A quick post to show a link to the blog of Tim Johnson at Heriot-Watt Unviersity.

Lots of writing on derivatives topics, from models to regulations, plus plenty on markets and the crisis.

Worth a look. Click here to visit.

Maths & Trading & Finance, Computing & Calculating & Coding, Languages & Learning

A quick post to show a link to the blog of Tim Johnson at Heriot-Watt Unviersity.

Lots of writing on derivatives topics, from models to regulations, plus plenty on markets and the crisis.

Worth a look. Click here to visit.

There is a trade off between the explanatory powers of a model and its complexity: the more a model explains, the more complex it will be.

Would you disagree with that?

Before you answer, let me make a claim:

Mathematics is about

revealing patterns that simplify.

The mathematician’s work is actually based on producing simplicity, showing how complex problems can be reduced to component pieces that are simpler.

Think about all the beautiful proofs you’ve known. They are beautiful because they have shown how a simple and harmonious vision can achieve a target better than alternatives that will seem like a hack in comparison. Wikipedia explains it well, here.

Armed with the *Hardy Decomposition* for option prices, it now becomes much easier to understand why the smile exists.

To be clear, options trader might use the smile to manage supply & demand, but here we discuss the *mathematical* basis for smile – which is important if you want to understand how to generate smile in a monte-carlo model.

I recently wrote quite a long post on swap spreads (click here to see that post), covering some general intuition about swap spreads: what does a swap spread represent, why does it move, when does it move, which direction does it go, etc.

My blog stats show that a *lot* of people have read it, so it seems that it has been quite useful.

Browsing through quant.stackexchange I found my way to a very interesting article written by Paul Tooter which builds a trading model for 10-year swap spreads.* Paul calls himself a quant developer and has written a book and plenty of articles on R, a programming language designed for statistical analysis.*

The model uses a linear regression of the 10-year swap spread onto:

- 10-year treasuries
- 5-year treasuries
- 5-year swap rates
- LIBOR
- S&P 500
- USD Bank stocks

The model is effectively using the 5-year swap spread as part of the signal generation for the 10-year spread. The use of LIBOR, S&P and Bank stocks are not surprising if you have read my post: they are indicators of activities which can move swap spreads.

The buy/sell signal is generated from the residuals combined with a momentum indicator on the residuals.

It’s a great read. Click here to read Paul’s article, and click here to go to his website.

The *N-year swap spread* is defined as:

N-yr swap spread := N-yr swap rate – N-yr government bond yield.

Since most quants spend much less time on the bond market than on the swaps market, they often don’t come to appreciate the central importance of the swap spread. Here is an unordered list of why the swap spread is important:

- it is the unhedgeable part left over after you hedge a bond portfolio with swaps,
- it is a value measure of whether investors should buy their exposure with swaps or bonds,
- it makes up one of the standard collection of arbitrage strategies in the fixed income space,
- it moves a lot (sometimes up, sometimes down) in times of market stress.

The swap spread is fascinating, believe it.

This post collects a few of my personal notes on the swap spread, including my tricks for remembering the rules-of-thumb, and gives links to well-written articles across the web.

In this post I present some tips on how to understand fixed-income trader jargon.

If you are a quant working closely with swaps or options traders (as I was once), then you won’t get very far in a discussion unless you have a certain amount of fluency with the following terms.

Some were passed on to me in my early times as a fixed-income trader, and others are my own inventions — mnemonics I designed which help me to see a simple logic in a terminology or mathematical equality.