Principles of financial engineering

[cojak]

I'm reaching out to the community and donating something that hopefully is of interest to some people. There is a lot of confusion around this material and I'd like to cut through that and present something useful that benefits the community, not me- I get nothing from this except satisfaction that I might have helped somebody.

Here you go then...

Could I try and move this discussion in something I'm interested in. Have you ever tried building models to give you an edge when betting on sports. Seems a much simpler and easier thing to predict than the stock market. I'm told cricket and tennis have lots of data available, and there is the bet fair market where you can bet and lay odds.

Specifically I'm talking about in game betting. Not trying to predict who will win before the game. As that no doubt requires in depth knowledge and a lot of luck. But more the betting whilst the game is in play. That way you can aggregate all past games together and build models off that. For example if someone goes a set down in tennis, how does the market react in terms of the odds given. Does the betting market over react to this new information, when compared to the actual historic odds. Stuff like that. Much simpler than financial instruments. Lets be honest, most people can't get their heads around mortgages and their costs/ how to compare never mind options futures and swaps.

[Cowboydave]

Specifically I'm talking about in game betting. Not trying to predict who will win before the game. As that no doubt requires in depth knowledge and a lot of luck. But more the betting whilst the game is in play. That way you can aggregate all past games together and build models off that. For example if someone goes a set down in tennis, how does the market react in terms of the odds given. Does the betting market over react to this new information, when compared to the actual historic odds. Stuff like that. Much simpler than financial instruments. Lets be honest, most people can't get their heads around mortgages and their costs/ how to compare never mind options futures and swaps.

I have no idea I'm afraid. Most of these sports betting firms are making money either not taking a position and just making the spread, or by analysing a users betting patterns and using that info to form a betting strategy against that user. ie. your Ascot bet may not be put on if they think you always back losers at Ascot,they just take a position and pocket your stake.

If you are talking about arbitrage I doubt you have the hardware necessary.

I'm not sure if you can pay for volume info for sports betting. Like "level 2" in stocks. If you can see order flow as it's coming onto the exchange you could jump on the bandwagon I guess. But you'll probably get shafted by very fast bots that pull the orders at the last minute, after you've committed, moving the market against you. That's what happens in algo trading.

[Cowboydave]

Part 2: Intro to curves

Ok guys, cowboydave back again for another community information session. Reaching out to the community with hands out and palms facing up!

Trust you've all read the previous post and now understand what an Interest Rate Swap is and how it works. Now lets get straight into some curves action. What is a curve in this context? It a graph of interest rate against length of borrowing.

Here's a curve:




As I said in Part 1, to price an interest rate swap you need two curves. You need a discount curve and a forecast (aka forward) curve.

First, think of the swap, it has two sides, usually Fixed and Floating. One bank pays fixed amounts at the end of each cashflow period, and the other bank pays a floating amount that is calculated from the notional ($1M here) and a rate based on LIBOR (for this example) and observed at the end of the cashflow period. The fixed cash flows are all known at the outset and are calculated from the notional ($1M) and the quoted fixed rate (4%), as per previous example.

The floating rate cash flows only become know as time passes. At the outset they are all unknown, they are all in the future. These are not known until the rate for each cash flow period has been set, at the end of that period. This is known as rate setting, funnily enough.

Below is a bunch of 3 month cashflow periods for a 1 year swap. As per my previous post, at the end of each cashflow period we observe LIBOR (+20bp) and use that to calculate the cashflow amount for the period in question on the floating side of the swap. For the fixed side its a constant (4%x$1M). Think of these cashflow periods as a series of variable rate payments on a mortgage, or whatever.

1/1/2000-1/4/2000
2/4/2000-1/7/2000
2/7/2000-1/10/2000
2/10/2000-1/12/2000
…


So in order to price a swap where its cash flows are going out into the future from today (where we don't have a real rate yet), we need to estimate what the future rates will be. Once we have the estimate of the forward rate - which is an estimate of the cost of borrowing starting at some time in the future - we can use that to work out the floating rate cashflow amount. For each cashflow date we then have both the fixed rate amount and the floating rate amount, and we can work out the net cashflow. Sweet. This is why we need a forward curve.

