Quants of the year - Paul Glasserman and Michael Giles

During a Risk training course in February 2005, one of the attendees approached Columbia Business School professor Paul Glasserman following the session he had just led on estimation of option sensitivities, or Greeks, by Monte Carlo methods. There's nothing too unusual about that, except for two things. First of all, the attendee in question was himself a professor. Secondly, when he approached Glasserman, Michael Giles, professor of scientific computing at the Oxford University Computer Laboratory, had in his hands a page of scribbled notes that would form the basis of the best cutting edge paper in 2006, as voted for by readers of Risk.

"In terms of the time from initial research to submitting for publication, this paper was one of the fastest I've been involved in," says Paul Glasserman, the Jack R Anderson professor at Columbia Business School. Published in the January 2006 issue of Risk, Giles and Glasserman's paper, called Smoking adjoints: fast Monte Carlo Greeks, describes how a mathematical technique widely used in computational fluid dynamics and engineering design optimisation can dramatically speed up computation times associated with the calculation of Greeks.

"The technique is generically applicable," says Glasserman, adding that the potential for using adjoint methods in derivatives pricing and risk management is huge. The adjoint method accelerates the calculation of Greeks via Monte Carlo simulation by, in essence, rearranging the order of calculations, as compared to the standard method.

Little happened following their initial encounter, but in mid-May 2005, the pair met again in England, at a conference in Cambridge, and agreed to collaborate. During the flight home to New York, drawing on the insights contained in Giles' page of notes, Glasserman drafted about half the paper that was eventually submitted. The paper progressed very quickly and smoothly after that, says Giles.

Aware that one of his students had written computer code for an implementation of the Libor Market Model, which is used in interest rate derivatives pricing, Glasserman passed on the code to Giles for adaptation. "I got the pathwise and adjoint code working within a week for a simple payoff," says Giles, referring to the coding for the standard and novel calculation techniques, respectively. Glasserman then proposed that a more complex portfolio evaluation would best showcase the adjoint technique. And it was this example that was included in the paper that was submitted to Risk in July 2005.

Specifically, the pair described in the cutting edge paper just how the Greeks - delta (the sensitivity of an option's value to changes in the price of the underlying), gamma (delta's sensitivity to changes in the underlying price) and vega (the sensitivity of an option's value to changes in volatility) - could be calculated with the adjoint method.

It was little surprise that the paper held great appeal for Risk's readers. After all, efficient calculation of option price sensitivities is an everyday practical challenge for traders and quants who use Monte Carlo methods. Without speedy calculations, hedges can be left wanting as markets move.

"We focused on the Libor market model, where you want sensitivities with respect to every point on the initial forward curve and all the volatilities," says Glasserman. "But this technique has broader application - anywhere there are a very large number of parameters with respect to which sensitivities are needed." An obvious area for implementation would be an equity volatility surface model, adds Glasserman.

The novel technique provides an alternative to existing methods for calculating Greeks, in which Monte Carlo simulation is carried out with different input parameters so that option price sensitivities can be estimated. In practice, so-called forward pathwise and likelihood ratio approaches are often used in preference to this basic method. These techniques are able to generate sensitivity estimates from a set of simulated paths, without the need to perturb parameters.

While improving estimation quality, these more sophisticated approaches require greater amounts of analysis and programming. The adjoint method developed by Giles and Glasserman is able to calculate estimates that are identical to those generated by forward pathwise methods, but with much greater speed.

Within their Risk cutting edge paper, Giles and Glasserman use a test portfolio of 15 swaptions, consisting of options on one-year, two-year, five-year, seven-year and 10-year swaps with quarterly payments and swap rates of 4.5%, 5.0% and 5.5%. They demonstrate that, while the computational cost of the forward pathwise method increases linearly with maturity, the cost of the adjoint method barely changes. Importantly, unlike with the forward pathwise method, adding a vega calculation to the delta computation in the adjoint approach has virtually no impact on computational cost, because the calculations use the same adjoint variables.

While Glasserman says he is not planning to do further work using the adjoint method, his co-author has presented the method to several dealers in London. Giles declines to comment on the identity of the houses, or how advanced their plans for implementation are.

London's trading floors are somewhat virgin territory for Giles, a veteran of computational fluid dynamics who, over the past five years, has largely shifted the focus of his work to quantitative finance. In engineering circles, Giles is best known for having worked on the initial development of the computational fluid dynamics simulation software that UK-based engineering firm Rolls-Royce's uses for jet engine design. "I still do a little work with Rolls-Royce, and I have no plans to work in the City - I'm an academic," he says.

Once he has finished a current endeavour to adapt another approach to Monte Carlo simulation that is popular within the computational fluid dynamics community for use in finance, Giles says he will look at the adjoint method within this context. "The work is on a more efficient approach to simulation known as the multi-level method," he explains. "I will then go on to investigate model calibration with this approach." Multi-level methods reduce the computational cost associated with achieving a given result accuracy by combining results from path simulations using a geometric sequence of time steps.

Giles' commitment to academia is echoed by Glasserman. Despite earning a reputation for conducting pioneering research that is a lot more practical than many of his peers', the Columbia professor has no desire to join the Street, where dog-eared copies of his book on Monte Carlo methods can be found on many a quant's desk.

So upon what is the widely cited, eminent specialist on the application of numerical methods in quantitative finance currently focused? "I'm excited about whatever I'm currently working on," says Glasserman, before opining that credit risk and credit derivatives are where many of the most interesting opportunities for quantitative finance research reside currently. "It's a field that hasn't quite matured yet around a single model or framework. In a sense, we only have interim solutions - it doesn't appear that any put forward yet will be the long-term widely accepted model."

Subscribers can read the full paper online at www.risk.net/public/showPage.html?page=310639