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Volatility Arbitrage

I continue to be staggered by the depth and detail of some people s understanding of complicated quant models while these same people have absolutely no appreciation of the bigger picture. A case in point is that of volatility modelling.

If you really get into the Heston stochastic volatility model you will find yourself having to do some numerical integration in the complex plane (thanks to the transform methods used to solve the governing equation). This can be quite tricky to do in practice. Is all that effort worth it? Well, in part this depends on how good the model is. So you might think people would test the accuracy of the model against the data. Do they do this? Rarely. It is deemed sufficient to calibrate to a static dataset of option values regardless of the dynamics of that dataset. Yes, I know you then hedge with vanillas to reduce model risk, but this is a fudge that is completely inconsistent with the initial modelling. The cynic in me says that the benefit of modelling in such oblivion is truly tested by the state of your bank balance at the end of the year. If you get a bonus, does it matter? I don t have too much of a problem with that, depending on where you are in the management structure. However, I suspect that this is not most people's justification for their inaccurate modelling. I suspect that people really do believe that they are doing good work, and the more complicated the mathematics the better.

So, many know all the ins and outs of the most advanced volatility models based in the classical no-arbitrage world. Well, what if your job is to find volatility arbitrage opportunities? 'There s no such thing as a free lunch is drummed into most quants, thanks to academics and authors who take an almost axiomatic approach to our subject (see Derman s blog). Those who know the details of volatility arbitrage are few and far between. Take the example of how to hedge when you think that options are mispriced.

You forecast volatility to be much higher or lower than current implied volatility. Clearly this is an arbitrage opportunity. But to get at that profit you must hedge stock risk. Now, working within an otherwise very simple Black-Scholes world but with two volatilities, implied and forecast, how should you hedge and how much profit will you make?

The Same Old Same Old

Events of the last year seem to have passed a lot of researchers by. I find it both amusing and disturbing that the same people are still giving the same lectures about the same models at the same conferences without any sign of embarrassment whatsoever.[1] It's like a parallel universe! You can fool some of the people all of the time.

Sadly the easy ones to fool are people doing Finance PhDs and MFEs. On the forum there's always plenty of discussion about which qualifications people should go for, and how many. I find that the people who pick up new ideas fastest are those with a mathematics or science background, those actually with little hard-core quant education. They still have an open mind, something which is surely needed now more than ever before. The more time spent in academia learning the 'received wisdom' of quant finance the more one's brain atrophies it seems. As has been said on the forum many times, a finance PhD is for someone who wants to be a finance professor. You are better off getting a job, any job, in a bank or fund asap, start earning asap, move up the food chain as quickly as possible and leave your degree-collecting friends behind. This business will not be this lucrative forever.

I worry that people just can t distinguish between good and bad quant finance. There's plenty of evidence for this in journals, at conferences and in textbooks. People will certainly spot a mathematical error in a paper, but can they make the more subjective distinction between a good paper that advances the subject and a bad paper that sets it back?

There is nothing new in this, journals have almost always preferred to publish the 'reliable, the 'brilliant new research by Professor X' that is really 'the same old stuff by a has-been plodder. At this point a plug for our magazine is in order. Portfolio magazine was very flattering in its recent article about our magazine, saying 'Paul Wilmott, publisher and editor in chief of Wilmott, is looking pretty smart these days. Wilmott and his magazine, which is aimed at the quantitative-finance community, the math geeks at banks and hedge funds, foresaw many of the problems that dominate the headlines today. He and the contributors to the magazine, whose influence far outstrips its small circulation, were railing about the limits of math and financial models far in advance of the meltdown.

It's not hard to find good research; our magazine seems to be particularly talented at this. The difficult part is knowing the difference between the good and the bad. This skill can be learned, but an open mind is needed. And they are increasingly hard to find.

  • [1] This essay was first published on 1 September 2008.
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