Mid-April I was lucky to get to the Global Derivatives Trading and Risk Management conference. It is the world's biggest annual event devoted to financial derivatives. In the past few years, the conference was held in Paris; for a change, this year it took place in Barcelona.

The conference was packed with talks, round tables and networking breaks. To help the delegates make the most of it, each day of the conference was split in four streams running in parallel. Each stream was covering a specific topic. The attendees could, of course, switch between the streams during the day, but even then I could not get to all talks that I wanted to hear. The feeling was close to that of having four TV channels runing the shows I cannot miss at the same time. I wish I had a video recorder to tape all the talks that I missed; maybe they will do it next year? The delegates got all the presentation slides, but the slides do not tell a half of the story.

Nothing beats the pleasure of hearing a life presentation by a person whose name you only saw on textbook covers, but this is not the only reason to come to the conference. For a quant it is important to get the feeling of what is going on in the industry, which problems are talked about, what other people's concerns are. Global Derivatives conference is a perfect indicator of the current most important topics in quantitative finance.

Last year, right after the derivatives industry took its share of blame for the financial crisis, quite a few financial institutions adopted some kind of “back to basics” policy, which meant dropping all but the most simple derivatives. The fear is now over, but caution is still there.

Our assumptions that seemed reasonable in the past proved to be false. We are not living in a lognormal world anymore. What can we do to avoid falling for wrong assumptions? This year's conference pointed out a few ways.

Several talks looked at *modelling assets under the historical measure*. Sandrine Ungari of Société Générale showed an example of applying macro-economic approach to what used to be a purely calibration exercise: modelling the term structure of interest rates. In her presentation, “Using Macro-Finance Models To Build A Simulation Framework For The Interest Rate Curve”, she demonstrated that incorporating such indicators as *real activity* (inversely related to unemployment) provides good out-of-sample matches between model and reality.

Another way of employing historical measure is modelling the *state-price density*, also known as *price deflator*. An example of such model was presented by Prof. Lane Hughston of University College London in his talk “Geometric Lévy Models With Applications To Interest Rate Dynamics”. An important property of state-price density models is that there we do not have to select a specific numeraire. This greatly simplifies computation in many cases, notably when working in multiple currencies.

A related but different way of incorporating realised asset returns into a pricing model was shown by Prof. Esteban Tabak of Courant Institute of Mathematical Sciences in his talk “Combining Historical Returns & Option Prices Through Density Estimation With Constraints”. When we estimate the distribution from a data series, we usually assume a certain law (say, lognormal) and then calibrate its parameters using maximum likelihood. Prof. Tabak's presentation demonstrated that one does not need to make upfront assumptions of the law; instead, we can deduce the law from the sample.

Can we price a complex derivative without a model of the underlying market variables? Pierre-Henry Labordere of Société Générale in his talk “Optimal Transport: A Pleasant Ride In Finance” presented a *super-replication technique* for derivatives that gives a model-independent upper and lower boundary for the price. Finding such a boundary is essentially an optimisation problem.

That was just a glimpse of what impressed me the most at the conference. I do not know what the conference next year will be like, but I am quite sure it will be different: mathemaical finance is a very young science yet, so each year brings new surprises. I cannot wait for Global Derivatives 2013.

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