Mathematica Demonstrations Project

This is a little gem that I found awhile back – Mathematica have a project whereby people can author a CDF document (computable document format) and publish them online for free.  The CDF documents can be played using the Mathematica CDF Player which is free. The usefulness of the player depends upon what CDFs have…

Jensen’s Inequality

Jensen’s Inequality is one of those lovely maths tricks that comes up in the most random of places and is just useful to have in your back pocket.  In particular it’s great for proving a number of other useful inequalities by choosing an appropriate function to use within the theorem and doing some rearranging. The…

The Value of a Forward Contract

The value of a forward contract and the forward price of an asset are something we will use again and again in various places.  Of equal importance are the techniques we can use to arrive at the equations for these.  We begin with some definitions and then I will take you though my thought process…

Interest Rate and Bond Definitions

Before we really get into the meat of any posts I think it’s a good idea to start with some basic definitions and notation around interest rates. I have chosen some conventions which I think are clear and avoid confusion and in most cases consistent with other literature I have come across (though not all).…

Delta and Gamma using the Achilles trick

In a previous post on the Achilles trick we developed a specific formula – here we show one example usage of that formula that allows us to quickly and easily derive closed form formulas to approximate the delta and gamma of a vanilla call or put option from the GK equations. Some definitions We begin with a…

The Achilles trick

There are various bits of clever maths I use here and there I like to refer to as “tricks”.  In fact I use them often enough to give them my own pet-names.  The one we are going to cover in this post is one I use quite a lot and in particular when deriving closed…

Simple annuities key formulas

Annuities are going to pop up everywhere on TAoQF so it’s a good idea to understand them and have some easy to remember ways of deriving key results. In this post we give a brief reminder of these and it’s intended it will be used as a reference for future (rather than a tutorial). Key…