Why do we need a discount curve? Once we know the estimated future cash flow amounts of the swap as I said in the last post, we need to discount them back to today in order to work out their present value to include them in the pricing. For that, we need an interest rate. That interest rate needs to be the rate at which I could invest an amount today, and at the future cashflow date get a return equal to the future cashflow amount. I don't want a forward rate for that (which is a rate for borrowing starting out in the future, at the beginning of a cash-flow period, and ending at the end of the period), I want a rate that i could invest at today, a spot rate ("on the spot" rate).

So where do we get these curves? We build them from observations of market data.

First we work out the discount curve. Lets take LIBOR, we can observe LIBOR in the market - to see what rate we have to pay for various lengths of borrowing. So we can knock up a LIBOR curve similar to the borrowed diagram above by observing the market data. However, most of the rates we see in the market are not effective rates, they are nominal rates. To work out the effective rate from the quoted rate we have to do a simple bit of maths. How do you back out a zero rate from a nominal rate? Well think of this. If there are two consecutive cash flows, and i invest $100 at X% in the first cashflow period and then invest what I get back ($100*X + $100) at Y% over the second cashflow period, I should end up with the same amount as if I invested $100 at Z% for the length of the two cashflow periods combined. If that wasn't the case, there would be arbitrage opportunities in the market. So, if i look at my market quote and i see the swap is paying 6% then i can do some simple maths to work out what interest rate gives me the same return at 6% invested for 6 months, reinvested for the next 6 months. That rate is known as the zero rate and its the rate we want on the curve, for convenience. Ok, so you can see we just keep repeating that until we have backed out all the zero rates until the long end of the curve out at 30Y. Zero rates are convenient for discounting, we don't want to keep turning nominal rates into zero rates before we use them for discounting.

Now we use this discount curve (aka zero curve or spot curve) to derive a forward curve (aka forecast curve or implied forward curve). If we know it pays X% to invest from today out to 1 year and Y% to invest from today out to two years, then we should be able to back out what it pays to invest for 1 year FROM 1 year out in the future TO 2 years out into the future. Again, this is simple maths. Forward substitution I think its called. So we can derive the interest rates for cashflow periods out in the future (as opposed to periods starting from today - use discount curve) by doing repeated forward substitution on the discount curve. we can derive the forward curve. Done, we have a forward LIBOR curve.

Once we have those two curves we can use the forward curve to get estimated amounts for the future dated cash flows on the floating side of the swap. And we can discount both floating and fixed rate cash flows using the discount curve. That's all we need to price a swap. If we need a rate for a date on the curve that we don't have, then we interpolate that rate from rates either side that we do have. If the curve is too jagged, it can be smoothed out.

Ok, that's the gist of it, in reality its a lot more involved and we use numerical analysis to solve for discount factors. Maybe i'll go into that next time, or I might jump into swaption pricing which is a bit more interesting and builds on swap pricing. That's cowboydave getting on his horse and moseying off into the sunset. Y'all take it easy, while I get saddle sores for ya

[Doggy Styles]

What none of this tells me is what interest rate swaps are for, and what is the principle behind them. In layman's terms. (Actually it might do, but I didn't find it before I gave up)

Without that, the rest is gobbledegook, like explaining a piece of machinery with only a list of nuts and bolts.

Bring back Gricerboy. I know what trains are for and have an idea of the principles behind them. And they are far more interesting.

[Cowboydave]

What none of this tells me is what interest rate swaps are for, and what is the principle behind them. In layman's terms. (Actually it might do, but I didn't find it before I gave up)

Without that, the rest is gobbledegook, like explaining a piece of machinery with only a list of nuts and bolts.

Bring back Gricerboy. I know what trains are for and have an idea of the principles behind them. And they are far more interesting.

An IRS is used to hedge your interest rate exposure. So if you already have a variable rate loan and you think rates are going up, you can take out an IRS. This means you swap your variable rate payments for fixed rate payments, avoiding the pain of rising rates. The party on the other end of the IRS has the opposite view on the direction rates are moving.

Apologies , I thought I explained that in Part 1

[doodab]

I may be alone in this, but I found that interesting and informative. Thanks.

[d000hg]

I may be alone in this, but I found that interesting and informative. Thanks.

It's all the drugs.