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Science in Finance II: '... ists'

A century or two ago, finance was the career for the less talented members of the family. Sons of the aristocracy would eventually go to sit in the House of Lords, while overseeing their property. One son would join the military, Catholic families would send a son off to the church. Perhaps if they were of an enquiring mind one son might become a scientist. But if a son turned out to be intellectually challenged he would be sent off to be 'something in the City. This didn't require any more brains than that required for an arts degree. This was the finance-is-for-artists (and long lunches) period, now long gone.

More often one now finds proper scientists working in finance. They have the analytical skills needed by investment banks and hedge funds. I imagine some must start out being frustrated by the lack of an established rigorous foundation for the subject. Where are the conservation laws? Where are the experimental results and the hypotheses? Quantitative finance has a well-used set of tools, but the popular models are essentially ad hoc.

Those in trading are undoubtedly pragmatists who really don't care for the port-and-cheese side of finance, nor for compact theories. Can it be put in a spreadsheet and does it make money? That s all that matters.

Unfortunately, most of the theory is built by axiomatists who really seem to believe in their models. These are the ones to be really frightened of. Speaking to them is like speaking to a god botherer, 'there is but one stochastic volatility model and its name is Heston.' (News flash: God and complete markets are simplifying assumptions that make life easier for the unimaginative, you aren't meant to believe in them once you've grown up!)

My feeling is that the best type of 'ist' working in finance is a pragmatic scientist, combining the curiosity and the scepticism of the scientist with the get-the-job-done attitude of the pragmatist.

Science in Finance IV: The Feedback Effect

For every buyer there is a seller and vice versa. So at a first glance derivatives is a zero-sum game, someone wins and someone loses, and the amounts are identical. Therefore there can be no impact on the rest of us or on the economy if two adults want to bet large sums of money on the outcome of what may just be the roll of a dice. Well, it isn't that simple for at least two reasons.

First, many of those trading derivatives are hedging with the underlying and this can affect the behaviour of the underlying: hedging positive gamma can decrease volatility and hedging negative gamma can increase volatility. When hedging positive gamma (i.e. replicating negative gamma) as the price rises you have to sell more of the underlying, and when the price falls you buy back, thus reducing volatility if your trades are in sufficient size to impact on the market. But hedging negative gamma is not so nice, you buy when the price rises and sell when it falls, exacerbating the moves and increasing volatility. The behaviour of stocks on which there are convertible bonds is often cited as a benign example, with the rather more dramatic '87 crash, replicating a put i.e. hedging negative gamma, as the evil version. (See Schonbucher, P and Wilmott, P 2000 The feedback effect of hedging in illiquid markets. SIAM J. Appl. Math. 61 232-272, also PS's dissertation.) You will probably find some reluctance for people to sell certain derivatives if they are not permitted to dynamically hedge. (Not that it works particularly well anyway, but that is what people do, and that is what most pricing theory is based on. Static hedging with other derivatives is better, and does not cause such (in)stability problems.)

(We've had newspaper headlines about damage done by excessive risk taking, whether by single, roguish, individuals or by larger institutions such as hedge funds, or banks and corporates investing in products they don t fully understand. I expect it won t be long before the attempt to reduce risk is the cause of similar headlines!)

Second, with the leverage available with derivatives it is possible, and actually rather simple, for people to trade so much as to get themselves into a pickle when things go wrong. This has many consequences. For example a trader loses his bank so much money that the bank collapses or is taken over, job losses ensue and possibly the man in the street loses his savings. Is wealth conserved during this process, as would be the case in a zero-sum game? I think not.

Of course, we don't know what proportion of derivatives trades are being used for hedging, speculation with leverage, etc. and how many are being dynamically hedged. But while derivatives trading is such a large business and while pricing theory is underpinned by dynamic hedging then we can say that the game of derivatives is not zero sum. Of course, this should spur on the implementation of mathematical models for feedback ... which may in turn help banks and regulators to ensure that the press that derivatives are currently getting is not as bad as it could be.

 
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