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…

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…