Principles of financial engineering

[Cowboydave]

I'm reaching out again to see if the community has any interest in this subject.

I would like to explain how to price complex derivatives. I can do that over three or four posts.

If the community is interested, I would like to contribute that.

This covers such diverse topics as numerical analysis, asset valuation, programming techniques and test driven development.

[russell]

I'm reaching out again to see if the community has any interest in this subject.

I would like to explain how to price complex derivatives. I can do that over three or four posts.

If the community is interested, I would like to contribute that.

This covers such diverse topics as numerical analysis, asset valuation, programming techniques and test driven development.

Go for it.

[cojak]

Go for it.

Yes, we'd all like to see that...

[Bellona]

when does the lesson start ?

[eek]

when does the lesson start ?

1 concern would be that this is Oztiny's latest sockie and given the fact his last post mentioned screwing up the pricing model just before go live I wouldn't trust his accuracy......

[Bellona]

Too much popcorn waiting for enlightenment from OP

[Bellona]

1 concern would be that this is Oztiny's latest sockie and given the fact his last post mentioned screwing up the pricing model just before go live I wouldn't trust his accuracy......

aaah
Thought I was getting better at this forum lark, but my naievety shines through !

[Scruff]

Seem like Fred the Shred has turned up as an IT Contractor. Going in to fix the RBS / Natworst issues and moonlight in Artificial Instruments...

An ex-city boy, Fred, moved to the country and bought a donkey from an old farmer for £100. The farmer agreed to deliver the donkey the next day.

The next day the farmer drove up and said: "Sorry son, but I have some bad news. The donkey died."

Fred replied, "Well then, just give me my money back."

The farmer said, "Can't do that. I went and spent it already."

Fred said, "OK, then just unload the donkey."

The farmer asked, "What ya gonna do with him?"

Fred: "I'm going to raffle him off."

Farmer: "You can't raffle off a dead donkey!"

Fred: "Sure I can. Watch me. I just won't tell anybody he is dead."

A month later the farmer met up with Fred and asked, "What happened with that dead donkey?"

Fred: "I raffled him off. I sold 500 tickets at £2 a piece and made a profit of £998.00."

Farmer: "Didn't anyone complain?"

Fred: "Just the guy who won. So I gave him his £2 back."

Fred used to be the chairman of "a very large Bank"

[Cowboydave]

Part 1: Intro to swaps

Ok, first lets talk about swaps. Swaps are a relatively easy instrument to understand and serve to introduce several key concepts involved in pricing derivatives. Namely, cash flows, curves and market value.

An interest rate swap is a very common interest rate derivative. It is traded both as customised OTC Over The Counter deals between (mainly) banks, and over exchanges as standardised contracts. This is important to know because when pricing an OTC swap, one needs to observe what a similar swap is trading for out in the market. A swap price is quoted as a fixed interest rate. This is convention. When one enters a swap, one usually buys fixed. ie. variable rate debt is easier to get in the market, market convention is to say we are buying fixed.

A swap deal has two sides. Floating rate and fixed interest rate. When you enter a swap, you usually seek to hedge an interest rate exposure and view that you have. For example, I might have a floating rate loan already. I may come to the belief that interest rates are going up and i don't want increasing interest payments. I go to the market and find someone with the opposite view and we get into a swap deal. From then on, I pay their fixed rate cash flows (I have swapped my floating rate cash flows for their fixed rate ones) and they pay my floating rate cash flows. If rates go up, I have won because I'm paying fixed. If rates go down, I was wrong and lose out on the benefit of falling rates but i have locked in a fixed rate, and banks like predictable cash flows. The game is usually in taking a slice off each transaction, not punting on the market direction. Swaps have been in the news lately so lets start here.

So how does a swap look like. First off , there are two participants, the so called counterparties to the deal. They agree a notional principal amount off which they both calculate future interest cash flows. Lets say $1M. Now, the fixed side of the swap is paying a pre agreed interest rate, lets says 4%. The floating rate of the swap is taken off an index, such as LIBOR, usually plus a spread. Lets say LIBOR+20 basis points. Now, LIBOR +20bp is changing all the time, so this rate is set on the swap at agreed intervals, lets say at three monthly intervals. So the cash flows look like this:

Start Date 1/1/2000
End Date 1/1/2030
Notional 1M
Interest period 3 months (ie. both sides pay or receive interest every 3 months, the variable interest rate is taken at the end of the 3m period)

Cashflow at end of first quarter:
On 1/4/2000 LIBOR + 20bp rate is 4.1%
On 1/4/2000 BankA pays BankB fixed sum $40000 (ie. 4% of 1M)
On 1/4/2000 BankB pays BankA 4.1% of 1M = $41000
The net cashflow for the first quarter is $1000 from BankB to BankA.

Cashflow at end of second quarter:
On 1/7/2000 LIBOR + 20bp is 3.9% (because LIBOR has moved down a bit)
On 1/7/2000 BankA pays BankB fixed sum $40000 (ie. 4% of 1M)
On 1/7/2000 BankB pays BankA 3.9% of 1M = $39000
The net cashflow for the first quarter is $1000 from BankA to BankB.


And that happens every quarter until the end of the swap. The floating rate is set at the end of the quarter (from the index), and the net cashflow is sorted out between the counterparties.

Ok, so lets say I have this swap on my books now for a while. How do I know how much it is worth? Why do i need to know? One reason is that I need to know its value because it is an asset (potentially has incoming cashflows) and therefore I need do accounting on it. I need to make daily adjustments to my view of my financial worth-these are reported to regulators etc, based on how this swaps value changes from day to day. Therefore i need to be able to value it. I need to know its so called present value.

Ok, would you rather have $1 today or $1 next week? $1 today is usually the right answer because you can invest it and have $1.1 next week, lets say. But what if i said, would you rather have $2 next week or $1.50 today? How would you be able to compare $1.50 today and $2 next week? You would have to kind of normalise the amounts, so that they are comparable. This is like bringing two amounts that are in different units, to the same unit, in order to be able to sum them. Or like converting two currency amounts to the same currency to compare them to see which is bigger. So, with money today or in the future, we have to normalise it similarly. We take either take the future amount and take off the interest that theoretically was be earned, giving the value today, or we do the reverse and add the interest to todays amount, which gives us the future value of an amount we have today. This is a very important concept used everywhere in derivative pricing. Why is it used here? Simply because the present value of a swap is the sum of the present value of all of its cash flows. So, to calculate the value of a swap today, i would have to work out the net cash flows going out to the end of the swap, and calculate their present values … and sum them.

Now, the fixed interest rate side of the swap is easy.

Cashflows are easy to calculate for the fixed rate payer
Cashflow 1 = 4%x1M
Cashflow 2 = 4%x1M
Cashflow 3 = 4%x1M
…


For the floating rate payer on the swap, we have to forecast the LIBOR rate and use that forecast to estimate the floating rate cash flows.

Cashflow 1 = 4.1%x1M
Cashflow 2 = 4.12%x1M
Cashflow 3 = 4.18%x1M

We simply net off the fixed and floating cash flows that happen on the same date, and then discount the net cash flow to work out how much it is worth today.

How do we know the interest rate to discount the cashflow? How do we know the estimated forecast rate for LIBOR? This is where curves come in. It turns out we need curves to be able to price swaps. And we also need swaps to be able to build curves. That's for the next post. After that i'll show you how you build this stuff from code and where the traps are.

[Scruff]

Can this please be moved to General so I can puke without a ban?