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In our usual fashion we have recruited a director of quantitative research from a leading bank to blog upon matters of interest to him

What is the purpose of derivative modelling? Is it, as some traders have suggested a way of reusing obscure mathematics so that it doesn’t feel unwanted? Is it a means by which society can cordon off socially inept individuals and keep them in one place thereby limiting the damage they can do to society?

I would of course suggest not. But there must be a reason for this branch of financial mathematics. There are the obvious ones that are bandied about, such as providing a value for derivatives that are seldom traded and hence difficult to value or helping traders manage their risk from complex derivatives. But in truth these are difficult objectives and if we set are targets too high there is every possibility that we will end up mangled on the ground, legs askew, bones broken and with significant brain damage. These are clearly not injuries to be trifled with.

            I would therefore suggest a slightly lower target, at least to start with. Traders and structurers work hard in their daily life creating wealth for our society. They make huge sacrifices for their goals, but it is important for them to make time for their own personal development.

            I have always seen mathematics as a way of communing with God. God reveals the structure, the rules of his world through the language of mathematics (long ago it was Latin, but that was just when mathematics was not fully developed). Fundamentally the beauty of his world is expressed, and can only be viewed in its full glory, via mathematics. The purpose of derivative valuations then is too help these shepherd’s of wealth (as I like to refer to front office staff) to appreciate the magnificence of God in their daily life. And without wishing to overstep the bounds of potential reality, not to mention taste, I think mathematics is also the ideal way to converse with God. Through their consideration of the equations which we somewhat foolishly use to model securities, traders are in their way talking to God. Appreciating the beauty of creation is always a necessary step to being able to understand the language in which God speaks. And of course this is wondrous thing, bringing light in to the lives of the exhausted workers of God.



An important part of the work of a financial mathematician is making assumptions. Frankly our current knowledge of mathematics, whilst perfectly adequate for communing with God, is woefully inadequate for modelling the financial markets. As such it is necessary to make a huge number of assumptions about the way financial securities act so as to make it possible to model them. The alternative, to push back the boundaries of mathematics, is seldom a cost effective way forward.

Much of the art of financial maths then is in making the right assumptions. But how does one define right and wrong in the world of assumptions? Is there an equivalent to the axis of evil that can be used? Well, as always, things are not that simple… and the devil is in the detail. Experience plays a key part as do random number generators (no only kidding). But there are guidelines to help the student through the potential minefield, and who doesn’t need guidelines when placed in a minefield.

Firstly it is important to make your assumptions relevant. They have to have impact, or what’s the point in having them? So relevant and I think fundamental. Your assumptions should be about the basic fundamental way a security behaves. There is no point in assuming a security will only turn left at traffic lights if it happens to be driving, this is not fundamental (nor as it happens relevant). The benefit to fundamental assumptions is their power. In one small sentence you can force a stock price to be continuous, with staggering implications for the simplicity of your model.


This is an important topic, and this is just a taster of the guidelines I hope to lay out. One day I even hope to publish a book on the topic

Cpmplexity works

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