and then, you know, you defaulting on your house. In the same breath, you can get something known as a floor. So if for some reason lower interest rates is detrimental to you, you can purchase this instrument, which will then make a payout if the interest rate goes below a certain level. So if interest rates are between say three and five percent, you could buy a floor at say four percent. And so if it is at say three point eight percent, it makes a payment to you. You could then purchase both of these things together, have a ceiling and a floor, and that is known as a collar. Now, when it comes to say pricing these things, like I said, the mathematics is very difficult. And it is something that you need to know for maybe the specialist technical subjects, but not necessarily for the specialist application subjects. For the fellowship, you just want to be aware of it. I think for the technical subjects, you might need to be able to actually do these calculations, which is quite tricky because they are quite quite difficult. But then I mean, this does open up a whole bunch of things. Once you have interest rate derivatives, you can start playing around with with bond options. There's actually one way that you can construct an interest rate ceiling or an interest rate floor by having a specific portfolio of bonds and arranging them in a certain way so that if interest rates go up, you sell some of the bonds that, you know, have the interest rate relevant to that. But we are getting quite complicated. And I want to just keep this video more around what makes interest rate derivatives complicated. The main one being that interest rate is used in both the discounting and the payoffs. And in the fact that with interest rates, we're trying to model an entire yield curve, instead of just a one dimensional price, and that this yield curve does have some varying volatility as the curve changes. There is the how do you pronounce this guy's name. And they did it in in 1977. I think it was Vasik. He managed to make a model of this interest rate that took account of the different volatility is was arbitrage free. I mean, that guy is quite the genius. But anyway, I think let's end this video here. Next time we're going to be talking about something really fun called securitization. So make sure you you tune in for that one because I really like securitization, which is quite fun because most of the time I've been talking about how I hate all these things. Securitization is something that I absolutely love. So hope to see you guys for that video. Otherwise, steady hot